TI-83 GRAPHING CALCULATOR GUIDEBOOK TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR, Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas Instruments Incorporated. IBM is a registered trademark of International Business Machines Corporation. Macintosh is a registered trademark of Apple Computer, Inc. Windows is a registered trademark of Microsoft Corporation. © 1996, 2000, 2001 Texas Instruments Incorporated. 8300INTR.
Important Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an “as-is” basis.
Table of Contents This manual describes how to use the TI.83 Graphing Calculator. Getting Started is an overview of TI.83 features. Chapter 1 describes how the TI.83 operates. Other chapters describe various interactive features. Chapter 17 shows how to combine these features to solve problems. Getting Started: Do This First! TI-83 Keyboard .......................................... TI-83 Menus ............................................. First Steps ...............................................
Chapter 2: Math, Angle, and Test Operations Getting Started: Coin Flip ................................ Keyboard Math Operations .............................. MATH Operations ........................................ Using the Equation Solver ............................... MATH NUM (Number) Operations........................ Entering and Using Complex Numbers................... MATH CPX (Complex) Operations ....................... MATH PRB (Probability) Operations ..................... ANGLE Operations ..
Chapter 6: Sequence Graphing Getting Started: Forest and Trees ........................ Defining and Displaying Sequence Graphs ............... Selecting Axes Combinations ............................ Exploring Sequence Graphs.............................. Graphing Web Plots...................................... Using Web Plots to Illustrate Convergence ............... Graphing Phase Plots .................................... Comparing TI-83 and TI.82 Sequence Variables ..........
Chapter 10: Matrices Getting Started: Systems of Linear Equations ............ 10-2 Defining a Matrix ........................................ 10-3 Viewing and Editing Matrix Elements .................... 10-4 Using Matrices with Expressions ........................ 10-7 Displaying and Copying Matrices ........................ 10-8 Using Math Functions with Matrices ..................... 10-9 Using the MATRX MATH Operations .....................
Chapter 14: Financial Functions Getting Started: Financing a Car ......................... 14-2 Getting Started: Computing Compound Interest.......... 14-3 Using the TVM Solver .................................... 14-4 Using the Financial Functions ........................... 14-5 Calculating Time Value of Money (TVM) ................. 14-6 Calculating Cash Flows .................................. 14-8 Calculating Amortization ................................ 14-9 Calculating Interest Conversion...........
Chapter 18: Memory Management Checking Available Memory ............................. Deleting Items from Memory ............................ Clearing Entries and List Elements ...................... Resetting the TI.83 ...................................... Chapter 19: Communication Link Getting Started: Sending Variables ....................... 19-2 TI-83 LINK ............................................... 19-3 Selecting Items to Send .................................. 19-4 Receiving Items ...........
Getting Started: Do This First! Contents TI-83 Keyboard .......................................... TI-83 Menus ............................................. First Steps ............................................... Entering a Calculation: The Quadratic Formula .......... Converting to a Fraction: The Quadratic Formula ........ Displaying Complex Results: The Quadratic Formula .... Defining a Function: Box with Lid ....................... Defining a Table of Values: Box with Lid .................
TI-83 Keyboard Generally, the keyboard is divided into these zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys. Keyboard Zones Graphing keys access the interactive graphing features. Editing keys allow you to edit expressions and values. Advanced function keys display menus that access the advanced functions. Scientific calculator keys access the capabilities of a standard scientific calculator.
Using the Color-Coded Keyboard The keys on the TI.83 are color-coded to help you easily locate the key you need. The gray keys are the number keys. The blue keys along the right side of the keyboard are the common math functions. The blue keys across the top set up and display graphs. The primary function of each key is printed in white on the key. For example, when you press , the MATH menu is displayed. Using the y and ƒ Keys The secondary function of each key is printed in yellow above the key.
TI-83 Menus Displaying a Menu While using your TI.83, you often will need to access items from its menus. When you press a key that displays a menu, that menu temporarily replaces the screen where you are working. For example, when you press , the MATH menu is displayed as a full screen. After you select an item from a menu, the screen where you are working usually is displayed again. Moving from One Menu to Another Some keys access more than one menu.
First Steps Before starting the sample problems in this chapter, follow the steps on this page to reset the TI.83 to its factory settings and clear all memory. This ensures that the keystrokes in this chapter will produce the illustrated results. To reset the TI.83, follow these steps. 1. Press É to turn on the calculator. 2. Press and release y, and then press [MEM] (above Ã). When you press y, you access the operation printed in yellow above the next key that you press.
Entering a Calculation: The Quadratic Formula Use the quadratic formula to solve the quadratic equations 3X2 + 5X + 2 = 0 and 2X2 N X + 3 = 0. Begin with the equation 3X2 + 5X + 2 = 0. 1. Press 3 ¿ ƒ [A] (above ) to store the coefficient of the X2 term. 2. Press ƒ [ : ] (above Ë). The colon allows you to enter more than one instruction on a line. 3. Press 5 ¿ ƒ [B] (above ) to store the coefficient of the X term. Press ƒ [ : ] to enter a new instruction on the same line.
Converting to a Fraction: The Quadratic Formula You can show the solution as a fraction. 1. Press to display the MATH menu. 2. Press 1 to select 1:4Frac from the MATH menu. When you press 1, Ans4Frac is displayed on the home screen. Ans is a variable that contains the last calculated answer. 3. Press Í to convert the result to a fraction. To save keystrokes, you can recall the last expression you entered, and then edit it for a new calculation. 4.
Displaying Complex Results: The Quadratic Formula Now solve the equation 2X2 N X + 3 = 0. When you set a+bi complex number mode, the TI.83 displays complex results. 1. Press z † † † † † † (6 times), and then press ~ to position the cursor over a+bi. Press Í to select a+bi complexnumber mode. 2. Press y [QUIT] (above z) to return to the home screen, and then press ‘ to clear it. 3. Press 2 ¿ ƒ [A] ƒ [ : ] Ì 1 ¿ ƒ [B] ƒ [ : ] 3 ¿ ƒ [C] Í.
Defining a Function: Box with Lid Take a 20 cm. × 25 cm. sheet of paper and cut X × X squares from two corners. Cut X × 12.5 cm. rectangles from the other two corners as shown in the diagram below. Fold the paper into a box with a lid. What value of X would give your box the maximum volume V? Use the table and graphs to determine the solution. Begin by defining a function that describes the volume of the box.
Defining a Table of Values: Box with Lid The table feature of the TI.83 displays numeric information about a function. You can use a table of values from the function defined on page 9 to estimate an answer to the problem. 1. Press y [TBLSET] (above p) to display the TABLE SETUP menu. 2. Press Í to accept TblStart=0. 3. Press 1 Í to define the table increment @Tbl=1. Leave Indpnt: Auto and Depend: Auto so that the table will be generated automatically. 4. Press y [TABLE] (above s) to display the table.
Zooming In on the Table: Box with Lid You can adjust the way a table is displayed to get more information about a defined function. With smaller values for @Tbl, you can zoom in on the table. 1. Press 3 Í to set TblStart. Press Ë 1 Í to set @Tbl. This adjusts the table setup to get a more accurate estimate of X for maximum volume Y1. 2. Press y [TABLE]. 3. Press † and } to scroll the table. Notice that the maximum value for Y1 is 410.26, which occurs at X=3.7. Therefore, the maximum occurs where 3.6
Setting the Viewing Window: Box with Lid You also can use the graphing features of the TI.83 to find the maximum value of a previously defined function. When the graph is activated, the viewing window defines the displayed portion of the coordinate plane. The values of the window variables determine the size of the viewing window. 1. Press p to display the window editor, where you can view and edit the values of the window variables. The standard window variables define the viewing window as shown.
Displaying and Tracing the Graph: Box with Lid Now that you have defined the function to be graphed and the window in which to graph it, you can display and explore the graph. You can trace along a function using the TRACE feature. 1. Press s to graph the selected function in the viewing window. The graph of Y1=(20N2X)(25à2NX)X is displayed. 2. Press ~ to activate the free-moving graph cursor. The X and Y coordinate values for the position of the graph cursor are displayed on the bottom line. 3.
4. Press r. The trace cursor is displayed on the Y1 function. The function that you are tracing is displayed in the top-left corner. 5. Press | and ~ to trace along Y1, one X dot at a time, evaluating Y1 at each X. You also can enter your estimate for the maximum value of X. 6. Press 3 Ë 8. When you press a number key while in TRACE, the X= prompt is displayed in the bottom-left corner. 7. Press Í. The trace cursor jumps to the point on the Y1 function evaluated at X=3.8. 8.
Zooming In on the Graph: Box with Lid To help identify maximums, minimums, roots, and intersections of functions, you can magnify the viewing window at a specific location using the ZOOM instructions. 1. Press q to display the ZOOM menu. This menu is a typical TI.83 menu. To select an item, you can either press the number or letter next to the item, or you can press † until the item number or letter is highlighted, and then press Í. 2. Press 2 to select 2:Zoom In. The graph is displayed again.
Finding the Calculated Maximum: Box with Lid You can use a CALCULATE menu operation to calculate a local maximum of a function. 1. Press y [CALC] (above r) to display the CALCULATE menu. Press 4 to select 4:maximum. The graph is displayed again with a Left Bound? prompt. 2. Press | to trace along the curve to a point to the left of the maximum, and then press Í. A 4 at the top of the screen indicates the selected bound. A Right Bound? prompt is displayed. 3.
Other TI-83 Features Getting Started has introduced you to basic TI.83 operation. This guidebook describes in detail the features you used in Getting Started. It also covers the other features and capabilities of the TI.83. Graphing You can store, graph, and analyze up to 10 functions (Chapter 3), up to six parametric functions (Chapter 4), up to six polar functions (Chapter 5), and up to three sequences (Chapter 6). You can use DRAW operations to annotate graphs (Chapter 8).
Inferential Statistics You can perform 16 hypothesis tests and confidence intervals and 15 distribution functions. You can display hypothesis test results graphically or numerically (Chapter 13). Financial Functions You can use time-value-of-money (TVM) functions to analyze financial instruments such as annuities, loans, mortgages, leases, and savings. You can analyze the value of money over equal time periods using cash flow functions. You can amortize loans with the amortization functions (Chapter 14).
1 Contents Operating the TI-83 Turning On and Turning Off the TI.83 .................... Setting the Display Contrast ............................. The Display .............................................. Entering Expressions and Instructions ................... TI.83 Edit Keys .......................................... Setting Modes ........................................... Using TI.83 Variable Names ............................. Storing Variable Values ..................................
Turning On and Turning Off the TI-83 Turning On the Calculator To turn on the TI.83, press É. • If you previously had turned off the calculator by pressing y [OFF], the TI.83 displays the home screen as it was when you last used it and clears any error. • If Automatic Power Down™ (APDé) had previously turned off the calculator, the TI.83 will return exactly as you left it, including the display, cursor, and any error. To prolong the life of the batteries, APD turns off the TI.
Setting the Display Contrast Adjusting the Display Contrast You can adjust the display contrast to suit your viewing angle and lighting conditions. As you change the contrast setting, a number from 0 (lightest) to 9 (darkest) in the top-right corner indicates the current level. You may not be able to see the number if contrast is too light or too dark. Note: The TI.83 has 40 contrast settings, so each number 0 through 9 represents four settings. The TI.
The Display Types of Displays The TI.83 displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describes how the TI.83 can display a horizontally or vertically split screen to show graphs and text simultaneously. Home Screen The home screen is the primary screen of the TI.83. On this screen, enter instructions to execute and expressions to evaluate. The answers are displayed on the same screen. Displaying Entries and Answers When text is displayed, the TI.
Display Cursors In most cases, the appearance of the cursor indicates what will happen when you press the next key or select the next menu item to be pasted as a character.
Entering Expressions and Instructions What Is an Expression? An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements. An expression evaluates to a single answer. On the TI.83, you enter an expression in the same order as you would write it on paper. For example, pR2 is an expression. You can use an expression on the home screen to calculate an answer. In most places where a value is required, you can use an expression to enter a value.
Entering a Number in Scientific Notation To enter a number in scientific notation, follow these steps. 1. Enter the part of the number that precedes the exponent. This value can be an expression. 2. Press y [EE]. å is pasted to the cursor location. 3. If the exponent is negative, press Ì, and then enter the exponent, which can be one or two digits. When you enter a number in scientific notation, the TI.83 does not automatically display answers in scientific or engineering notation.
TI-83 Edit Keys Keystrokes Result ~ or | Moves the cursor within an expression; these keys repeat. } or † Moves the cursor from line to line within an expression that occupies more than one line; these keys repeat. On the top line of an expression on the home screen, } moves the cursor to the beginning of the expression. On the bottom line of an expression on the home screen, † moves the cursor to the end of the expression. y| Moves the cursor to the beginning of an expression.
Setting Modes Checking Mode Settings Mode settings control how the TI.83 displays and interprets numbers and graphs. Mode settings are retained by the Constant Memory feature when the TI.83 is turned off. All numbers, including elements of matrices and lists, are displayed according to the current mode settings. To display the mode settings, press z. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail.
Normal, Sci, Eng Notation modes only affect the way an answer is displayed on the home screen. Numeric answers can be displayed with up to 10 digits and a two-digit exponent. You can enter a number in any format. Normal notation mode is the usual way we express numbers, with digits to the left and right of the decimal, as in 12345.67. Sci (scientific) notation mode expresses numbers in two parts. The significant digits display with one digit to the left of the decimal.
Radian, Degree Angle modes control how the TI.83 interprets angle values in trigonometric functions and polar/rectangular conversions. Radian mode interprets angle values as radians. Answers display in radians. Degree mode interprets angle values as degrees. Answers display in degrees. Func, Par, Pol, Seq Graphing modes define the graphing parameters. Chapters 3, 4, 5, and 6 describe these modes in detail. Func (function) graphing mode plots functions, where Y is a function of X (Chapter 3).
Sequential, Simul Sequential graphing-order mode evaluates and plots one function completely before the next function is evaluated and plotted. Simul (simultaneous) graphing-order mode evaluates and plots all selected functions for a single value of X and then evaluates and plots them for the next value of X. Note: Regardless of which graphing mode is selected, the TI.83 will sequentially graph all stat plots before it graphs any functions.
Using TI-83 Variable Names Variables and Defined Items On the TI.83 you can enter and use several types of data, including real and complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures, and strings. The TI.83 uses assigned names for variables and other items saved in memory. For lists, you also can create your own five-character names. Variable Type Names Real numbers A, B, . . . , Z, q Complex numbers A, B, . . .
Storing Variable Values Storing Values in a Variable Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evaluated, the value of the variable at that time is used. To store a value to a variable from the home screen or a program using the ¿ key, begin on a blank line and follow these steps. 1. Enter the value you want to store. The value can be an expression. 2. Press ¿. ! is copied to the cursor location. 3.
Recalling Variable Values Using Recall (RCL) To recall and copy variable contents to the current cursor location, follow these steps. To leave RCL, press ‘. 1. Press y ãRCLä. Rcl and the edit cursor are displayed on the bottom line of the screen. 2. Enter the name of the variable in any of five ways. • Press ƒ and then the letter of the variable. • Press y ãLISTä, and then select the name of the list, or press y [Ln]. • Press , and then select the name of the matrix.
ENTRY (Last Entry) Storage Area Using ENTRY (Last Entry) When you press Í on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called ENTRY (last entry). When you turn off the TI.83, ENTRY is retained in memory. To recall ENTRY, press y [ENTRY]. The last entry is pasted to the current cursor location, where you can edit and execute it.
Reexecuting the Previous Entry After you have pasted the last entry to the home screen and edited it (if you chose to edit it), you can execute the entry. To execute the last entry, press Í. To reexecute the displayed entry, press Í again. Each reexecution displays an answer on the right side of the next line; the entry itself is not redisplayed.
Ans (Last Answer) Storage Area Using Ans in an Expression When an expression is evaluated successfully from the home screen or from a program, the TI.83 stores the answer to a storage area called Ans (last answer). Ans may be a real or complex number, a list, a matrix, or a string. When you turn off the TI.83, the value in Ans is retained in memory. You can use the variable Ans to represent the last answer in most places. Press y [ANS] to copy the variable name Ans to the cursor location.
TI-83 Menus Using a TI-83 Menu You can access most TI.83 operations using menus. When you press a key or key combination to display a menu, one or more menu names appear on the top line of the screen. • The menu name on the left side of the top line is highlighted. Up to seven items in that menu are displayed, beginning with item 1, which also is highlighted. • A number or letter identifies each menu item’s place in the menu. The order is 1 through 9, then 0, then A, B, C, and so on.
Selecting an Item from a Menu You can select an item from a menu in either of two ways. • Press the number or letter of the item you want to select. The cursor can be anywhere on the menu, and the item you select need not be displayed on the screen. • Press † or } to move the cursor to the item you want, and then press Í. After you select an item from a menu, the TI.83 typically displays the previous screen.
VARS and VARS Y-VARS Menus VARS Menu You can enter the names of functions and system variables in an expression or store to them directly. To display the VARS menu, press . All VARS menu items display secondary menus, which show the names of the system variables. 1:Window, 2:Zoom, and 5:Statistics each access more than one secondary menu. VARS Y-VARS 1: Window... 2: Zoom... 3: GDB... 4: Picture... 5: Statistics... 6: Table... 7: String...
Equation Operating System (EOS™) Order of Evaluation The Equation Operating System (EOSé) defines the order in which functions in expressions are entered and evaluated on the TI.83. EOS lets you enter numbers and functions in a simple, straightforward sequence.
Implied Multiplication The TI.83 recognizes implied multiplication, so you need not press ¯ to express multiplication in all cases. For example, the TI.83 interprets 2p, 4sin(46), 5(1+2), and (2ä5)7 as implied multiplication. Note: TI.83 implied multiplication rules differ from those of the TI.82. For example, the TI.83 evaluates 1à2X as (1à2)äX, while the TI.82 evaluates 1à2X as 1/(2äX) (Chapter 2). Parentheses All calculations inside a pair of parentheses are completed first.
Error Conditions Diagnosing an Error The TI.83 detects errors while performing these tasks. • • • • Evaluating an expression Executing an instruction Plotting a graph Storing a value When the TI.83 detects an error, it returns an error message as a menu title, such as ERR:SYNTAX or ERR:DOMAIN. Appendix B describes each error type and possible reasons for the error. • If you select 1:Quit (or press y [QUIT] or ‘), then the home screen is displayed.
2 Contents Math, Angle, and Test Operations Getting Started: Coin Flip ................................ Keyboard Math Operations .............................. MATH Operations ........................................ Using the Equation Solver ............................... MATH NUM (Number) Operations........................ Entering and Using Complex Numbers................... MATH CPX (Complex) Operations ....................... MATH PRB (Probability) Operations ..................... ANGLE Operations ..
Getting Started: Coin Flip Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this simulation 40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a coin flip resulting in tails is 0.5. 1. Begin on the home screen. Press | to display the MATH PRB menu.
Keyboard Math Operations Using Lists with Math Operations Math operations that are valid for lists return a list calculated element by element. If you use two lists in the same expression, they must be the same length. + (Addition), N (Subtraction), ä (Multiplication), à (Division) You can use + (addition, Ã), N (subtraction, ¹), ä (multiplication, ¯), and à (division, ¥) with real and complex numbers, expressions, lists, and matrices. You cannot use à with matrices.
log(, 10^(, ln( You can use log( (logarithm, «), 10^( (power of 10, y [10x]), and ln( (natural log, µ) with real or complex numbers, expressions, and lists. log(value) e^( (Exponential) 10^(power) ln(value) e^( (exponential, y ãex]) returns the constant e raised to a power. You can use e^( with real or complex numbers, expressions, and lists. e^(power) e (Constant) e (constant, y [e]) is stored as a constant on the TI-83. Press y [e] to copy e to the cursor location.
MATH Operations MATH Menu To display the MATH menu, press . MATH NUM CPX PRB 1: 4Frac Displays the answer as a fraction. 2: 4Dec Displays the answer as a decimal. 3: 3 Calculates the cube. 4: 3‡( Calculates the cube root. 5: x‡ Calculates the xth root. 6: fMin( Finds the minimum of a function. 7: fMax( Finds the maximum of a function. 8: nDeriv( Computes the numerical derivative. 9: fnInt( Computes the function integral. 0: Solver... Displays the equation solver.
3(Cube), 3‡( (Cube Root) 3 (cube) returns the cube of value. You can use 3 with real or complex numbers, expressions, lists, and square matrices. value3 3‡( 3‡( (cube root) returns the cube root of value. You can use with real or complex numbers, expressions, and lists. 3‡(value) x‡ (Root) x‡ (xth root) returns the xth root of value. You can use x‡ with real or complex numbers, expressions, and lists.
nDeriv( nDeriv( (numerical derivative) returns an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and H (if not specified, the default is 1âL3). nDeriv( is valid only for real numbers. nDeriv(expression,variable,value[,H]) nDeriv( uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points.
Using the Equation Solver Solver Solver displays the equation solver, in which you can solve for any variable in an equation. The equation is assumed to be equal to zero. Solver is valid only for real numbers. When you select Solver, one of two screens is displayed. • The equation editor (see step 1 picture below) is displayed when the equation variable eqn is empty. • The interactive solver editor (see step 3 picture on page 2.9) is displayed when an equation is stored in eqn.
3. Press Í or †. The interactive solver editor is displayed. • The equation stored in eqn is set equal to zero and displayed on the top line. • Variables in the equation are listed in the order in which they appear in the equation. Any values stored to the listed variables also are displayed. • The default lower and upper bounds appear in the last line of the editor (bound={L1å99,1å99}). • A $ is displayed in the first column of the bottom line if the editor continues beyond the screen.
Solving for a Variable in the Equation Solver To solve for a variable using the equation solver after an equation has been stored to eqn, follow these steps. 1. Select 0:Solver from the MATH menu to display the interactive solver editor, if not already displayed. 2. Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press Í or †. 3. Enter an initial guess for the variable for which you are solving.
4. Edit bound={lower,upper}. lower and upper are the bounds between which the TI-83 searches for a solution. This is optional, but it may help find the solution more quickly. The default is bound={L1å99,1å99}. 5. Move the cursor to the variable for which you want to solve and press ƒ [SOLVE] (above the Í key). • The solution is displayed next to the variable for which you solved. A solid square in the first column marks the variable for which you solved and indicates that the equation is balanced.
Editing an Equation Stored to eqn To edit or replace an equation stored to eqn when the interactive equation solver is displayed, press } until the equation editor is displayed. Then edit the equation. Equations with Multiple Roots Some equations have more than one solution. You can enter a new initial guess (page 2.10) or new bounds (page 2.11) to look for additional solutions. Further Solutions After you solve for a variable, you can continue to explore solutions from the interactive solver editor.
MATH NUM (Number) Operations MATH NUM Menu To display the MATH NUM menu, press ~. MATH NUM CPX PRB 1: abs( 2: round( 3: iPart( 4: fPart( 5: int( 6: min( 7: max( 8: lcm( 9: gcd( abs( Absolute value Round Integer part Fractional part Greatest integer Minimum value Maximum value Least common multiple Greatest common divisor abs( (absolute value) returns the absolute value of real or complex (modulus) numbers, expressions, lists, and matrices. abs(value) Note: abs( is also available on the MATH CPX menu.
iPart(, fPart( iPart( (integer part) returns the integer part or parts of real or complex numbers, expressions, lists, and matrices. iPart(value) fPart( (fractional part) returns the fractional part or parts of real or complex numbers, expressions, lists, and matrices. fPart(value) int( int( (greatest integer) returns the largest integer real or complex numbers, expressions, lists, and matrices.
min(, max( min( (minimum value) returns the smaller of valueA and valueB or the smallest element in list. If listA and listB are compared, min( returns a list of the smaller of each pair of elements. If list and value are compared, min( compares each element in list with value. max( (maximum value) returns the larger of valueA and valueB or the largest element in list. If listA and listB are compared, max( returns a list of the larger of each pair of elements.
Entering and Using Complex Numbers Complex-Number The TI-83 displays complex numbers in rectangular form and polar form. To select a complex-number mode, press Modes z, and then select either of the two modes. • a+bi (rectangular-complex mode) • re^qi (polar-complex mode) On the TI-83, complex numbers can be stored to variables. Also, complex numbers are valid list elements. In Real mode, complex-number results return an error, unless you entered a complex number as input.
Interpreting Complex Results Complex numbers in results, including list elements, are displayed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction (page 2.19). In the example below, re^qi and Radian modes are set. RectangularComplex Mode Rectangular-complex mode recognizes and displays a complex number in the form a+bi, where a is the real component, b is the imaginary component, and i is a constant equal to -1.
MATH CPX (Complex) Operations MATH CPX Menu To display the MATH CPX menu, press ~ ~. MATH NUM CPX PRB 1: conj( Returns the complex conjugate. 2: real( Returns the real part. 3: imag( Returns the imaginary part. 4: angle( Returns the polar angle. 5: abs( Returns the magnitude (modulus). 6: 4Rect Displays the result in rectangular form. 7: 4Polar Displays the result in polar form. conj( conj( (conjugate) returns the complex conjugate of a complex number or list of complex numbers.
angle( angle( returns the polar angle of a complex number or list of complex numbers, calculated as tanL1 (b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by +p in the second quadrant or Np in the third quadrant. angle(a+bi) returns tanL1(b/a). angle(re^(qi)) returns q, where Lp
MATH PRB (Probability) Operations MATH PRB Menu To display the MATH PRB menu, press |. MATH NUM CPX PRB 1: rand 2: nPr 3: nCr 4: ! 5: randInt( 6: randNorm( 7: randBin( rand Random-number generator Number of permutations Number of combinations Factorial Random-integer generator Random # from Normal distribution Random # from Binomial distribution rand (random number) generates and returns one or more random numbers > 0 and < 1.
nPr, nCr nPr (number of permutations) returns the number of permutations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists. items nPr number nCr (number of combinations) returns the number of combinations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists. items nCr number ! (Factorial) ! (factorial) returns the factorial of either an integer or a multiple of .5.
randInt( randInt( (random integer) generates and displays a random integer within a range specified by lower and upper integer bounds. To generate a list of random numbers, specify an integer >1 for numtrials (number of trials); if not specified, the default is 1. randInt(lower,upper[,numtrials]) randNorm( randNorm( (random Normal) generates and displays a random real number from a specified Normal distribution.
ANGLE Operations ANGLE Menu To display the ANGLE menu, press y [ANGLE]. The ANGLE menu displays angle indicators and instructions. The Radian/Degree mode setting affects the TI-83’s interpretation of ANGLE menu entries.
r (Radians) r (radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In Degree mode, you can use r to convert radians to degrees. valuer Degree mode 8DMS 8DMS (degree/minute/second) displays answer in DMS format (page 2.23). The mode setting must be Degree for answer to be interpreted as degrees, minutes, and seconds. 8DMS is valid only at the end of a line.
TEST (Relational) Operations TEST Menu =, ƒ, >, ‚, <, To display the TEST menu, press y [TEST]. This operator... Returns 1 (true) if... TEST LOGIC 1: = 2: ƒ 3: > 4: ‚ 5: < 6: Equal Not equal to Greater than Greater than or equal to Less than Less than or equal to Relational operators compare valueA and valueB and return 1 if the test is true or 0 if the test is false. valueA and valueB can be real numbers, expressions, or lists.
TEST LOGIC (Boolean) Operations TEST LOGIC Menu To display the TEST LOGIC menu, press y ãTESTä ~. This operator... Returns a 1 (true) if... TEST LOGIC 1: and 2: or 3: xor 4: not( Both values are nonzero (true). At least one value is nonzero (true). Only one value is zero (false). The value is zero (false). Boolean Operators Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values.
3 Contents Function Graphing Getting Started: Graphing a Circle ....................... Defining Graphs ......................................... Setting the Graph Modes ................................. Defining Functions ...................................... Selecting and Deselecting Functions ..................... Setting Graph Styles for Functions ....................... Setting the Viewing Window Variables ................... Setting the Graph Format ................................
Getting Started: Graphing a Circle Getting Started is a fast-paced introduction. Read the chapter for details. Graph a circle of radius 10, centered on the origin in the standard viewing window. To graph this circle, you must enter separate formulas for the upper and lower portions of the circle. Then use ZSquare (zoom square) to adjust the display and make the functions appear as a circle. 1. In Func mode, press o to display the Y= editor.
Defining Graphs TI-83—Graphing Mode Similarities Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-83 graphing mode. Chapters 4, 5, and 6 describe aspects that are unique to parametric graphing, polar graphing, and sequence graphing. Defining a Graph To define a graph in any graphing mode, follow these steps. Some steps are not always necessary. 1. Press z and set the appropriate graph mode (page 3.4). 2.
Setting the Graph Modes Checking and Changing the Graphing Mode To display the mode screen, press z. The default settings are highlighted below. To graph functions, you must select Func mode before you enter values for the window variables and before you enter the functions. The TI-83 has four graphing modes. • Func (function graphing) • Par (parametric graphing; Chapter 4) • Pol (polar graphing; Chapter 5) • Seq (sequence graphing; Chapter 6) Other mode settings affect graphing results.
Defining Functions Displaying Functions in the Y= Editor To display the Y= editor, press o. You can store up to 10 functions to the function variables Y1 through Y9, and Y0. You can graph one or more defined functions at once. In this example, functions Y1 and Y2 are defined and selected. Defining or Editing a Function To define or edit a function, follow these steps. 1. Press o to display the Y= editor. 2. Press † to move the cursor to the function you want to define or edit.
Defining a Function from the Home Screen or a Program To define a function from the home screen or a program, begin on a blank line and follow these steps. 1. Press ƒ [ã], enter the expression, and then press ƒ [ã] again. 2. Press ¿. 3. Press ~ 1 to select 1:Function from the VARS Y.VARS menu. 4. Select the function name, which pastes the name to the cursor location on the home screen or program editor. 5. Press Í to complete the instruction.
Selecting and Deselecting Functions Selecting and Deselecting a Function You can select and deselect (turn on and turn off) a function in the Y= editor. A function is selected when the = sign is highlighted. The TI-83 graphs only the selected functions. You can select any or all functions Y1 through Y9, and Y0. To select or deselect a function in the Y= editor, follow these steps. 1. Press o to display the Y= editor. 2. Move the cursor to the function you want to select or deselect. 3.
Selecting and Deselecting Functions from the Home Screen or a Program To select or deselect a function from the home screen or a program, begin on a blank line and follow these steps. 1. Press ~ to display the VARS Y.VARS menu. 2. Select 4:On/Off to display the ON/OFF secondary menu. 3. Select 1:FnOn to turn on one or more functions or 2:FnOff to turn off one or more functions. The instruction you select is copied to the cursor location. 4.
Setting Graph Styles for Functions Graph Style Icons in the Y= Editor This table describes the graph styles available for function graphing. Use the styles to visually differentiate functions to be graphed together. For example, you can set Y1 as a solid line, Y2 as a dotted line, and Y3 as a thick line.
Shading Above and Below When you select é or ê for two or more functions, the TI-83 rotates through four shading patterns. • Vertical lines shade the first function with a é or ê graph style. • Horizontal lines shade the second. • Negatively sloping diagonal lines shade the third. • Positively sloping diagonal lines shade the fourth. • The rotation returns to vertical lines for the fifth é or ê function, repeating the order described above. When shaded areas intersect, the patterns overlap.
Setting the Viewing Window Variables The TI-83 Viewing The viewing window is the portion of the coordinate plane defined by Xmin, Xmax, Ymin, and Ymax. Xscl (X scale) Window defines the distance between tick marks on the x-axis. Yscl (Y scale) defines the distance between tick marks on the y-axis. To turn off tick marks, set Xscl=0 and Yscl=0. Ymax Xscl Xmin Xmax Yscl Ymin Displaying the Window Variables To display the current window variable values, press p.
Storing to a Window Variable from the Home Screen or a Program To store a value, which can be an expression, to a window variable, begin on a blank line and follow these steps. 1. Enter the value you want to store. 2. Press ¿. 3. Press to display the VARS menu. 4. Select 1:Window to display the Func window variables (X/Y secondary menu). • Press ~ to display the Par and Pol window variables (T/q secondary menu). • Press ~ ~ to display the Seq window variables (U/V/W secondary menu). 5.
Setting the Graph Format Displaying the Format Settings To display the format settings, press y [FORMAT]. The default settings are highlighted below. RectGC PolarGC CoordOn CoordOff GridOff GridOn AxesOn AxesOff LabelOff LabelOn ExprOn ExprOff Sets cursor coordinates. Sets coordinates display on or off. Sets grid off or on. Sets axes on or off. Sets axes label off or on. Sets expression display on or off. Format settings define a graph’s appearance on the display.
CoordOn, CoordOff CoordOn (coordinates on) displays the cursor coordinates at the bottom of the graph. If ExprOff format is selected, the function number is displayed in the top-right corner. CoordOff (coordinates off) does not display the function number or coordinates. GridOff, GridOn Grid points cover the viewing window in rows that correspond to the tick marks (page 3.11) on each axis. GridOff does not display grid points. GridOn displays grid points. AxesOn, AxesOff AxesOn displays the axes.
Displaying Graphs Displaying a New Graph To display the graph of the selected function or functions, press s. TRACE, ZOOM instructions, and CALC operations display the graph automatically. As the TI-83 plots the graph, the busy indicator is on. As the graph is plotted, X and Y are updated. While plotting a graph, you can pause or stop graphing. Pausing or Stopping a Graph • Press Í to pause; then press Í to resume. • Press É to stop; then press s to redraw.
Overlaying Functions on a Graph On the TI-83, you can graph one or more new functions without replotting existing functions. For example, store sin(X) to Y1 in the Y= editor and press s. Then store cos(X) to Y2 and press s again. The function Y2 is graphed on top of Y1, the original function. Graphing a Family of Curves If you enter a list (Chapter 11) as an element in an expression, the TI-83 plots the function for each value in the list, thereby graphing a family of curves.
Exploring Graphs with the Free-Moving Cursor Free-Moving Cursor When a graph is displayed, press |, ~, }, or † to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press |, ~, }, or †, the cursor moves from the center of the viewing window. As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen if CoordOn format is selected.
Exploring Graphs with TRACE Beginning a Trace Use TRACE to move the cursor from one plotted point to the next along a function. To begin a trace, press r. If the graph is not displayed already, press r to display it. The trace cursor is on the first selected function in the Y= editor, at the middle X value on the screen. The cursor coordinates are displayed at the bottom of the screen if CoordOn format is selected.
Moving the Trace Cursor to Any Valid X Value To move the trace cursor to any valid X value on the current function, enter the value. When you enter the first digit, an X= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the X= prompt. The value must be valid for the current viewing window. When you have completed the entry, press Í to move the cursor. Note: This feature does not apply to stat plots.
Exploring Graphs with the ZOOM Instructions ZOOM Menu To display the ZOOM menu, press q. You can adjust the viewing window of the graph quickly in several ways. All ZOOM instructions are accessible from programs. ZOOM MEMORY 1: ZBox 2: Zoom In 3: Zoom Out 4: ZDecimal 5: ZSquare 6: ZStandard 7: ZTrig 8: ZInteger 9: ZoomStat 0: ZoomFit Draws a box to define the viewing window. Magnifies the graph around the cursor. Views more of a graph around the cursor. Sets @X and @Y to 0.1.
Zoom In, Zoom Out Zoom In magnifies the part of the graph that surrounds the cursor location. Zoom Out displays a greater portion of the graph, centered on the cursor location. The XFact and YFact settings determine the extent of the zoom. To zoom in on a graph, follow these steps. 1. Check XFact and YFact (page 3.24); change as needed. 2. Select 2:Zoom In from the ZOOM menu. The zoom cursor is displayed. 3. Move the zoom cursor to the point that is to be the center of the new viewing window. 4. Press Í.
ZStandard ZStandard replots the functions immediately. It updates the window variables to the standard values shown below. Xmin=L10 Xmax=10 Xscl=1 ZTrig Ymin=L10 Ymax=10 Yscl=1 Xres=1 ZTrig replots the functions immediately. It updates the window variables to preset values that are appropriate for plotting trig functions. Those preset values in Radian mode are shown below.
Using ZOOM MEMORY ZOOM MEMORY Menu ZPrevious To display the ZOOM MEMORY menu, press q ~. ZOOM MEMORY 1:ZPrevious 2:ZoomSto 3:ZoomRcl 4:SetFactors... Uses the previous viewing window. Stores the user-defined window. Recalls the user-defined window. Changes Zoom In and Zoom Out factors. ZPrevious replots the graph using the window variables of the graph that was displayed before you executed the last ZOOM instruction. ZoomSto ZoomSto immediately stores the current viewing window.
ZOOM FACTORS The zoom factors, XFact and YFact, are positive numbers (not necessarily integers) greater than or equal to 1. They define the magnification or reduction factor used to Zoom In or Zoom Out around a point. Checking XFact and YFact To display the ZOOM FACTORS screen, where you can review the current values for XFact and YFact, select 4:SetFactors from the ZOOM MEMORY menu. The values shown are the defaults. Changing XFact and YFact You can change XFact and YFact in either of two ways.
Using the CALC (Calculate) Operations CALCULATE Menu To display the CALCULATE menu, press y ãCALCä. Use the items on this menu to analyze the current graph functions. CALCULATE 1: value 2: zero 3: minimum 4: maximum 5: intersect 6: dy/dx 7: ‰f(x)dx value Calculates a function Y value for a given X. Finds a zero (x-intercept) of a function. Finds a minimum of a function. Finds a maximum of a function. Finds an intersection of two functions. Finds a numeric derivative of a function.
zero zero finds a zero (x-intercept or root) of a function using solve(. Functions can have more than one x-intercept value; zero finds the zero closest to your guess. The time zero spends to find the correct zero value depends on the accuracy of the values you specify for the left and right bounds and the accuracy of your guess. To find a zero of a function, follow these steps. 1. Select 2:zero from the CALCULATE menu. The current graph is displayed with Left Bound? in the bottom-left corner. 2.
minimum, maximum minimum and maximum find a minimum or maximum of a function within a specified interval to a tolerance of 1âL5. To find a minimum or maximum, follow these steps. 1. Select 3:minimum or 4:maximum from the CALCULATE menu. The current graph is displayed. 2. Select the function and set left bound, right bound, and guess as described for zero (steps 2 through 4; page 3.26).
dy/dx dy/dx (numerical derivative) finds the numerical derivative (slope) of a function at a point, with H=1âL3. To find a function’s slope at a point, follow these steps. 1. Select 6:dy/dx from the CALCULATE menu. The current graph is displayed. 2. Press } or † to select the function for which you want to find the numerical derivative. 3. Press | or ~ (or enter a value) to select the X value at which to calculate the derivative, and then press Í.
4 Contents Parametric Graphing Getting Started: Path of a Ball ........................... Defining and Displaying Parametric Graphs .............. Exploring Parametric Graphs ............................ 4-2 4-4 4-7 Parametric Graphing 4-1 8304PARA.
Getting Started: Path of a Ball Getting Started is a fast-paced introduction. Read the chapter for details. Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal from ground level. How far does the ball travel? When does it hit the ground? How high does it go? Ignore all forces except gravity.
The horizontal component vector is defined by X3T and Y3T. 6. Press ~ 2, and then press 1 Í to define X3T. Press 0 Í to define Y3T. 7. Press | | } Í to change the graph style to è for X3T and Y3T. Press } Í Í to change the graph style to ë for X2T and Y2T. Press } Í Í to change the graph style to ë for X1T and Y1T. (These keystrokes assume that all graph styles were set to ç originally.) 8. Press p. Enter these values for the window variables. Tmin=0 Tmax=5 Tstep=.
Defining and Displaying Parametric Graphs TI-83 Graphing Mode Similarities The steps for defining a parametric graph are similar to the steps for defining a function graph. Chapter 4 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 4 details aspects of parametric graphing that differ from function graphing. Setting Parametric Graphing Mode To display the mode screen, press z.
Defining and Editing Parametric Equations To define or edit a parametric equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a parametric equation is T. In Par graphing mode, you can enter the parametric variable T in either of two ways. • Press „. • Press ƒ ãTä. Two components, X and Y, define a single parametric equation. You must define both of them.
Setting the Graph To display the current graph format settings, press y [FORMAT]. Chapter 3 describes the format settings in detail. Format The other graphing modes share these format settings; Seq graphing mode has an additional axes format setting. Displaying a Graph When you press s, the TI-83 plots the selected parametric equations. It evaluates the X and Y components for each value of T (from Tmin to Tmax in intervals of Tstep), and then plots each point defined by X and Y.
Exploring Parametric Graphs Free-Moving Cursor The free-moving cursor in Par graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed. TRACE To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one Tstep at a time.
Moving the Trace Cursor to Any Valid T Value To move the trace cursor to any valid T value on the current function, enter the number. When you enter the first digit, a T= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the T= prompt. The value must be valid for the current viewing window. When you have completed the entry, press Í to move the cursor. ZOOM ZOOM operations in Par graphing work the same as in Func graphing.
5 Contents Polar Graphing Getting Started: Polar Rose .............................. Defining and Displaying Polar Graphs ................... Exploring Polar Graphs .................................. 5-2 5-3 5-6 Polar Graphing 5-1 8305POLR.
Getting Started: Polar Rose Getting Started is a fast-paced introduction. Read the chapter for details. The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B. 1. Press z to display the mode screen. Press † † † ~ ~ Í to select Pol graphing mode. Select the defaults (the options on the left) for the other mode settings. 2. Press o to display the polar Y= editor. Press 8 ˜ 2.5 „ ¤ Í to define r 1. 3.
Defining and Displaying Polar Graphs TI-83 Graphing Mode Similarities The steps for defining a polar graph are similar to the steps for defining a function graph. Chapter 5 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 5 details aspects of polar graphing that differ from function graphing. Setting Polar Graphing Mode To display the mode screen, press z.
Defining and Editing Polar Equations To define or edit a polar equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a polar equation is q. In Pol graphing mode, you can enter the polar variable q in either of two ways. • Press „. • Press ƒ ãqä. The TI-83 graphs only the selected polar equations. In the Selecting and Deselecting Polar Y= editor, a polar equation is selected when the = sign is highlighted.
Setting the Graph To display the current graph format settings, press y [FORMAT]. Chapter 3 describes the format settings in detail. Format The other graphing modes share these format settings. Displaying a Graph When you press s, the TI-83 plots the selected polar equations. It evaluates R for each value of q (from qmin to qmax in intervals of qstep) and then plots each point. The window variables define the viewing window. As the graph is plotted, X, Y, R, and q are updated.
Exploring Polar Graphs Free-Moving Cursor The free-moving cursor in Pol graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed. TRACE To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one qstep at a time.
6 Contents Sequence Graphing Getting Started: Forest and Trees ........................ Defining and Displaying Sequence Graphs ............... Selecting Axes Combinations ............................ Exploring Sequence Graphs.............................. Graphing Web Plots...................................... Using Web Plots to Illustrate Convergence ............... Graphing Phase Plots .................................... Comparing TI-83 and TI.82 Sequence Variables ..........
Getting Started: Forest and Trees Getting Started is a fast-paced introduction. Read the chapter for details. A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the trees will be harvested and 1,000 new trees will be planted. Will the forest eventually disappear? Will the forest size stabilize? If so, in how many years and with how many trees? 1. Press z. Press † † † ~ ~ ~ Í to select Seq graphing mode. 2.
Defining and Displaying Sequence Graphs TI-83 Graphing Mode Similarities The steps for defining a sequence graph are similar to the steps for defining a function graph. Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 6 details aspects of sequence graphing that differ from function graphing. Setting Sequence To display the mode screen, press z.
Displaying the Sequence Y= Editor After selecting Seq mode, press o to display the sequence Y= editor. In this editor, you can display and enter sequences for u(n), v(n), and w(n). Also, you can edit the value for nMin, which is the sequence window variable that defines the minimum n value to evaluate. The sequence Y= editor displays the nMin value because of its relevance to u(nMin), v(nMin), and w(nMin), which are the initial values for the sequence equations u(n), v(n), and w(n), respectively.
Defining and Editing a Sequence Function To define or edit a sequence function, follow the steps in Chapter 3 for defining a function. The independent variable in a sequence is n. In Seq graphing mode, you can enter the sequence variable in either of two ways. • Press „. • Press y [CATALOG] [N]. You can enter the function name from the keyboard. • To enter the function name u, press y [u] (above ¬). • To enter the function name v, press y [v] (above −).
Recursive Sequences In a recursive sequence, the nth term in the sequence is defined in relation to the previous term or the term that precedes the previous term, represented by u(nN1) and u(nN2). A recursive sequence may also be defined in relation to n, as in u(n)=u(nN1)+n. For example, in the sequence below you cannot calculate u(5) without first calculating u(1), u(2), u(3), and u(4). Using an initial value u(nMin) = 1, the sequence above returns 1, 2, 4, 8, 16, . . .
Setting Window Variables To display the window variables, press p. These variables define the viewing window. The values below are defaults for Seq graphing in both Radian and Degree angle modes.
Selecting Axes Combinations Setting the Graph To display the current graph format settings, press y [FORMAT]. Chapter 3 describes the format settings in detail. Format The other graphing modes share these format settings. The axes setting on the top line of the screen is available only in Seq mode.
Exploring Sequence Graphs Free-Moving Cursor The free-moving cursor in Seq graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed. TRACE The axes format setting affects TRACE.
ZOOM ZOOM operations in Seq graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected. PlotStart, PlotStep, nMin, and nMax are only affected when you select ZStandard. The VARS Zoom secondary menu ZU items 1 through 7 are the ZOOM MEMORY variables for Seq graphing. CALC The only CALC operation available in Seq graphing is value. • When Time axes format is selected, value displays Y (the u(n) value) for a specified n value.
Graphing Web Plots Graphing a Web Plot To select Web axes format, press y [FORMAT] ~ Í. A web plot graphs u(n) versus u(nN1), which you can use to study long-term behavior (convergence, divergence, or oscillation) of a recursive sequence. You can see how the sequence may change behavior as its initial value changes. Valid Functions for Web Plots When Web axes format is selected, a sequence will not graph properly or will generate an error.
Using Web Plots to Illustrate Convergence Example: Convergence 1. Press o in Seq mode to display the sequence Y= editor. Make sure the graph style is set to í (dot), and then define nMin, u(n) and u(nMin) as shown below. 2. Press y [FORMAT] Í to set Time axes format. 3. Press p and set the variables as shown below. nMin=1 nMax=25 PlotStart=1 PlotStep=1 Xmin=0 Xmax=25 Xscl=1 Ymin=L10 Ymax=10 Yscl=1 4. Press s to graph the sequence. 5. Press y [FORMAT] and select the Web axes setting. 6.
Graphing Phase Plots Graphing with uv, The phase-plot axes settings uv, vw, and uw show relationships between two sequences. To select a vw, and uw phase-plot axes setting, press y [FORMAT], press ~ until the cursor is on uv, vw, or uw, and then press Í.
2. Press y [FORMAT] Í to select Time axes format. 3. Press p and set the variables as shown below. nMin=0 nMax=400 PlotStart=1 PlotStep=1 Xmin=0 Xmax=400 Xscl=100 Ymin=0 Ymax=300 Yscl=100 4. Press s to graph the sequence. 5. Press r ~ to individually trace the number of rabbits (u(n)) and wolves (v(n)) over time (n). Tip: Press a number, and then press Í to jump to a specific n value (month) while in TRACE. 6. Press y [FORMAT] ~ ~ Í to select uv axes format. 7.
Comparing TI-83 and TI-82 Sequence Variables Sequences and Window Variables Refer to the table if you are familiar with the TI-82. It shows TI-83 sequences and sequence window variables, as well as their TI-82 counterparts. TI.83 TI.
Keystroke Differences Between TI-83 and TI-82 Sequence Keystroke Changes Refer to the table if you are familiar with the TI-82. It compares TI-83 sequence-name syntax and variable syntax with TI.82 sequence-name syntax and variable syntax. TI.83 / TI.82 On TI.83, press: On TI.82, press: n/n „ y [n] u(n) / Un y [u] £„¤ y [Y.VARS] ¶ À v(n) / Vn y [v ] £„¤ y [Y.
7 Contents Tables Getting Started: Roots of a Function ..................... Setting Up the Table ..................................... Defining the Dependent Variables........................ Displaying the Table ..................................... 7-2 7-3 7-4 7-5 Tables 7-1 8307TABL.
Getting Started: Roots of a Function Getting Started is a fast-paced introduction. Read the chapter for details. Evaluate the function Y = X3 N 2X at each integer between L10 and 10. How many sign changes occur, and at what X values? 1. Press z † † † Í to set Func graphing mode. 2. Press o. Press „ 3 to select 3. Then press ¹ 2 „ to enter the function Y1=X3N2X. 3. Press y [TBLSET] to display the TABLE SETUP screen. Press Ì 10 Í to set TblStart=L10. Press 1 Í to set @Tbl=1.
Setting Up the Table TABLE SETUP Screen To display the TABLE SETUP screen, press y [TBLSET]. TblStart, @Tbl TblStart (table start) defines the initial value for the independent variable. TblStart applies only when the independent variable is generated automatically (when Indpnt: Auto is selected). @Tbl (table step) defines the increment for the independent variable. Note: In Seq mode, both TblStart and @Tbl must be integers.
Defining the Dependent Variables Defining Dependent Variables from the Y= Editor In the Y= editor, enter the functions that define the dependent variables. Only functions that are selected in the Y= editor are displayed in the table. The current graphing mode is used. In Par mode, you must define both components of each parametric equation (Chapter 4). Editing Dependent Variables from the Table Editor To edit a selected Y= function from the table editor, follow these steps. 1.
Displaying the Table The Table To display the table, press y [TABLE]. Current cell Dependentvariable values in the second and third columns Independentvariable values in the first column Current cell’s full value Note: The table abbreviates the values, if necessary. Independent and Dependent Variables Clearing the Table from the Home Screen or a Program The current graphing mode determines which independent and dependent variables are displayed in the table (Chapter 1).
Scrolling IndependentVariable Values If Indpnt: Auto is selected, you can press } and † in the independent-variable column to display more values. As you scroll the column, the corresponding dependentvariable values also are displayed. All dependent-variable values may not be displayed if Depend: Ask is selected. Note: You can scroll back from the value entered for TblStart. As you scroll, TblStart is updated automatically to the value shown on the top line of the table.
8 Contents Draw Instructions Getting Started: Drawing a Tangent Line ................. Using the DRAW Menu ................................... Clearing Drawings ....................................... Drawing Line Segments .................................. Drawing Horizontal and Vertical Lines ................... Drawing Tangent Lines .................................. Drawing Functions and Inverses ......................... Shading Areas on a Graph ............................... Drawing Circles.........
Getting Started: Drawing a Tangent Line Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to find the equation of the tangent line at X = ‡2/2 for the function Y = sinX. Before you begin, select Radian and Func mode from the mode screen, if necessary. 1. Press o to display the Y= editor. Press ˜ „ ¤ to store sin(X) in Y1. 2. Press q 7 to select 7:ZTrig, which graphs the equation in the Zoom Trig window. 3. Press y [DRAW] 5 to select 5:Tangent(.
Using the DRAW Menu DRAW Menu To display the DRAW menu, press y [DRAW]. The TI-83’s interpretation of these instructions depends on whether you accessed the menu from the home screen or the program editor or directly from a graph. DRAW POINTS STO 1: ClrDraw Clears all drawn elements. 2: Line( Draws a line segment between 2 points. 3: Horizontal Draws a horizontal line. 4: Vertical Draws a vertical line. 5: Tangent( Draws a line segment tangent to a function. 6: DrawF Draws a function.
Clearing Drawings Clearing Drawings When a Graph Is Displayed Clearing Drawings from the Home Screen or a Program All points, lines, and shading drawn on a graph with DRAW instructions are temporary. To clear drawings from the currently displayed graph, select 1:ClrDraw from the DRAW menu. The current graph is replotted and displayed with no drawn elements. To clear drawings on a graph from the home screen or a program, begin on a blank line on the home screen or in the program editor.
Drawing Line Segments Drawing a Line Segment Directly on a Graph To draw a line segment when a graph is displayed, follow these steps. 1. Select 2:Line( from the DRAW menu. 2. Place the cursor on the point where you want the line segment to begin, and then press Í. 3. Move the cursor to the point where you want the line segment to end. The line is displayed as you move the cursor. Press Í. To continue drawing line segments, repeat steps 2 and 3. To cancel Line(, press ‘.
Drawing Horizontal and Vertical Lines Drawing a Line Directly on a Graph To draw a horizontal or vertical line when a graph is displayed, follow these steps. 1. Select 3:Horizontal or 4:Vertical from the DRAW menu. A line is displayed that moves as you move the cursor. 2. Place the cursor on the y-coordinate (for horizontal lines) or x-coordinate (for vertical lines) through which you want the drawn line to pass. 3. Press Í to draw the line on the graph. To continue drawing lines, repeat steps 2 and 3.
Drawing a Line from the Home Screen or a Program Horizontal (horizontal line) draws a horizontal line at Y=y. y can be an expression but not a list. Horizontal y Vertical (vertical line) draws a vertical line at X=x. x can be an expression but not a list. Vertical x To instruct the TI-83 to draw more than one horizontal or vertical line, separate each instruction with a colon ( : ). DRAW Instructions 8-7 8308DRAW.
Drawing Tangent Lines Drawing a Tangent Line Directly on a Graph To draw a tangent line when a graph is displayed, follow these steps. 1. Select 5:Tangent( from the DRAW menu. 2. Press † and } to move the cursor to the function for which you want to draw the tangent line. The current graph’s Y= function is displayed in the top-left corner, if ExprOn is selected. 3. Press ~ and | or enter a number to select the point on the function at which you want to draw the tangent line. 4. Press Í.
Drawing Functions and Inverses Drawing a Function DrawF (draw function) draws expression as a function in terms of X on the current graph. When you select 6:DrawF from the DRAW menu, the TI-83 returns to the home screen or the program editor. DrawF is not interactive. DrawF expression Note: You cannot use a list in expression to draw a family of curves. Drawing an Inverse of a Function DrawInv (draw inverse) draws the inverse of expression by plotting X values on the y-axis and Y values on the x-axis.
Shading Areas on a Graph Shading a Graph To shade an area on a graph, select 7:Shade( from the DRAW menu. The instruction is pasted to the home screen or to the program editor. Shade( draws lowerfunc and upperfunc in terms of X on the current graph and shades the area that is specifically above lowerfunc and below upperfunc. Only the areas where lowerfunc < upperfunc are shaded. Xleft and Xright, if included, specify left and right boundaries for the shading.
Drawing Circles Drawing a Circle Directly on a Graph To draw a circle directly on a displayed graph using the cursor, follow these steps. 1. Select 9:Circle( from the DRAW menu. 2. Place the cursor at the center of the circle you want to draw. Press Í. 3. Move the cursor to a point on the circumference. Press Í to draw the circle on the graph. Note: This circle is displayed as circular, regardless of the window variable values, because you drew it directly on the display.
Placing Text on a Graph Placing Text Directly on a Graph To place text on a graph when the graph is displayed, follow these steps. 1. Select 0:Text( from the DRAW menu. 2. Place the cursor where you want the text to begin. 3. Enter the characters. Press ƒ or y [A.LOCK] to enter letters and q. You may enter TI-83 functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the graph.
Using Pen to Draw on a Graph Using Pen to Draw on a Graph Pen draws directly on a graph only. You cannot execute Pen from the home screen or a program. To draw on a displayed graph, follow these steps. 1. Select A:Pen from the DRAW menu. 2. Place the cursor on the point where you want to begin drawing. Press Í to turn on the pen. 3. Move the cursor. As you move the cursor, you draw on the graph, shading one pixel at a time. 4. Press Í to turn off the pen.
Drawing Points on a Graph DRAW POINTS Menu To display the DRAW POINTS menu, press y [DRAW] ~. The TI-83’s interpretation of these instructions depends on whether you accessed this menu from the home screen or the program editor or directly from a graph. DRAW POINTS STO 1: Pt-On( Turns on a point. 2: Pt-Off( Turns off a point. 3: Pt-Change( Toggles a point on or off. 4: Pxl-On( Turns on a pixel. 5: Pxl-Off( Turns off a pixel. 6: Pxl-Change( Toggles a pixel on or off.
Erasing Points with Pt-Off( To erase (turn off) a drawn point on a graph, follow these steps. 1. Select 2:Pt.Off( (point off) from the DRAW POINTS menu. 2. Move the cursor to the point you want to erase. 3. Press Í to erase the point. To continue erasing points, repeat steps 2 and 3. To cancel Pt.Off(, press ‘. Changing Points with Pt-Change( To change (toggle on or off) a point on a graph, follow these steps. 1. Select 3:Pt.Change( (point change) from the DRAW POINTS menu. 2.
Drawing Pixels TI-83 Pixels A pixel is a square dot on the TI-83 display. The Pxl. (pixel) instructions let you turn on, turn off, or reverse a pixel (dot) on the graph using the cursor. When you select a pixel instruction from the DRAW POINTS menu, the TI-83 returns to the home screen or the program editor. The pixel instructions are not interactive. Turning On and Off Pixels with Pxl-On( and Pxl-Off( Pxl.
Storing Graph Pictures (Pics) DRAW STO Menu To display the DRAW STO menu, press y [DRAW] |. When you select an instruction from the DRAW STO menu, the TI-83 returns to the home screen or the program editor. The picture and graph database instructions are not interactive. DRAW POINTS STO 1:StorePic 2:RecallPic 3:StoreGDB 4:RecallGDB Storing a Graph Picture Stores the current picture. Recalls a saved picture. Stores the current graph database. Recalls a saved graph database.
Recalling Graph Pictures (Pics) Recalling a Graph Picture To recall a graph picture, follow these steps. 1. Select 2:RecallPic from the DRAW STO menu. RecallPic is pasted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the picture variable from which you want to recall a picture. For example, if you enter 3, the TI-83 will recall the picture stored to Pic3. Note: You also can select a variable from the PICTURE secondary menu ( 4). The variable is pasted next to RecallPic. 3.
Storing Graph Databases (GDBs) What Is a Graph Database? A graph database (GDB) contains the set of elements that defines a particular graph. You can recreate the graph from these elements. You can store up to 10 GDBs in variables GDB1 through GDB9, or GDB0 and recall them to recreate graphs. A GDB stores five elements of a graph.
Recalling Graph Databases (GDBs) Recalling a Graph Database CAUTION: When you recall a GDB, it replaces all existing Y= functions. Consider storing the current Y= functions to another database before recalling a stored GDB. To recall a graph database, follow these steps. 1. Select 4:RecallGDB from the DRAW STO menu. RecallGDB is pasted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the GDB variable from which you want to recall a GDB.
9 Contents Split Screen Getting Started: Exploring the Unit Circle................ Using Split Screen ....................................... Horiz (Horizontal) Split Screen .......................... G.T (Graph-Table) Split Screen .......................... TI-83 Pixels in Horiz and G.T Mode ...................... 9-2 9-3 9-4 9-5 9-6 Split Screen 9-1 8309SPLT.
Getting Started: Exploring the Unit Circle Getting Started is a fast-paced introduction. Read the chapter for details. Use G.T (graph-table) split-screen mode to explore the unit circle and its relationship to the numeric values for the commonly used trigonometric angles of 0°, 30°, 45°, 60°, 90°, and so on. 1. Press z to display the mode screen. Press † † ~ Í to select Degree mode. Press † ~ Í to select Par (parametric) graphing mode. Press † † † † ~ ~ Í to select G.T (graph-table) split-screen mode. 2.
Using Split Screen Setting a SplitScreen Mode To set a split-screen mode, press z, and then move the cursor to the bottom line of the mode screen. • Select Horiz (horizontal) to display the graph screen and another screen split horizontally. • Select G.T (graph-table) to display the graph screen and table screen split vertically. $ $ The split screen is activated when you press any key that applies to either half of the split screen. Some screens are never displayed as split screens.
Horiz (Horizontal) Split Screen Horiz Mode In Horiz (horizontal) split-screen mode, a horizontal line splits the screen into top and bottom halves. The top half displays the graph. The bottom half displays any of these editors. • • • • • Moving from Half to Half in Horiz Mode Home screen (four lines) Y= editor (four lines) Stat list editor (two rows) Window editor (three settings) Table editor (two rows) To use the top half of the split screen: • Press s or r. • Select a ZOOM or CALC operation.
G-T (Graph-Table) Split Screen G-T Mode In G.T (graph-table) split-screen mode, a vertical line splits the screen into left and right halves. The left half displays the graph. The right half displays the table. Moving from Half to Half in G-T Mode To use the left half of the split screen: • Press s or r. • Select a ZOOM or CALC operation. To use the right half of the split screen, press y [TABLE]. Using r in G-T Mode As you move the trace cursor along a graph in the split screen’s left half in G.
TI-83 Pixels in Horiz and G-T Modes TI-83 Pixels in Horiz and G-T Modes Note: Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on. DRAW POINTS Menu Pixel Instructions For Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.Test(: • In Horiz mode, row must be {30; column must be {94. • In G.T mode, row must be {50; column must be {46. Pxl.
10 Contents Matrices Getting Started: Systems of Linear Equations ............ 10-2 Defining a Matrix ........................................ 10-2 Viewing and Editing Matrix Elements .................... 10-4 Using Matrices with Expressions ........................ 10-7 Displaying and Copying Matrices ........................ 10-8 Using Math Functions with Matrices ..................... 10-9 Using the MATRX MATH Operations ..................... 10-12 Matrices 10-1 8310MTRX.
Getting Started: Systems of Linear Equations Getting Started is a fast-paced introduction. Read the chapter for details. Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-83, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using rref( to obtain the reduced row-echelon form. 1. Press . Press ~ ~ to display the MATRX EDIT menu. Press 1 to select 1: [A]¸ 2. Press 2 Í 4 Í to define a 2×4 matrix.
Defining a Matrix What Is a Matrix? A matrix is a two-dimensional array. You can display, define, or edit a matrix in the matrix editor. The TI-83 has 10 matrix variables, [A] through [J]. You can define a matrix directly in an expression. A matrix, depending on available memory, may have up to 99 rows or columns. You can store only real numbers in TI-83 matrices. Selecting a Matrix Before you can define or display a matrix in the editor, you first must select the matrix name.
Viewing and Editing Matrix Elements Displaying Matrix Elements After you have set the dimensions of the matrix, you can view the matrix and enter values for the matrix elements. In a new matrix, all values are zero. Select the matrix from the MATRX EDIT menu and enter or accept the dimensions. The center portion of the matrix editor displays up to seven rows and three columns of a matrix, showing the values of the elements in abbreviated form if necessary.
Viewing a Matrix The matrix editor has two contexts, viewing and editing. In viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the highlighted element is displayed on the bottom line. Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions. Viewing-Context Keys Key Function | or ~ Moves the rectangular cursor within the current row.
Editing a Matrix Element In editing context, an edit cursor is active on the bottom line. To edit a matrix element value, follow these steps. 1. Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions. 2. Press |, }, ~, and † to move the cursor to the matrix element you want to change. 3. Switch to editing context by pressing Í, ‘, or an entry key. 4. Change the value of the matrix element using the editing-context keys described below.
Using Matrices with Expressions Using a Matrix in an Expression To use a matrix in an expression, you can do any of the following. • Copy the name from the MATRX NAMES menu. • Recall the contents of the matrix into the expression with y [RCL] (Chapter 1). • Enter the matrix directly (see below). Entering a Matrix in an Expression You can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix directly in an expression. To enter a matrix in an expression, follow these steps. 1.
Displaying and Copying Matrices Displaying a Matrix To display the contents of a matrix on the home screen, select the matrix from the MATRX NAMES menu, and then press Í. Ellipses in the left or right column indicate additional columns. # or $ in the right column indicate additional rows. Press ~, |, †, and } to scroll the matrix. Copying One Matrix to Another To copy a matrix, follow these steps. 1. Press to display the MATRX NAMES menu. 2. Select the name of the matrix you want to copy. 3. Press ¿.
Using Math Functions with Matrices Using Math Functions with Matrices You can use many of the math functions on the TI-83 keyboard, the MATH menu, the MATH NUM menu, and the MATH TEST menu with matrices. However, the dimensions must be appropriate. Each of the functions below creates a new matrix; the original matrix remains the same. + (Add), – (Subtract), ä (Multiply) To add (Ã) or subtract (¹) matrices, the dimensions must be the same.
abs( abs( (absolute value, MATH NUM menu) returns a matrix containing the absolute value of each element of matrix. abs(matrix) round( round( (MATH NUM menu) returns a matrix. It rounds every element in matrix to #decimals ( 9). If #decimals is omitted, the elements are rounded to 10 digits. round(matrix[,#decimals]) M1 (Inverse) Use the L1 function (— ) to invert a matrix (^L1 is not valid). matrix must be square. The determinant cannot equal zero.
Relational Operations To compare two matrices using the relational operations = and ƒ (TEST menu), they must have the same dimensions. = and ƒ compare matrixA and matrixB on an element-byelement basis. The other relational operations are not valid with matrices. matrixA=matrixB returns 1 if every comparison is true; it returns 0 if any comparison is false. matrixAƒmatrixB returns 1 if at least one comparison is false; it returns 0 if no comparison is false.
Using the MATRX MATH Operations MATRX MATH Menu To display the MATRX MATH menu, press ~. det( det( (determinant) returns the determinant (a real number) NAMES MATH EDIT 1: det( Calculates the determinant. 2: T Transposes the matrix. 3: dim( Returns the matrix dimensions. 4: Fill( Fills all elements with a constant. 5: identity( Returns the identity matrix. 6: randM( Returns a random matrix. 7: augment( Appends two matrices. 8: Matr4list( Stores a matrix to a list.
Creating a Matrix with dim( Use dim( with ¿ to create a new matrixname of dimensions rows × columns with 0 as each element. {rows,columns}!dim(matrixname) Redimensioning a Matrix with dim( Use dim( with ¿ to redimension an existing matrixname to dimensions rows × columns. The elements in the old matrixname that are within the new dimensions are not changed. Additional created elements are zeros. Matrix elements that are outside the new dimensions are deleted.
augment( augment( appends matrixA to matrixB as new columns. matrixA and matrixB both must have the same number of rows. augment(matrixA,matrixB) Matr4list( Matr4list( (matrix stored to list) fills each listname with elements from each column in matrix. Matr4list( ignores extra listname arguments. Likewise, Matr4list( ignores extra matrix columns. Matr4list(matrix,listnameA,...,listname n) & Matr4list( also fills a listname with elements from a specified column# in matrix.
cumSum( cumSum( returns cumulative sums of the elements in matrix, starting with the first element. Each element is the cumulative sum of the column from top to bottom. cumSum(matrix) Row Operations MATRX MATH menu items A through F are row operations. You can use a row operation in an expression. Row operations do not change matrix in memory. You can enter all row numbers and values as expressions. You can select the matrix from the MATRX NAMES menu.
rowSwap( rowSwap( returns a matrix. It swaps rowA and rowB of matrix. rowSwap(matrix,rowA,rowB) row+( row+( (row addition) returns a matrix. It adds rowA and rowB of matrix and stores the results in rowB. row+(matrix,rowA,rowB) ärow( ärow( (row multiplication) returns a matrix. It multiplies row of matrix by value and stores the results in row. ärow(value,matrix,row) ärow+( ärow+( (row multiplication and addition) returns a matrix.
11 Contents Lists Getting Started: Generating a Sequence .................. 11-2 Naming Lists ............................................. 11-3 Storing and Displaying Lists ............................. 11-4 Entering List Names ..................................... 11-6 Attaching Formulas to List Names ....................... 11-7 Using Lists in Expressions ............................... 11-9 LIST OPS Menu .......................................... 11-10 LIST MATH Menu ..................................
Getting Started: Generating a Sequence Getting Started is a fast-paced introduction. Read the chapter for details. Calculate the first eight terms of the sequence 1/A2. Store the results to a usercreated list. Then display the results in fraction form. Begin this example on a blank line on the home screen. 1. Press y [LIST] ~ to display the LIST OPS menu. 2. Press 5 to select 5:seq(, which pastes seq( to the current cursor location. 3. Press 1 ¥ ƒ [A] ¡ ¢ ƒ [A] ¢ 1 ¢ 8 ¢ 1 ¤ to enter the sequence. 4.
Naming Lists Using TI-83 List Names L1 through L6 The TI-83 has six list names in memory: L1, L2, L3, L4, L5, and L6. The list names L1 through L6 are on the keyboard above the numeric keys À through ¸. To paste one of these names to a valid screen, press y, and then press the appropriate key. L1 through L6 are stored in stat list editor columns 1 through 6 when you reset memory. Creating a List Name on the Home Screen To create a list name on the home screen, follow these steps. 1.
Storing and Displaying Lists Storing Elements to a List You can store list elements in either of two ways. • Use braces and ¿ on the home screen. • Use the stat list editor (Chapter 12). The maximum dimension of a list is 999 elements. Tip: When you store a complex number to a list, the entire list is converted to a list of complex numbers. To convert the list to a list of real numbers, display the home screen, and then enter real(listname)!listname.
Copying One List to Another To copy a list, store it to another list. Accessing a List Element You can store a value to or recall a value from a specific list element. You can store to any element within the current list dimension or one element beyond. listname(element) Deleting a List from Memory To delete lists from memory, including L1 through L6, use the MEMORY DELETE FROM secondary menu (Chapter 18). Resetting memory restores L1 through L6.
Entering List Names Using the LIST NAMES Menu To display the LIST NAMES menu, press y [LIST]. Each item is a user-created list name. LIST NAMES menu items are sorted automatically in alphanumerical order. Only the first 10 items are labeled, using 1 through 9, then 0. To jump to the first list name that begins with a particular alpha character or q, press ƒ [letter from A to Z or q]. Tip: From the top of a menu, press } to move to the bottom. From the bottom, press † to move to the top.
Attaching Formulas to List Names Attaching a Formula to a List Name You can attach a formula to a list name so that each list element is a result of the formula. When executed, the attached formula must resolve to a list. When anything in the attached formula changes, the list to which the formula is attached is updated automatically. • When you edit an element of a list that is referenced in the formula, the corresponding element in the list to which the formula is attached is updated.
Attaching a Formula to a List on the Home Screen or in a Program To attach a formula to a list name from a blank line on the home screen or from a program, follow these steps. 1. Press ƒ [ã], enter the formula (which must resolve to a list), and press ƒ [ã] again. Note: When you include more than one list name in a formula, each list must have the same dimension. 2. Press ¿. 3. Enter the name of the list to which you want to attach the formula. • Press y, and then enter a TI-83 list name L1 through L6.
Using Lists in Expressions Using a List in an Expression You can use lists in an expression in any of three ways. When you press Í, any expression is evaluated for each list element, and a list is displayed. • Use L1–L6 or any user-created list name in an expression. • Enter the list elements directly (step 1 on page 11.3). • Use y [RCL] to recall the contents of the list into an expression at the cursor location (Chapter 1).
LIST OPS Menu LIST OPS Menu To display the LIST OPS menu, press y [LIST] ~. NAMES OPS MATH 1:SortA( 2:SortD( 3:dim( 4:Fill( 5:seq( 6:cumSum( 7: @List( 8:Select( 9:augment( 0:List4matr( A:Matr4list( B:Ù SortA(, SortD( Sorts lists in ascending order. Sorts lists in descending order. Sets the list dimension. Fills all elements with a constant. Creates a sequence. Returns a list of cumulative sums. Returns difference of successive elements. Selects specific data points. Concatenates two lists.
Using dim( to Find List Dimensions dim( (dimension) returns the length (number of elements) Using dim( to Create a List You can use dim( with ¿ to create a new listname with dimension length from 1 to 999. The elements are zeros. of list. dim(list) length!dim(listname) Using dim( to Redimension a List You can use dim with ¿ to redimension an existing listname to dimension length from 1 to 999. • The elements in the old listname that are within the new dimension are not changed.
seq( seq( (sequence) returns a list in which each element is the result of the evaluation of expression with regard to variable for the values ranging from begin to end at steps of increment. variable need not be defined in memory. increment can be negative; the default value for increment is 1. seq( is not valid within expression. seq(expression,variable,begin,end[,increment]) cumSum( cumSum( (cumulative sum) returns the cumulative sums of the elements in list, starting with the first element.
Before Using Select( Before using Select(, follow these steps. 1. Create two list names and enter the data. 2. Turn on a stat plot, select " (scatter plot) or Ó (xyLine), and enter the two list names for Xlist: and Ylist: (Chapter 12). 3. Use ZoomStat to plot the data (Chapter 3). Using Select( to Select Data Points from a Plot To select data points from a scatter plot or xyLine plot, follow these steps. 1. Press y [LIST] ~ 8 to select 8:Select( from the LIST OPS menu.
6. Press Í. A 4 indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottomleft corner. 7. Press | or ~ to move the cursor to the stat plot point that you want for the right bound, and then press Í. The x-values and y-values of the selected points are stored in xlistname and ylistname. A new stat plot of xlistname and ylistname replaces the stat plot from which you selected data points. The list names are updated in the stat plot editor.
augment( augment( concatenates the elements of listA and listB. The list elements can be real or complex numbers. augment(listA,listB) List4matr( List4matr( (lists stored to matrix) fills matrixname column by column with the elements from each list. If the dimensions of all lists are not equal, then List4matr( fills each extra matrixname row with 0. Complex lists are not valid. List4matr(list1,list2, . . . ,list n,matrixname) & Lists 11-15 8311LIST.
Matr4list( Matr4list( (matrix stored to lists) fills each listname with elements from each column in matrix. If the number of listname arguments exceeds the number of columns in matrix, then Matr4list( ignores extra listname arguments. Likewise, if the number of columns in matrix exceeds the number of listname arguments, then Matr4list( ignores extra matrix columns. Matr4list(matrix,listname1,listname2, . . .
LIST MATH Menu LIST MATH Menu To display the LIST MATH menu, press y [LIST] |. NAMES OPS MATH 1: min( 2: max( 3: mean( 4: median( 5: sum( 6: prod( 7: stdDev( 8: variance( min(, max( Returns minimum element of a list. Returns maximum element of a list. Returns mean of a list. Returns median of a list. Returns sum of elements in a list. Returns product of elements in list. Returns standard deviation of a list. Returns the variance of a list.
sum(, prod( sum( (summation) returns the sum of the elements in list. start and end are optional; they specify a range of elements. list elements can be real or complex numbers. prod( returns the product of all elements of list. start and end elements are optional; they specify a range of list elements. list elements can be real or complex numbers.
12 Contents Statistics Getting Started: Pendulum Lengths and Periods ......... 12-2 Setting Up Statistical Analyses ........................... 12-10 Using the Stat List Editor ................................ 12-11 Attaching Formulas to List Names ....................... 12-14 Detaching Formulas from List Names .................... 12-16 Switching Stat List Editor Contexts ...................... 12-17 Stat List Editor Contexts ................................. 12-18 STAT EDIT Menu .......................
Getting Started: Pendulum Lengths and Periods Getting Started is a fast-paced introduction. Read the chapter for details. A group of students is attempting to determine the mathematical relationship between the length of a pendulum and its period (one complete swing of a pendulum). The group makes a simple pendulum from string and washers and then suspends it from the ceiling. They record the pendulum’s period for each of 12 string lengths.* Length (cm) Time (sec) 6.5 11.0 13.2 15.0 18.0 23.1 24.4 26.
4. Press 6 Ë 5 Í to store the first pendulum string length (6.5 cm) in L1. The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 string length values in the table on page 12.2. 5. Press ~ to move the rectangular cursor to the first row in L2. Press Ë 51 Í to store the first time measurement (.51 sec) in L2. The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 time values in the table on page 12.2. 6. Press o to display the Y= editor.
Since the scatter plot of time-versus-length data appears to be approximately linear, fit a line to the data. 10. Press … ~ 4 to select 4:LinReg(ax+b) (linear regression model) from the STAT CALC menu. LinReg(ax+b) is pasted to the home screen. 11. Press y [L1] ¢ y [L2] ¢. Press ~ 1 to display the VARS Y.VARS FUNCTION secondary menu, and then press 1 to select 1:Y1. L1, L2, and Y1 are pasted to the home screen as arguments to LinReg(ax+b). 12. Press Í to execute LinReg(ax+b).
The regression line appears to fit the central portion of the scatter plot well. However, a residual plot may provide more information about this fit. 14. Press … 1 to select 1:Edit. The stat list editor is displayed. Press ~ and } to move the cursor onto L3. Press y [INS]. An unnamed column is displayed in column 3; L3, L4, L5, and L6 shift right one column. The Name= prompt is displayed in the entry line, and alpha-lock is on. 15. Press y [LIST] to display the LIST NAMES menu.
18. Press y [STAT PLOT] 2 to select 2:Plot2 from the STAT PLOTS menu. The stat plot editor is displayed for plot 2. 19. Press Í to select On, which turns on plot 2. Press † Í to select " (scatter plot). Press † y [L1] to specify Xlist:L1 for plot 2. Press † [R] [E] [S] [I] [D] (alpha-lock is on) to specify Ylist:RESID for plot 2. Press † Í to select › as the mark for each data point on the scatter plot. 20. Press o to display the Y= editor.
The residual pattern indicates a curvature associated with this data set for which the linear model did not account. The residual plot emphasizes a downward curvature, so a model that curves down with the data would be more accurate. Perhaps a function such as square root would fit. Try a power regression to fit a function of the form y = a ä xb. 22. Press o to display the Y= editor. Press ‘ to clear the linear regression equation from Y1. Press } Í to turn on plot 1. Press ~ Í to turn off plot 2. 23.
The new function y=.192x.522 appears to fit the data well. To get more information, examine a residual plot. 27. Press o to display the Y= editor. Press | Í to deselect Y1. Press } Í to turn off plot 1. Press ~ Í to turn on plot 2. Note: Step 19 defined plot 2 to plot residuals (RESID) versus string length (L1). 28. Press q 9 to select 9:ZoomStat from the ZOOM menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals.
Now that you have a good model for the relationship between length and period, you can use the model to predict the period for a given string length. To predict the periods for a pendulum with string lengths of 20 cm and 50 cm, continue with these steps. 30. Press ~ 1 to display the VARS Y.VARS FUNCTION secondary menu, and then press 1 to select 1:Y1. Y1 is pasted to the home screen. 31. Press £ 20 ¤ to enter a string length of 20 cm. Press Í to calculate the predicted time of about 0.92 seconds.
Setting Up Statistical Analyses Using Lists to Store Data Data for statistical analyses is stored in lists, which you can create and edit using the stat list editor. The TI-83 has six list variables in memory, L1 through L6, to which you can store data for statistical calculations. Also, you can store data to list names that you create (Chapter 11). Setting Up a Statistical Analysis To set up a statistical analysis, follow these steps. Read the chapter for details. 1.
Using the Stat List Editor Entering a List Name in the Stat List Editor To enter a list name in the stat list editor, follow these steps. 1. Display the Name= prompt in the entry line in either of two ways. • Move the cursor onto the list name in the column where you want to insert a list, and then press y [INS]. An unnamed column is displayed and the remaining lists shift right one column. • Press } until the cursor is on the top line, and then press ~ until you reach the unnamed column.
Creating a Name in the Stat List Editor To create a name in the stat list editor, follow these steps. 1. Follow step 1 on page 12.11 to display the Name= prompt. 2. Press [letter from A to Z or q] to enter the first letter of the name. The first character cannot be a number. 3. Enter zero to four letters, q, or numbers to complete the new user-created list name. List names can be one to five characters long. 4. Press Í or † to store the list name in the current column of the stat list editor.
Editing a List Element To edit a list element, follow these steps. 1. Move the rectangular cursor onto the element you want to edit. 2. Press Í to move the cursor to the entry line. Note: If you want to replace the current value, you can enter a new value without first pressing Í. When you enter the first character, the current value is cleared automatically. 3. Edit the element in the entry line. • Press one or more keys to enter the new value.
Attaching Formulas to List Names Attaching a Formula to a List Name in Stat List Editor You can attach a formula to a list name in the stat list editor, and then display and edit the calculated list elements. When executed, the attached formula must resolve to a list. Chapter 11 describes in detail the concept of attaching formulas to list names. To attach a formula to a list name that is stored in the stat list editor, follow these steps. 1. Press … Í to display the stat list editor. 2.
Using the Stat List Editor When FormulaGenerated Lists Are Displayed When you edit an element of a list referenced in an attached formula, the TI-83 updates the corresponding element in the list to which the formula is attached (Chapter 11). When a list with a formula attached is displayed in the stat list editor and you edit or enter elements of another displayed list, then the TI-83 takes slightly longer to accept each edit or entry than when no lists with formulas attached are in view.
Detaching Formulas from List Names Detaching a Formula from a List Name You can detach (clear) a formula from a list name in any of four ways. Editing an Element of a FormulaGenerated List As described above, one way to detach a formula from a list name is to edit an element of the list to which the formula is attached. The TI-83 protects against inadvertently detaching the formula from the list name by editing an element of the formula-generated list.
Switching Stat List Editor Contexts Stat List Editor Contexts The stat list editor has four contexts. • View-elements context • View-names context • Edit-elements context • Enter-name context The stat list editor is first displayed in view-elements context. To switch through the four contexts, select 1:Edit from the STAT EDIT menu and follow these steps. 1. Press } to move the cursor onto a list name. You are now in view-names context.
Stat List Editor Contexts View-Elements Context In view-elements context, the entry line displays the list name, the current element’s place in that list, and the full value of the current element, up to 12 characters at a time. An ellipsis (...) indicates that the element continues beyond 12 characters. To page down the list six elements, press ƒ †. To page up six elements, press ƒ }. To delete a list element, press {. Remaining elements shift up one row. To insert a new element, press y [INS].
View-Names Context In view-names context, the entry line displays the list name and the list elements. To remove a list from the stat list editor, press {. Remaining lists shift to the left one column. The list is not deleted from memory. To insert a name in the current column, press y [INS]. Remaining columns shift to the right one column. Enter-Name Context In enter-name context, the Name= prompt is displayed in the entry line, and alpha-lock is on.
STAT EDIT Menu STAT EDIT Menu To display the STAT EDIT menu, press …. EDIT CALC TESTS 1: Edit... 2: SortA( 3: SortD( 4: ClrList 5: SetUpEditor Displays the stat list editor. Sorts a list in ascending order. Sorts a list in descending order. Deletes all elements of a list. Stores lists in the stat list editor. Note: Chapter 13: Inferential Statistics describes the STAT TESTS menu items. SortA(, SortD( SortA( (sort ascending) sorts list elements from low to high values.
SetUpEditor With SetUpEditor you can set up the stat list editor to display one or more listnames in the order that you specify. You can specify zero to 20 listnames. SetUpEditor [listname1,listname2,...,listname n] SetUpEditor with one to 20 listnames removes all list names from the stat list editor and then stores listnames in the stat list editor columns in the specified order, beginning in column 1.
Regression Model Features Regression Model Features STAT CALC menu items 3 through C are regression models (page 12.24). The automatic residual list and automatic regression equation features apply to all regression models. Diagnostics display mode applies to some regression models. Automatic Residual List When you execute a regression model, the automatic residual list feature computes and stores the residuals to the list name RESID. RESID becomes an item on the LIST NAMES menu (Chapter 11).
Diagnostics Display Mode When you execute some regression models, the TI-83 computes and stores diagnostics values for r (correlation coefficient) and r2 (coefficient of determination) or for R2 (coefficient of determination). r and r2 are computed and stored for these regression models. LinReg(ax+b) LinReg(a+bx) LnReg ExpReg PwrReg R2 is computed and stored for these regression models.
STAT CALC Menu STAT CALC Menu To display the STAT CALC menu, press … ~. EDIT CALC TESTS 1: 1-Var Stats 2: 2-Var Stats 3: Med-Med 4: LinReg(ax+b) 5: QuadReg 6: CubicReg 7: QuartReg 8: LinReg(a+bx) 9: LnReg 0: ExpReg A: PwrReg B: Logistic C: SinReg Calculates 1-variable statistics. Calculates 2-variable statistics. Calculates a median-median line. Fits a linear model to data. Fits a quadratic model to data. Fits a cubic model to data. Fits a quartic model to data. Fits a linear model to data.
1-Var Stats 1.Var Stats (one-variable statistics) analyzes data with one measured variable. Each element in freqlist is the frequency of occurrence for each corresponding data point in Xlistname. freqlist elements must be real numbers > 0. 1.Var Stats [Xlistname,freqlist] 2-Var Stats 2.Var Stats (two-variable statistics) analyzes paired data. Xlistname is the independent variable. Ylistname is the dependent variable.
CubicReg (ax 3+bx 2+cx+d) CubicReg (cubic regression) fits the third-degree polynomial y=ax 3+bx 2+cx+d to the data. It displays values for a, b, c, and d; when DiagnosticOn is set, it also displays a value for R2. For four points, the equation is a polynomial fit; for five or more, it is a polynomial regression. At least four points are required.
PwrReg (axb) PwrReg (power regression) fits the model equation y=axb to the data using a least-squares fit and transformed values ln(x) and ln(y). It displays values for a and b; when DiagnosticOn is set, it also displays values for r2 and r. PwrReg [Xlistname,Ylistname,freqlist,regequ] Logistic c / (1+aäeLbx) Logistic fits the model equation y=c / (1+aäeLbx) to the data using an iterative least-squares fit. It displays values for a, b, and c.
SinReg Example: Daylight Hours in Alaska for One Year Compute the regression model for the number of hours of daylight in Alaska during one year. & & 1 period With noisy data, you will achieve better convergence results when you specify an accurate estimate for period. You can obtain a period guess in either of two ways. • Plot the data and trace to determine the x-distance between the beginning and end of one complete period, or cycle.
Statistical Variables The statistical variables are calculated and stored as indicated below. To access these variables for use in expressions, press , and select 5:Statistics. Then select the VARS menu shown in the column below under VARS menu. If you edit a list or change the type of analysis, all statistical variables are cleared. Variables 1.Var Stats 2.
Statistical Analysis in a Program Entering Stat Data You can enter statistical data, calculate statistical results, and fit models to data from a program. You can enter statistical data into lists directly within the program (Chapter 11). Statistical Calculations To perform a statistical calculation from a program, follow these steps. 1. On a blank line in the program editor, select the type of calculation from the STAT CALC menu. 2. Enter the names of the lists to use in the calculation.
Statistical Plotting Steps for Plotting You can plot statistical data that is stored in lists. The six Statistical Data in types of plots available are scatter plot, xyLine, histogram, modified box plot, regular box plot, and normal probability Lists plot. You can define up to three plots. To plot statistical data in lists, follow these steps. 1. Store the stat data in one or more lists. 2. Select or deselect Y= functions as appropriate. 3. Define the stat plot. 4. Turn on the plots you want to display. 5.
Ò (Histogram) Õ (ModBoxplot) Histogram plots one-variable data. The Xscl window variable value determines the width of each bar, beginning at Xmin. ZoomStat adjusts Xmin, Xmax, Ymin, and Ymax to include all values, and also adjusts Xscl. The inequality (Xmax N Xmin) à Xscl 47 must be true. A value that occurs on the edge of a bar is counted in the bar to the right. ModBoxplot (modified box plot) plots one-variable data, like the regular box plot, except points that are 1.
Ö (Boxplot) Boxplot (regular box plot) plots one-variable data. The whiskers on the plot extend from the minimum data point in the set (minX) to the first quartile (Q1) and from the third quartile (Q3) to the maximum point (maxX). The box is defined by Q1, Med (median), and Q3 (page 12.29). Box plots are plotted with respect to Xmin and Xmax, but ignore Ymin and Ymax. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle.
Defining the Plots To define a plot, follow these steps. 1. Press y [STAT PLOT]. The STAT PLOTS menu is displayed with the current plot definitions. 2. Select the plot you want to use. The stat plot editor is displayed for the plot you selected. 3. Press Í to select On if you want to plot the statistical data immediately. The definition is stored whether you select On or Off. 4. Select the type of plot. Each type prompts for the options checked in this table.
Displaying Other Stat Plot Editors Each stat plot has a unique stat plot editor. The name of the current stat plot (Plot1, Plot2, or Plot3) is highlighted in the top line of the stat plot editor. To display the stat plot editor for a different plot, press }, ~, and | to move the cursor onto the name in the top line, and then press Í. The stat plot editor for the selected plot is displayed, and the selected name remains highlighted.
Defining the Viewing Window Stat plots are displayed on the current graph. To define the viewing window, press p and enter values for the window variables. ZoomStat redefines the viewing window to display all statistical data points. Tracing a Stat Plot When you trace a scatter plot or xyLine, tracing begins at the first element in the lists. When you trace a histogram, the cursor moves from the top center of one column to the top center of the next, starting at the first column.
Statistical Plotting in a Program Defining a Stat Plot in a Program To display a stat plot from a program, define the plot, and then display the graph. To define a stat plot from a program, begin on a blank line in the program editor and enter data into one or more lists; then, follow these steps. 1. Press y [STAT PLOT] to display the STAT PLOTS menu. 2. Select the plot to define, which pastes Plot1(, Plot2(, or Plot3( to the cursor location. 3. Press y [STAT PLOT] ~ to display the STAT TYPE menu. 4.
5. Press ¢. Enter the list names, separated by commas. 6. Press ¢ y [STAT PLOT] | to display the STAT PLOT MARK menu. (This step is not necessary if you selected 3:Histogram or 5:Boxplot in step 4.) Select the type of mark (› or + or ¦) for each data point. The selected mark symbol is pasted to the cursor location. 7. Press ¤ Í to complete the command line.
13 Contents Inferential Statistics and Distributions Getting Started: Mean Height of a Population ............ 13-2 Inferential Stat Editors................................... 13-6 STAT TESTS Menu ...................................... 13-9 Inferential Statistics Input Descriptions .................. 13-26 Test and Interval Output Variables ....................... 13-28 Distribution Functions ................................... 13-29 Distribution Shading .....................................
Getting Started: Mean Height of a Population Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to estimate the mean height of a population of women given the random sample below. Because heights among a biological population tend to be normally distributed, a t distribution confidence interval can be used when estimating the mean.
4. Press … | to display the STAT TESTS menu, and then press † until 8:TInterval is highlighted. 5. Press Í to select 8:TInterval. The inferential stat editor for TInterval is displayed. If Data is not selected for Inpt:, press | Í to select Data. Press † and [H] [G] [H] [T] at the List: prompt (alpha-lock is on). Press † † Ë 99 to enter a 99 percent confidence level at the C.Level: prompt. 6. Press † to move the cursor onto Calculate, and then press Í.
To obtain a more precise bound on the population mean m of women’s heights, increase the sample size to 90. Use a sample mean þ of 163.8 and sample standard deviation Sx of 7.1 calculated from the larger random sample (introduction; page 13.2). This time, use the Stats (summary statistics) input option. 7. Press … | 8 to display the inferential stat editor for TInterval. Press ~ Í to select Inpt:Stats. The editor changes so that you can enter summary statistics as input. 8. Press † 163 Ë 8 Í to store 163.
11. Press 3 to paste invNorm( to the home screen. Press Ë 95 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤ Í. .95 is the area, 165.1 is µ, and 6.35 is σ. The result is displayed on the home screen; it shows that five percent of the women are taller than 175.5 cm. Now graph and shade the top 5 percent of the population. 12. Press p and set the window variables to these values. Xmin=145 Xmax=185 Xscl=5 Ymin=L.02 Ymax=.08 Yscl=0 Xres=1 13. Press y [DISTR] ~ to display the DISTR DRAW menu. 14.
Inferential Stat Editors Displaying the Inferential Stat Editors When you select a hypothesis test or confidence interval instruction from the home screen, the appropriate inferential statistics editor is displayed. The editors vary according to each test or interval’s input requirements. Below is the inferential stat editor for T.Test. Note: When you select the ANOVA( instruction, it is pasted to the home screen. ANOVA( does not have an editor screen.
Select Data or Stats input Select an alternative hypothesis Enter values for arguments Selecting Data or Stats Select Calculate or Draw output Most inferential stat editors prompt you to select one of two types of input. (1.PropZInt and 2.PropZTest, 1.PropZInt and 2.PropZInt, c2.Test, and LinRegTTest do not.) • Select Data to enter the data lists as input. • Select Stats to enter summary statistics, such as þ, Sx, and n, as input.
Selecting the Pooled Option Pooled (2.SampTTest and 2.SampTInt only) specifies whether the variances are to be pooled for the calculation. • Select No if you do not want the variances pooled. Population variances can be unequal. • Select Yes if you want the variances pooled. Population variances are assumed to be equal. To select the Pooled option, move the cursor to Yes, and then press Í.
STAT TESTS Menu STAT TESTS Menu To display the STAT TESTS menu, press … |. When you select an inferential statistics instruction, the appropriate inferential stat editor is displayed. Most STAT TESTS instructions store some output variables to memory. Most of these output variables are in the TEST secondary menu (VARS menu; 5:Statistics). For a list of these variables, see page 13.28. EDIT CALC TESTS 1: Z-Test... Test for 1 m, known s 2: T-Test... Test for 1 m, unknown s 3: 2-SampZTest...
Z.Test (one-sample z test; item 1) performs a hypothesis test for a single unknown population mean m when the Z.Test population standard deviation s is known. It tests the null hypothesis H0: m=m0 against one of the alternatives below. • Ha: mƒm0 (m:ƒm0) • Ha: mm0 (m:>m0) In the example: L1={299.4 297.7 301 298.9 300.2 297} Data Stats , , , , Input: Calculated results: Drawn results: Note: All examples on pages13.10 through 13.
T.Test (one-sample t test; item 2) performs a hypothesis test for a single unknown population mean m when the T.Test population standard deviation s is unknown. It tests the null hypothesis H0: m=m0 against one of the alternatives below. • Ha: mƒm0 (m:ƒm0) • Ha: mm0 (m:>m0) In the example: TEST={91.9 97.8 111.4 122.3 105.4 95} Data Stats , , , , Input: Calculated results: Drawn results: Inferential Statistics and Distributions 13-11 8313INFE.
2.SampZTest 2.SampZTest (two-sample z test; item 3) tests the equality of the means of two populations (m1 and m2) based on independent samples when both population standard deviations (s1 and s2) are known. The null hypothesis H0: m1=m2 is tested against one of the alternatives below.
2.SampTTest 2.SampTTest (two-sample t test; item 4) tests the equality of the means of two populations (m1 and m2) based on independent samples when neither population standard deviation (s1 or s2) is known. The null hypothesis H0: m1=m2 is tested against one of the alternatives below. • Ha: m1ƒm2 (m1:ƒm2) • Ha: m1m2 (m1:>m2) In the example: SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.
) 1.PropZTest (one-proportion z test; item 5) computes a test for an unknown proportion of successes (prop). It takes as input the count of successes in the sample x and the count of observations in the sample n. 1.PropZTest tests the null hypothesis H0: prop=p0 against one of the alternatives below. 1-PropZTest • Ha: propƒp 0 (prop:ƒp0) • Ha: propp 0 (prop:>p0) Input: , Calculated results: , Drawn results: 13-14 Inferential Statistics and Distributions 8313INFE.
2.PropZTest (two-proportion z test; item 6) computes a test to compare the proportion of successes (p1 and p2) from two populations. It takes as input the count of successes in each sample (x1 and x2) and the count of observations in each sample (n1 and n2). 2.PropZTest tests the null hypothesis H0: p1=p2 (using the pooled sample proportion Ç) against one of the alternatives below.
ZInterval (one-sample z confidence interval; item 7) computes a confidence interval for an unknown population mean m when the population standard deviation s is known. The computed confidence interval depends on the user-specified confidence level. ZInterval In the example: L1={299.4 297.7 301 298.9 300.2 297} Data Stats , , Input: Calculated results: 13-16 Inferential Statistics and Distributions 8313INFE.
TInterval (one-sample t confidence interval; item 8) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. The computed confidence interval depends on the user-specified confidence level. TInterval In the example: L6={1.6 1.7 1.8 1.9} Data Stats , , Input: Calculated results: Inferential Statistics and Distributions 13-17 8313INFE.
2.SampZInt (two-sample z confidence interval; item 9) 2-SampZInt computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations ( s1 and s2) are known. The computed confidence interval depends on the user-specified confidence level. In the example: LISTC={154 109 137 115 140} LISTD={108 115 126 92 146} Data Stats , , Input: Calculated results: 13-18 Inferential Statistics and Distributions 8313INFE.
2.SampTInt (two-sample t confidence interval; item 0) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are unknown. The computed confidence interval depends on the userspecified confidence level. 2-SampTInt In the example: SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.
) 1.PropZInt (one-proportion z confidence interval; item A) computes a confidence interval for an unknown proportion of successes. It takes as input the count of successes in the sample x and the count of observations in the sample n. The computed confidence interval depends on the userspecified confidence level. 1-PropZInt Input: , Calculated results: 13-20 Inferential Statistics and Distributions 8313INFE.
2.PropZInt (two-proportion z confidence interval; item B) computes a confidence interval for the difference between the proportion of successes in two populations (p1Np2). It takes as input the count of successes in each sample (x 1 and x 2) and the count of observations in each sample (n1 and n2). The computed confidence interval depends on the user-specified confidence level. 2-PropZInt Input: , Calculated results: Inferential Statistics and Distributions 13-21 8313INFE.
c2.Test (chi-square test; item C) computes a chi-square test c2-Test for association on the two-way table of counts in the specified Observed matrix. The null hypothesis H 0 for a two-way table is: no association exists between row variables and column variables. The alternative hypothesis is: the variables are related. Before computing a c2.Test, enter the observed counts in a matrix. Enter that matrix variable name at the Observed: prompt in the c2.Test editor; default=[A].
2-SampÜTest 2.SampÜTest (two-sample Û-test; item D) computes an Û-test to compare two normal population standard deviations (s1 and s2). The population means and standard deviations are all unknown. 2.SampÜTest, which uses the ratio of sample variances Sx12/Sx22, tests the null hypothesis H0: s1=s2 against one of the alternatives below.
LinRegTTest (linear regression t test; item E) computes a LinRegTTest linear regression on the given data and a t test on the value of slope b and the correlation coefficient r for the equation y=a+bx. It tests the null hypothesis H0: b=0 (equivalently, r =0) against one of the alternatives below. • Ha: bƒ0 and rƒ0 (b & r:ƒ0) • Ha: b<0 and r<0 (b & r:<0) • Ha: b>0 and r>0 (b & r:>0) The regression equation is automatically stored to RegEQ (VARS Statistics EQ secondary menu).
ANOVA( (one-way analysis of variance; item F) computes a one-way analysis of variance for comparing the means of two to 20 populations. The ANOVA procedure for comparing these means involves analysis of the variation in the sample data. The null hypothesis H0: m1=m2=...=m k is tested against the alternative Ha: not all m1...mk are equal. ANOVA( ANOVA(list1,list2[,...
Inferential Statistics Input Descriptions The tables in this section describe the inferential statistics inputs discussed in this chapter. You enter values for these inputs in the inferential stat editors. The tables present the inputs in the same order that they appear in this chapter. Input Description m0 Hypothesized value of the population mean that you are testing. s The known population standard deviation; must be a real number > 0. List The name of the list containing the data you are testing.
Input Description p0 The expected sample proportion for 1.PropZTest. Must be a real number, such that 0 < p0 < 1. x The count of successes in the sample for the 1.PropZTest and 1.PropZInt. Must be an integer ‚ 0. n The count of observations in the sample for the 1.PropZTest and 1.PropZInt. Must be an integer > 0. x1 The count of successes from sample one for the 2.PropZTest and 2.PropZInt. Must be an integer ‚ 0. x2 The count of successes from sample two for the 2.PropZTest and 2.PropZInt.
Test and Interval Output Variables The inferential statistics variables are calculated as indicated below. To access these variables for use in expressions, press , 5 (5:Statistics), and then select the VARS menu listed in the last column below.
Distribution Functions DISTR menu To display the DISTR menu, press y [DISTR].
normalcdf( normalcdf( computes the normal distribution probability between lowerbound and upperbound for the specified mean m and standard deviation s. The defaults are m=0 and s=1. normalcdf(lowerbound,upperbound[,m,s]) invNorm( invNorm( computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by mean m and standard deviation s. It calculates the x value associated with an area to the left of the x value. 0 area 1 must be true.
tcdf( tcdf( computes the Student-t distribution probability between lowerbound and upperbound for the specified df (degrees of freedom), which must be > 0. tcdf(lowerbound,upperbound,df) c2pdf( c2pdf( computes the probability density function (pdf) for the c2 (chi-square) distribution at a specified x value. df (degrees of freedom) must be an integer > 0. To plot the c2 distribution, paste c2pdf( to the Y= editor.
Üpdf( Üpdf( computes the probability density function (pdf) for the Û distribution at a specified x value. numerator df (degrees of freedom) and denominator df must be integers > 0. To plot the Û distribution, paste Üpdf( to the Y= editor.
binompdf( binompdf( computes a probability at x for the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial. x can be an integer or a list of integers. 0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a list of probabilities from 0 to numtrials is returned.
poissoncdf( poissoncdf( computes a cumulative probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be a real number or a list of real numbers. poissoncdf(m,x ) geometpdf( geometpdf( computes a probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. 0p1 must be true. x can be an integer or a list of integers.
Distribution Shading DISTR DRAW Menu To display the DISTR DRAW menu, press y [DISTR] ~. DISTR DRAW instructions draw various types of density functions, shade the area specified by lowerbound and upperbound, and display the computed area value. To clear the drawings, select 1:ClrDraw from the DRAW menu (Chapter 8). Note: Before you execute a DISTR DRAW instruction, you must set the window variables so that the desired distribution fits the screen.
Shade_t( Shade_t( draws the density function for the Student-t distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound. Shade_t(lowerbound,upperbound,df) Note: For this example, Xmin = L3 Xmax = 3 Ymin = L.15 Ymax = .5 Shadec2( Shadec2( draws the density function for the c2 (chi-square) distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound.
14 Contents Financial Functions Getting Started: Financing a Car ......................... 14-2 Getting Started: Computing Compound Interest.......... 14-3 Using the TVM Solver .................................... 14-4 Using the Financial Functions ........................... 14-5 Calculating Time Value of Money (TVM) ................. 14-6 Calculating Cash Flows .................................. 14-8 Calculating Amortization ................................ 14-9 Calculating Interest Conversion..........
Getting Started: Financing a Car Getting Started is a fast-paced introduction. Read the chapter for details. You have found a car you would like to buy. The car costs 9,000. You can afford payments of 250 per month for four years. What annual percentage rate (APR) will make it possible for you to afford the car? 1. Press z † ~ ~ ~ Í to set the fixed-decimal mode setting to 2. The TI-83 will display all numbers with two decimal places. 2. Press y [FINANCE] to display the FINANCE CALC menu. 3.
Getting Started: Computing Compound Interest At what annual interest rate, compounded monthly, will 1,250 accumulate to 2,000 in 7 years? Note: Because there are no payments when you solve compound interest problems, PMT must be set to 0 and P/Y must be set to 1. 1. Press y [FINANCE] to display the FINANCE CALC menu. 2. Press Í to select 1:TVM Solver. Press 7 to enter the number of periods in years. Press † † Ì 1250 to enter the present value as a cash outflow (investment).
Using the TVM Solver Using the TVM Solver The TVM Solver displays the time-value-of-money (TVM) variables. Given four variable values, the TVM Solver solves for the fifth variable. The FINANCE VARS menu section (page 14.14) describes the five TVM variables (Ú, æ, PV, PMT, and FV) and P/Y and C/Y. PMT: END BEGIN in the TVM Solver corresponds to the FINANCE CALC menu items Pmt_End (payment at the end of each period) and Pmt_Bgn (payment at the beginning of each period).
Using the Financial Functions Entering Cash Inflows and Cash Outflows When using the TI-83 financial functions, you must enter cash inflows (cash received) as positive numbers and cash outflows (cash paid) as negative numbers. The TI-83 follows this convention when computing and displaying answers. FINANCE CALC Menu To display the FINANCE CALC menu, press y [FINANCE]. CALC VARS 1: TVM Solver...
Calculating Time Value of Money (TVM) Calculating Time Value of Money Use time-value-of-money (TVM) functions (menu items 2 through 6) to analyze financial instruments such as annuities, loans, mortgages, leases, and savings. Each TVM function takes zero to six arguments, which must be real numbers. The values that you specify as arguments for these functions are not stored to the TVM variables (page 14.14). Note: To store a value to a TVM variable, use the TVM Solver (page 14.
tvm_æ tvm_æ computes the annual interest rate. tvm_æ[(Ú,PV,PMT,FV,P/Y,C/Y)] tvm_PV tvm_PV computes the present value. tvm_PV[(Ú,æ,PMT,FV,P/Y,C/Y)] tvm_Ú tvm_Ú computes the number of payment periods. tvm_Ú[(æ,PV,PMT,FV,P/Y,C/Y)] tvm_FV tvm_FV computes the future value. tvm_FV[(Ú,æ,PV,PMT,P/Y,C/Y)] Financial Functions 14-7 8314FINA.
Calculating Cash Flows Calculating a Cash Flow Use the cash flow functions (menu items 7 and 8) to analyze the value of money over equal time periods. You can enter unequal cash flows, which can be cash inflows or outflows. The syntax descriptions for npv( and irr( use these arguments. • interest rate is the rate by which to discount the cash flows (the cost of money) over one period. • CF0 is the initial cash flow at time 0; it must be a real number.
Calculating Amortization Calculating an Amortization Schedule Use the amortization functions (menu items 9, 0, and A) to calculate balance, sum of principal, and sum of interest for an amortization schedule. bal( bal( computes the balance for an amortization schedule using stored values for æ, PV, and PMT. npmt is the number of the payment at which you want to calculate a balance. It must be a positive integer < 10,000.
Amortization Example: Calculating an Outstanding Loan Balance You want to buy a home with a 30-year mortgage at 8 percent APR. Monthly payments are 800. Calculate the outstanding loan balance after each payment and display the results in a graph and in the table. 1. Press z. Press † ~ ~ ~ Í to set the fixed-decimal mode setting to 2. Press † † ~ Í to select Par graphing mode. 2. Press y [FINANCE] Í to display the TVM Solver. 3. Press 360 to enter number of payments. Press † 8 to enter the interest rate.
6. Press p to display the window variables. Enter the values below. Tmin=0 Tmax=360 Tstep=12 Xmin=0 Xmax=360 Xscl=50 Ymin=0 Ymax=125000 Yscl=10000 7. Press r to draw the graph and activate the trace cursor. Press ~ and | to explore the graph of the outstanding balance over time. Press a number and then press Í to view the balance at a specific time T. 8. Press y [TBLSET] and enter the values below. TblStart=0 @Tbl=12 9. Press y [TABLE] to display the table of outstanding balances (Y1T). 10.
Calculating Interest Conversion Calculating an Interest Conversion Use the interest conversion functions (menu items B and C) to convert interest rates from an annual effective rate to a nominal rate (4Nom( ) or from a nominal rate to an annual effective rate (4Eff( ). 4Nom( 4Nom( computes the nominal interest rate. effective rate and compounding periods must be real numbers. compounding periods must be >0. 4Nom(effective rate,compounding periods) 4Eff( 4Eff( computes the effective interest rate.
Finding Days between Dates/Defining Payment Method dbd( Use the date function dbd( (menu item D) to calculate the number of days between two dates using the actual-daycount method. date1 and date2 can be numbers or lists of numbers within the range of the dates on the standard calendar. Note: Dates must be between the years 1950 through 2049. dbd(date1,date2) You can enter date1 and date2 in either of two formats. • MM.DDYY (United States) • DDMM.
Using the TVM Variables FINANCE VARS Menu To display the FINANCE VARS menu, press y [FINANCE] ~. You can use TVM variables in TVM functions and store values to them on the home screen. CALC VARS 1: Ú 2: æ 3: PV 4: PMT 5: FV 6: P/Y 7: C/Y Total number of payment periods Annual interest rate Present value Payment amount Future value Number of payment periods per year Number of compounding periods/year Ú, æ, PV, PMT, FV Ú, æ, PV, PMT, and FV are the five TVM variables.
15 Contents CATALOG, Strings, Hyperbolic Functions Browsing the TI-83 CATALOG ........................... 15-2 Entering and Using Strings ............................... 15-3 Storing Strings to String Variables ....................... 15-4 String Functions and Instructions in the CATALOG ...... 15-6 Hyperbolic Functions in the CATALOG .................. 15-10 CATALOG, Strings, Hyperbolic Functions 15-1 8315CATS.
Browsing the TI-83 CATALOG What Is the CATALOG? The CATALOG is an alphabetical list of all functions and instructions on the TI-83. You also can access each CATALOG item from a menu or the keyboard, except: • The six string functions (page 15.6) • The six hyperbolic functions (page 15.
Entering and Using Strings What Is a String? A string is a sequence of characters that you enclose within quotation marks. On the TI-83, a string has two primary applications. • It defines text to be displayed in a program. • It accepts input from the keyboard in a program. Characters are the units that you combine to form a string. • Count each number, letter, and space as one character.
Storing Strings to String Variables String Variables The TI-83 has 10 variables to which you can store strings. You can use string variables with string functions and instructions. To display the VARS STRING menu, follow these steps. 1. Press to display the VARS menu. Move the cursor to 7:String. 2. Press Í to display the STRING secondary menu. 15-4 CATALOG, Strings, Hyperbolic Functions 8315CATS.
Storing a String to a String Variable To store a string to a string variable, follow these steps. 1. Press ƒ [ã], enter the string, and press ƒ [ã]. 2. Press ¿. 3. Press 7 to display the VARS STRING menu. 4. Select the string variable (from Str1 to Str9, or Str0) to which you want to store the string. The string variable is pasted to the current cursor location, next to the store symbol (!). 5. Press Í to store the string to the string variable.
String Functions and Instructions in the CATALOG Displaying String Functions and Instructions in the CATALOG String functions and instructions are available only from the CATALOG. The table below lists the string functions and instructions in the order in which they appear among the other CATALOG menu items. The ellipses in the table indicate the presence of additional CATALOG items. CATALOG ... Equ4String( expr( ... inString( ... length( ... String4Equ( sub( ...
Equ4String( Equ4String( converts to a string an equation that is stored to any VARS Y.VARS variable. Yn contains the equation. Strn (from Str1 to Str9, or Str0) is the string variable to which you want the equation to be stored as a string. Equ4String(Yn,Strn) expr( expr( converts the character string contained in string to an expression and executes it. string can be a string or a string variable.
length( length( returns the number of characters in string. string can be a string or string variable. Note: An instruction or function name, such as sin( or cos(, counts as one character. length(string) String4Equ( String4Equ( converts string into an equation and stores the equation to Yn. string can be a string or string variable. String4Equ( is the inverse of Equ4String(. String4Equ(string,Yn) 15-8 CATALOG, Strings, Hyperbolic Functions 8315CATS.
sub( sub( returns a string that is a subset of an existing string. string can be a string or a string variable. begin is the position number of the first character of the subset. length is the number of characters in the subset. sub(string,begin,length) Entering a Function to Graph during Program Execution In a program, you can enter a function to graph during program execution using these commands. Note: When you execute this program, enter a function to store to Y3 at the ENTRY= prompt.
Hyperbolic Functions in the CATALOG Hyperbolic Functions The hyperbolic functions are available only from the CATALOG. The table below lists the hyperbolic functions in the order in which they appear among the other CATALOG menu items. The ellipses in the table indicate the presence of additional CATALOG items. CATALOG ... cosh( cosh L1( ... sinh( sinh L1( ... tanh( tanh L1( ...
16 Contents Programming Getting Started: Volume of a Cylinder .................... 16-2 Creating and Deleting Programs ......................... 16-4 Entering Command Lines and Executing Programs ...... 16-5 Editing Programs ........................................ 16-6 Copying and Renaming Programs ........................ 16-7 PRGM CTL (Control) Instructions ....................... 16-8 PRGM I/O (Input/Output) Instructions ................... 16-16 Calling Other Programs as Subroutines .................
Getting Started: Volume of a Cylinder Getting Started is a fast-paced introduction. Read the chapter for details. A program is a set of commands that the TI-83 executes sequentially, as if you had entered them from the keyboard. Create a program that prompts for the radius R and the height H of a cylinder and then computes its volume. 1. Press ~ ~ to display the PRGM NEW menu. 2. Press Í to select 1:Create New. The Name= prompt is displayed, and alpha-lock is on.
5. Press ~ 3 to select 3:Disp from the PRGM I/O menu. Disp is pasted to the command line. Press y [A.LOCK] ããä [V] [O] [L] [U] [M] [E]['] [I] [S] ããä ƒ ¢ ƒ [V] Í to set up the program to display the text VOLUME IS on one line and the calculated value of V on the next. 6. Press y [QUIT] to display the home screen. 7. Press to display the PRGM EXEC menu. The items on this menu are the names of stored programs. 8. Press Í to paste prgmCYLINDER to the current cursor location.
Creating and Deleting Programs What Is a Program? A program is a set of one or more command lines. Each line contains one or more instructions. When you execute a program, the TI-83 performs each instruction on each command line in the same order in which you entered them. The number and size of programs that the TI-83 can store is limited only by available memory. Creating a New Program To create a new program, follow these steps. 1. Press | to display the PRGM NEW menu. 2.
Entering Command Lines and Executing Programs Entering a Program Command Line You can enter on a command line any instruction or expression that you could execute from the home screen. In the program editor, each new command line begins with a colon. To enter more than one instruction or expression on a single command line, separate each with a colon. Note: A command line can be longer than the screen is wide; long command lines wrap to the next screen line.
Editing Programs Editing a Program To edit a stored program, follow these steps. 1. Press ~ to display the PRGM EDIT menu. 2. Select a program name from the PRGM EDIT menu (page 16.7). Up to the first seven lines of the program are displayed. Note: The program editor does not display a $ to indicate that a program continues beyond the screen. 3. Edit the program command lines. • Move the cursor to the appropriate location, and then delete, overwrite, or insert.
Copying and Renaming Programs Copying and Renaming a Program To copy all command lines from one program into a new program, follow steps 1 through 5 for Creating a New Program (page 16.4), and then follow these steps. 1. Press y [RCL]. Rcl is displayed on the bottom line of the program editor in the new program (Chapter 1). 2. Press | to display the PRGM EXEC menu. 3. Select a name from the menu. prgmname is pasted to the bottom line of the program editor. 4. Press Í.
PRGM CTL (Control) Instructions PRGM CTL Menu To display the PRGM CTL (program control) menu, press from the program editor only. CTL I/O EXEC 1: If 2: Then 3: Else 4: For( 5: While 6: Repeat 7: End 8: Pause 9: Lbl 0: Goto A: IS>( B: DS<( C: Menu( D: prgm E: Return F: Stop G: DelVar H: GraphStyle( Creates a conditional test. Executes commands when If is true. Executes commands when If is false. Creates an incrementing loop. Creates a conditional loop. Creates a conditional loop.
If Use If for testing and branching. If condition is false (zero), then the command immediately following If is skipped. If condition is true (nonzero), then the next command is executed. If instructions can be nested. :If condition :command (if true) :command Program If.Then Output Then following an If executes a group of commands if condition is true (nonzero). End identifies the end of the group of commands.
If-Then-Else Else following If.Then executes a group of commands if condition is false (zero). End identifies the end of the group of commands. :If condition :Then :command (if true) :command (if true) :Else :command (if false) :command (if false) :End :command Program For( Output For( loops and increments. It increments variable from begin to end by increment. increment is optional (default is 1) and can be negative (end
While While performs a group of commands while condition is true. condition is frequently a relational test (Chapter 2). condition is tested when While is encountered. If condition is true (nonzero), the program executes a group of commands. End signifies the end of the group. When condition is false (zero), the program executes each command following End. While instructions can be nested.
End End identifies the end of a group of commands. You must include an End instruction at the end of each For(, While, or Repeat loop. Also, you must paste an End instruction at the end of each If.Then group and each If.Then.Else group. Pause Pause suspends execution of the program so that you can see answers or graphs. During the pause, the pause indicator is on in the top-right corner. Press Í to resume execution. • Pause without a value temporarily pauses the program.
Lbl, Goto Lbl (label) and Goto (go to) are used together for branching. Lbl specifies the label for a command. label can be one or two characters (A through Z, 0 through 99, or q). Lbl label Goto causes the program to branch to label when Goto is encountered. Goto label Program IS>( Output IS>( (increment and skip) adds 1 to variable. If the answer is > value (which can be an expression), the next command is skipped; if the answer is { value, the next command is executed.
DS<( DS<( (decrement and skip) subtracts 1 from variable. If the answer is < value (which can be an expression), the next command is skipped; if the answer is | value, the next command is executed. variable cannot be a system variable. :DS<(variable,value) :command (if answer ‚ value) :command (if answer < value) Program Output Note: DS<( is not a looping instruction. Menu( Menu( sets up branching within a program.
prgm Use prgm to execute other programs as subroutines (page 16.22). When you select prgm, it is pasted to the cursor location. Enter characters to spell a program name. Using prgm is equivalent to selecting existing programs from the PRGM EXEC menu; however, it allows you to enter the name of a program that you have not yet created. prgmname Note: You cannot directly enter the subroutine name when using RCL. You must paste the name from the PRGM EXEC menu (page 16.7).
PRGM I/O (Input/Output) Instructions PRGM I/O Menu To display the PRGM I/O (program input/output) menu, press ~ from within the program editor only. CTL I/O EXEC 1: Input 2: Prompt 3: Disp 4: DispGraph 5: DispTable 6: Output( 7: getKey 8: ClrHome 9: ClrTable 0: GetCalc( A: Get( B: Send( Enters a value or uses the cursor. Prompts for entry of variable values. Displays text, value, or the home screen. Displays the current graph. Displays the current table. Displays text at a specified position.
Storing a Variable Value with Input Input with variable displays a ? (question mark) prompt during execution. variable may be a real number, complex number, list, matrix, string, or Y= function. During program execution, enter a value, which can be an expression, and then press Í. The value is evaluated and stored to variable, and the program resumes execution. Input [variable] You can display text or the contents of Strn (a string variable) of up to 16 characters as a prompt.
Prompt During program execution, Prompt displays each variable, one at a time, followed by =?. At each prompt, enter a value or expression for each variable, and then press Í. The values are stored, and the program resumes execution. Prompt variableA[,variableB,...,variable n] Program Output Note: Y= functions are not valid with Prompt. Displaying the Home Screen Disp (display) without a value displays the home screen.
DispGraph DispGraph (display graph) displays the current graph. If Pause is encountered after DispGraph, the program halts temporarily so you can examine the screen. Press Í to resume execution. DispTable DispTable (display table) displays the current table. The program halts temporarily so you can examine the screen. Press Í to resume execution.
getKey getKey returns a number corresponding to the last key pressed, according to the key code diagram below. If no key has been pressed, getKey returns 0. Use getKey inside loops to transfer control, for example, when creating video games. Program Output Note: , , , and Í were pressed during program execution. Note: You can press É at any time during execution to break the program (page 16.5).
GetCalc( GetCalc( gets the contents of variable on another TI-83 and stores it to variable on the receiving TI-83. variable can be a real or complex number, list element, list name, matrix element, matrix name, string, Y= variable, graph database, or picture. GetCalc(variable) Note: GetCalc( does not work between TI.82s and TI-83s. Get(, Send( Get( gets data from the Calculator-Based Laboratoryé (CBL 2é, CBLé) System or Calculator-Based Rangeré (CBRé) and stores it to variable on the receiving TI-83.
Calling Other Programs as Subroutines Calling a Program from Another Program On the TI-83, any stored program can be called from another program as a subroutine. Enter the name of the program to use as a subroutine on a line by itself. You can enter a program name on a command line in either of two ways. • Press | to display the PRGM EXEC menu and select the name of the program (page 16.7). prgmname is pasted to the current cursor location on a command line.
17 Contents Applications Comparing Test Results Using Box Plots ................ 17-2 Graphing Piecewise Functions ........................... 17-4 Graphing Inequalities .................................... 17-5 Solving a System of Nonlinear Equations ................ 17-6 Using a Program to Create the Sierpinski Triangle ....... 17-7 Graphing Cobweb Attractors ............................ 17-8 Using a Program to Guess the Coefficients ...............
Comparing Test Results Using Box Plots Problem An experiment found a significant difference between boys and girls pertaining to their ability to identify objects held in their left hands, which are controlled by the right side of their brains, versus their right hands, which are controlled by the left side of their brains. The TI Graphics team conducted a similar test for adult men and women. The test involved 30 small objects, which participants were not allowed to see.
6. Press o. Turn off all functions. 7. Press p. Set Xscl=1 and Yscl=0. Press q 9 to select 9:ZoomStat. This adjusts the viewing window and displays the box plots for the women’s results. 8. Press r. % Women’s left-hand data % Women’s right-hand data Use | and ~ to examine minX, Q1, Med, Q3, and maxX for each plot. Notice the outlier to the women’s righthand data. What is the median for the left hand? For the right hand? With which hand were the women more accurate guessers, according to the box plots? 9.
Graphing Piecewise Functions Problem The fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50; plus 5 for each kph from 46 to 55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for each kph from 66 kph and above. Graph the piecewise function that describes the cost of the ticket.
Graphing Inequalities Problem Graph the inequality 0.4X 3 N 3X + 5 < 0.2X + 4. Use the TEST menu operations to explore the values of X where the inequality is true and where it is false. Procedure 1. Press z. Select Dot, Simul, and the default settings. Setting Dot mode changes all graph style icons to í (dot) in the Y= editor. 2. Press o. Turn off all functions and stat plots. Enter the left side of the inequality as Y4 and the right side as Y5. 3. Enter the statement of the inequality as Y6.
Solving a System of Nonlinear Equations Problem Using a graph, solve the equation X3 N 2X = 2cos(X). Stated another way, solve the system of two equations and two unknowns: Y = X 3N2X and Y = 2cos(X). Use ZOOM factors to control the decimal places displayed on the graph. Procedure 1. Press z. Select the default mode settings. Press o. Turn off all functions and stat plots. Enter the functions. 2. Press q 4 to select 4:ZDecimal.
Using a Program to Create the Sierpinski Triangle Setting up the Program This program creates a drawing of a famous fractal, the Sierpinski Triangle, and stores the drawing to a picture. To begin, press ~ ~ 1. Name the program SIERPINS, and then press Í. The program editor is displayed. Program PROGRAM:SIERPINS :FnOff :ClrDraw :PlotsOff :AxesOff :0!Xmin:1!Xmax :0!Ymin:1!Ymax :rand!X:rand!Y :For(K,1,3000) :rand!N :If N1 à 3 :Then :.5X!X :.5Y!Y :End :If 1 à 3
Graphing Cobweb Attractors Problem Using Web format, you can identify points with attracting and repelling behavior in sequence graphing. Procedure 1. Press z. Select Seq and the default mode settings. Press y [FORMAT]. Select Web format and the default format settings. 2. Press o. Clear all functions and turn off all stat plots. Enter the sequence that corresponds to the expression Y = K X(1NX). u(n)=Ku(nN1)(1Nu(nN1)) u(nMin)=.01 3. Press y [QUIT] to return to the home screen, and then store 2.9 to K.
Using a Program to Guess the Coefficients Setting Up the Program This program graphs the function A sin(BX) with random integer coefficients between 1 and 10. Try to guess the coefficients and graph your guess as C sin(DX). The program continues until your guess is correct.
Graphing the Unit Circle and Trigonometric Curves Problem Using parametric graphing mode, graph the unit circle and the sine curve to show the relationship between them. Any function that can be plotted in Func mode can be plotted in Par mode by defining the X component as T and the Y component as F(T). Procedure 1. Press z. Select Par, Simul, and the default settings. 2. Press p. Set the viewing window. Tmin=0 Tmax=2p Tstep=.1 Xmin=L2 Xmax=7.4 Xscl=pà2 Ymin=L3 Ymax=3 Yscl=1 3. Press o.
Finding the Area between Curves Problem Find the area of the region bounded by f(x) g(x) x Procedure = 300x / ( x2 + 625) = 3cos(.1x) = 75 1. Press z. Select the default mode settings. 2. Press p. Set the viewing window. Xmin=0 Xmax=100 Xscl=10 Ymin=L5 Ymax=10 Yscl=1 Xres=1 3. Press o. Turn off all functions and stat plots. Enter the upper and lower functions. Y1=300Xà(X2+625) Y2=3cos(.1X) 4. Press y [CALC] 5 to select 5:Intersect. The graph is displayed.
Using Parametric Equations: Ferris Wheel Problem Problem Using two pairs of parametric equations, determine when two objects in motion are closest to each other in the same plane. A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate (s) of one revolution every 12 seconds.
4. Press s to graph the equations. Watch closely as they are plotted. Notice that the ball and the ferris wheel passenger appear to be closest where the paths cross in the top-right quadrant of the ferris wheel. 5. Press p. Change the viewing window to concentrate on this portion of the graph. Tmin=1 Tmax=3 Tstep=.03 Xmin=0 Xmax=23.5 Xscl=10 Ymin=10 Ymax=25.5 Yscl=10 6. Press r. After the graph is plotted, press ~ to move near the point on the ferris wheel where the paths cross.
Demonstrating the Fundamental Theorem of Calculus Problem 1 Using the functions fnInt( and nDeriv( from the MATH menu to graph functions defined by integrals and derivatives demonstrates graphically that: x F(x) = ‰1 1àt dt = ln(x), x > 0 and that x [‰1 Dx Procedure 1 ] 1àt dt = 1àx 1. Press z. Select the default settings. 2. Press p. Set the viewing window. Xmin=.01 Xmax=10 Xscl=1 Ymin=M1.5 Ymax=2.5 Yscl=1 Xres=3 3. Press o. Turn off all functions and stat plots.
Problem 2 Explore the functions defined by x y= Procedure 2 ‰2 M t2 dt, x ‰0 t 2 dt, x and ‰2 t2 dt 1. Press o. Turn off all functions and stat plots. Use a list to define these three functions simultaneously. Store the function in Y5. 2. Press q 6 to select 6:ZStandard. 3. Press r. Notice that the functions appear identical, only shifted vertically by a constant. 4. Press o. Enter the numerical derivative of Y5 in Y6. 5. Press r.
Computing Areas of Regular N-Sided Polygons Problem Use the equation solver to store a formula for the area of a regular N-sided polygon, and then solve for each variable, given the other variables. Explore the fact that the limiting case is the area of a circle, pr2. Consider the formula A = NB 2 sin(pàN) cos(pàN) for the area of a regular polygon with N sides of equal length and B distance from the center to a vertex. N = 4 sides Procedure N = 8 sides N = 12 sides 1.
Find the area given B=6, and N=10, 100, 150, 1000, and 10000. Compare your results with p62 (the area of a circle with radius 6), which is approximately 113.097. 7. Enter B=6. To find the area A, move the cursor onto A, and then press ƒ [SOLVE]. Find A for N=10, then N=100, then N=150, then N=1000, and finally N=10000. Notice that as N gets large, the area A approaches pB2. Now graph the equation to see visually how the area changes as the number of sides gets large. 8. Press z.
Computing and Graphing Mortgage Payments Problem You are a loan officer at a mortgage company, and you recently closed on a 30-year home mortgage at 8 percent interest with monthly payments of 800. The new home owners want to know how much will be applied to the interest and how much will be applied to the principal when they make the 240th payment 20 years from now. Procedure 1. Press z and set the fixed-decimal mode to 2 decimal places. Set the other mode settings to the defaults. 2.
Now compare the graph of the amount of interest with the graph of the amount of principal for each payment. 4. Press z. Set Par and Simul. 5. Press o. Turn off all functions and stat plots. Enter these equations and set the graph styles as shown. Note: GPrn( and GInt( are located on the FINANCE CALC menu. 6. Press p. Set these window variables. Tmin=1 Tmax=360 Tstep=12 Xmin=0 Xmax=360 Xscl=10 Ymin=0 Ymax=1000 Yscl=100 Tip: To increase the graph speed, change Tstep to 24. 7. Press r.
8. Press † to move the cursor onto the function for interest defined by X2T and Y2T. Enter 240. The graph shows that for the 240th payment (X=240), 441.97 of the 800 payment is interest (Y=441.97). 9. Press y [QUIT] y [FINANCE] 9 to paste 9:bal( to the home screen. Check the figures from the graph. At which monthly payment will the principal allocation surpass the interest allocation? 17-20 Applications 8317APPS.
18 Contents Memory Management Checking Available Memory ............................. Deleting Items from Memory ............................ Clearing Entries and List Elements ...................... Resetting the TI-83 ...................................... 18-2 18-3 18-4 18-5 Memory Management 18-1 8318MEMR.
Checking Available Memory MEMORY Menu To display the MEMORY menu, press y [MEM]. MEMORY 1: Check RAM... 2: Delete... 3: Clear Entries 4: ClrAllLists 5: Reset... Displaying the Check RAM Screen Reports memory availability/usage. Displays DELETE FROM menu. Clears ENTRY (last-entry storage). Clears all lists in memory. Displays RESET menu (all/defaults). Check RAM displays the Check RAM screen. The top line reports the total amount of available memory.
Deleting Items from Memory Deleting an Item To increase available memory by deleting the contents of any variable (real or complex number, list, matrix, Y= variable, program, picture, graph database, or string), follow these steps. 1. Press y [MEM] to display the MEMORY menu. 2. Select 2:Delete to display the DELETE FROM secondary menu. 3. Select the type of data you want to delete, or select 1:All for a list of all variables of all types.
Clearing Entries and List Elements Clear Entries Clear Entries clears the contents of the ENTRY (last entry) storage area (Chapter 1). To clear the ENTRY storage area, follow these steps. 1. Press y [MEM] to display the MEMORY menu. 2. Select 3:Clear Entries to paste the instruction to the home screen. 3. Press Í to clear the ENTRY storage area. To cancel Clear Entries, press ‘.
Resetting the TI-83 RESET Secondary Menu The RESET secondary menu gives you the option of resetting all memory (including default settings) or resetting the default settings while preserving other data stored in memory, such as programs and Y= functions. Resetting All Memory Resetting all memory on the TI-83 restores memory to the factory settings. It deletes all nonsystem variables and all programs. It resets all system variables to the default settings.
Resetting Defaults When you reset defaults on the TI-83, all defaults are restored to the factory settings. Stored data and programs are not changed. These are some examples of TI-83 defaults that are restored by resetting the defaults.
19 Contents Communication Link Getting Started: Sending Variables ....................... 19-2 TI-83 LINK ............................................... 19-3 Selecting Items to Send .................................. 19-4 Receiving Items .......................................... 19-5 Transmitting Items....................................... 19-6 Transmitting Lists to a TI-82 ............................. 19-8 Transmitting from a TI-82 to a TI-83 ..................... 19-9 Backing Up Memory .............
Getting Started: Sending Variables Getting Started is a fast-paced introduction. Read the chapter for details. Create and store a variable and a matrix, and then transfer them to another TI-83. 1. On the home screen of the sending unit, press 5 Ë 5 ¿ ƒ Q. Press Í to store 5.5 to Q. 2. Press y [ [ ] y [ [ ] 1 ¢ 2 y [ ] ] y [ [ ] 3 ¢ 4 y [ ] ] y [ ] ] ¿ 1. Press Í to store the matrix to [A]. 3. Connect the calculators with the link cable. Push both ends in firmly. 4.
TI-83 LINK TI-83 Link Capabilities The TI-83 has a port to connect and communicate with another TI-83, a TI-82, the Calculator-Based Laboratoryé (CBL 2é, CBLé) System, the Calculator-Based Rangeré (CBRé), or a personal computer. The unit-to-unit link cable is included with the TI-83. This chapter describes how to communicate with another calculator. Linking Two TI-83s You can transfer all variables and programs to another TI-83 or backup the entire memory of a TI-83.
Selecting Items to Send LINK SEND Menu To display the LINK SEND menu, press y [LINK]. SEND RECEIVE 1: All+... 2: AllN... 3: Prgm... 4: List... 5: Lists to TI82... 6: GDB... 7: Pic... 8: Matrix... 9: Real... 0: Complex... A: Y-Vars... B: String... C: Back Up... Displays all items selected. Displays all items deselected. Displays all programs names. Displays all list names. Displays list names L1 through L6. Displays all graph databases. Displays all picture data types. Displays all matrix data types.
Receiving Items LINK RECEIVE Menu Receiving Unit To display the LINK RECEIVE menu, press y [LINK] ~. SEND RECEIVE 1: Receive Sets unit to receive data transmission. When you select 1:Receive from the LINK RECEIVE menu on the receiving unit, the message Waiting... and the busy indicator are displayed. The receiving unit is ready to receive transmitted items. To exit the receive mode without receiving items, press É, and then select 1:Quit from the Error in Xmit menu.
Transmitting Items Transmitting Items To transmit selected items after you have selected items to send on the sending unit (page 19.4) and set the receiving unit to receive (page 19.5), follow these steps. 1. Press ~ on the sending unit to display the TRANSMIT menu. 2. Confirm that Waiting... is displayed on the receiving unit, which indicates it is set to receive (page 19.5). 3. Press Í to select 1:Transmit.
Transmitting Items to an Additional TI-83 After sending or receiving data, you can repeat the same transmission to additional TI-83 units—from either the sending unit or the receiving unit—without having to reselect data to send. The current items remain selected. Note: You cannot repeat transmission if you selected All+ or All.. To transmit to an additional TI-83, follow these steps. 1. Set the TI-83 to receive (page 19.5). 2. Do not select or deselect any new items to send.
Transmitting Lists to a TI-82 Transmitting Lists to a TI-82 The only data type you can transmit from a TI-83 to a TI-82 is list data stored in L1 through L6. To transmit to a TI-82 the list data that is stored to TI-83 lists L1, L2, L3, L4, L5, or L6, follow these steps. 1. Set the TI-82 to receive (page 19.5). 2. Press y [LINK] 5 on the sending TI-83 to select 5:Lists to TI82. The SELECT screen is displayed. 3. Select each list to transmit. 4. Press ~ to display the LINK TRANSMIT menu. 5.
Transmitting from a TI-82 to a TI-83 Resolved Differences between the TI-82 and TI-83 Generally, you can transmit items to a TI-83 from a TI-82, but differences between the two products may affect some transmitted data. This table shows differences for which the software built into the TI-83 automatically adjusts when a TI-83 receives TI-82 data. TI.82 nMin nStart Un Vn UnStart VnStart TblMin TI.
Backing Up Memory Memory Backup To copy the exact contents of memory in the sending TI-83 to the memory of the receiving TI-83, put the other unit in receive mode. Then, on the receiving unit, select C:Back Up from the LINK SEND menu. • Warning: C:Back Up overwrites the memory in the receiving unit; all information in the memory of the receiving unit is lost. Note: If you do not want to do a backup, select 2:Quit to return to the LINK SEND menu. • Select 1:Transmit to begin transmission.
A Contents Tables and Reference Information Table of Functions and Instructions ..................... TI.83 Menu Map ......................................... Variables ................................................ Statistics Formulas ...................................... Financial Formulas ...................................... A-2 A-39 A-49 A-50 A-54 Tables and Reference Information A-1 8399APXA.
Table of Functions and Instructions Functions return a value, list, or matrix. You can use functions in an expression. Instructions initiate an action. Some functions and instructions have arguments. Optional arguments and accompanying commas are enclosed in brackets ( [ ] ). For details about an item, including argument descriptions and restrictions, turn to the page listed on the right side of the table.
Function or Instruction/ Arguments Result augment(matrixA,matrixB) Returns a matrix, which is matrixB appended to matrixA as new columns. Returns a list, which is listB augment(listA,listB) concatenated to the end of listA. Turns off the graph axes. AxesOff Key or Keys/ Menu or Screen/Item MATH 7:augment( OPS 9:augment( Turns on the graph axes. 3-14 † y [FORMAT] AxesOn Sets the mode to rectangular complex number mode (a+bi).
Function or Instruction/ Arguments c2pdf(x,df) c2.Test(observedmatrix, expectedmatrix [,drawflag]) Circle(X,Y,radius) Result Computes the probability density function (pdf) for the c2 distribution at a specified x value for the specified degrees of freedom df. Performs a chi-square test. drawflag=1 draws results; drawflag=0 calculates results. Draws a circle with center (X,Y) and radius. Key or Keys/ Menu or Screen/Item y [DISTR] DISTR 6:c2pdf( 13-31 †… TESTS C:c2.
Function or Instruction/ Arguments CoordOff CoordOn cos(value) cosL1(value) cosh(value) coshL1(value) CubicReg [Xlistname, Ylistname,freqlist, regequ] cumSum(list) cumSum(matrix) dbd(date1,date2) value4Dec Result Turns off cursor coordinate value display. Turns on cursor coordinate value display. Returns cosine of a real number, expression, or list. Returns arccosine of a real number, expression, or list. Returns hyperbolic cosine of a real number, expression, or list.
Function or Instruction/ Arguments Degree Result Sets degree angle mode. Key or Keys/ Menu or Screen/Item †z Degree Deletes from memory the contents of variable. † Sets table to ask for dependent-variable values. Sets table to generate dependent-variable values automatically. Returns determinant of matrix. † y [TBLSET] Sets diagnostics-off mode; r, r2, and R2 are not displayed as regression model results. Sets diagnostics-on mode; r, r2, and R2 are displayed as regression model results.
Function or Instruction/ Arguments DispGraph Result Displays the graph. Key or Keys/ Menu or Screen/Item † I/O 4:DispGraph 16-19 DispTable Displays the table. † I/O 5:DispTable 16-19 value4DMS Displays value in DMS format. y [ANGLE] ANGLE 4:4DMS Dot DrawF expression Sets dot plotting mode; resets †z all Y= editor graph-style settings Dot to í . Draws expression (in terms of y [DRAW] X) on the graph.
Function or Instruction/ Arguments End Eng Key or Keys/ Result Menu or Screen/Item Identifies end of For(, † CTL If-Then-Else, Repeat, or While loop. 7:End 16-12 Sets engineering display mode. † z Eng Equ4String(Y= var,Strn) expr(string) ExpReg [Xlistname, Ylistname,freqlist,regequ] ExprOff ExprOn Ücdf(lowerbound, upperbound, numerator df, denominator df) Fill(value,matrixname) Converts the contents of a Y= var to a string and stores it in Strn. Converts string to an expression and executes it.
Function or Instruction/ Arguments fMax(expression,variable, lower,upper[,tolerance]) Key or Keys/ Menu or Screen/Item FnOff [function#, function#,...,function n] Result Returns the value of variable where the local maximum of expression occurs, between lower and upper, with specified tolerance. Returns the value of variable where the local minimum of expression occurs, between lower and upper, with specified tolerance.
Function or Instruction/ Arguments value4Frac Key or Keys/ Menu or Screen/Item Full Result Displays a real or complex number, expression, list, or matrix as a fraction simplified to its simplest terms. Sets full screen mode. Func Sets function graphing mode. †z gcd(valueA,valueB) Returns the greatest common divisor of valueA and valueB, which can be real numbers or lists.
Function or Instruction/ Arguments GraphStyle(function#, graphstyle#) Result Sets a graphstyle for function#. Key or Keys/ Menu or Screen/Item † GridOff Turns off grid format. † y [FORMAT] GridOn Turns on grid format. † y [FORMAT] G-T Sets graph-table vertical split-screen mode. Sets horizontal split-screen mode. Draws a horizontal line at y.
Function or Instruction/ Arguments IndpntAsk IndpntAuto Input Result Sets table to ask for independent-variable values. Sets table to generate independent-variable values automatically. Displays graph. Key or Keys/ Menu or Screen/Item † y [TBLSET] Indpnt: Ask Indpnt: Auto 7-3 † I/O 1:Input Input [variable] Input ["text",variable] Prompts for value to store to variable. † Input [Strn,variable] Displays Strn and stores entered value to variable.
Function or Instruction/ Arguments irr(CF0,CFList[,CFFreq]) Result Returns the interest rate at which the net present value of the cash flows is equal to zero. Key or Keys/ Menu or Screen/Item y [FINANCE] CALC 8:irr( 14-8 Increments variable by 1; skips commandA if variable>value. † y [LIST] LabelOff Identifies the next one to five characters as a user-created list name. Turns off axes labels. LabelOn Turns on axes labels. † y [FORMAT] Lbl label Creates a label of one or two characters.
Function or Instruction/ Arguments LinReg(a+bx) [Xlistname, Ylistname,freqlist, regequ] Result Fits a linear regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. LinReg(ax+b) [Xlistname, Fits a linear regression model Ylistname,freqlist, to Xlistname and Ylistname regequ] with frequency freqlist, and stores the regression equation to regequ. Performs a linear regression LinRegTTest [Xlistname, Ylistname,freqlist, and a t-test.
Function or Instruction/ Arguments Logistic [Xlistname, Ylistname,freqlist, regequ] Result Fits a logistic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. Fills each listname with Matr 4 list(matrix, listnameA,...,listname n) elements from each column in matrix. Fills a listname with elements Matr 4 list(matrix, column#,listname) from a specified column# in matrix. Returns the larger of valueA max(valueA,valueB) and valueB.
Function or Instruction/ Arguments min(valueA,valueB) min(list) Result Returns smaller of valueA and valueB. Returns smallest real or complex element in list. Returns real or complex list of the smaller of each pair of elements in listA and listB. Returns a real or complex list min(value,list) of the smaller of value or each list element. valueA nCr valueB Returns the number of combinations of valueA taken valueB at a time.
Function or Instruction/ Arguments normalcdf(lowerbound, upperbound[,m,s]) normalpdf(x[,m,s]) not(value) valueA nPr valueB value nPr list list nPr value listA nPr listB npv(interest rate,CF0, CFList[,CFFreq]) valueA or valueB Result Computes the normal distribution probability between lowerbound and upperbound for the specified m and s. Computes the probability density function for the normal distribution at a specified x value for the specified m and s. Returns 0 if value is ƒ 0.
Function or Instruction/ Arguments Result Output(row,column,"text") Displays text beginning at specified row and column. Output(row,column,value) Param Pause Pause [value] Plot#(type,Xlistname, Ylistname,mark) I/O 6:Output( † Sets parametric graphing mode. Suspends program execution until you press Í. †z Displays value; suspends program execution until you press Í. Defines Plot# (1, 2, or 3) of type Scatter or xyLine for Xlistname and Ylistname using mark.
Function or Instruction/ Arguments Pmt_Bgn Pmt_End poissoncdf(m,x) poissonpdf(m,x) Polar Result Specifies an annuity due, where payments occur at the beginning of each payment period. Specifies an ordinary annuity, where payments occur at the end of each payment period. Computes a cumulative probability at x for the discrete Poisson distribution with specified mean m. Computes a probability at x for the discrete Poisson distribution with the specified mean m. Sets polar graphing mode.
Function or Instruction/ Arguments 1.PropZInt(x,n [,confidence level]) Result Computes a one-proportion z confidence interval. 2.PropZInt(x1,n1,x2,n2 [,confidence level]) Computes a two-proportion z confidence interval. 1.PropZTest(p0,x,n [,alternative,drawflag]) Computes a one-proportion †… z test. alternative=L1 is <; TESTS alternative=0 is ƒ; 5:1.PropZTest( alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. 13-14 Computes a two-proportion †… z test.
Function or Instruction/ Arguments Pxl.Change(row,column) Pxl.Off(row,column) Pxl.On(row,column) pxl.Test(row,column) P4Rx(r,q) P4Ry(r,q) QuadReg [Xlistname, Ylistname,freqlist, regequ] QuartReg [Xlistname, Ylistname,freqlist, regequ] Radian Result Reverses pixel at (row,column); 0 row 62 and 0 column 94. Erases pixel at (row,column); 0 row 62 and 0 column 94. Draws pixel at (row,column); 0 row 62 and 0 column 94.
Function or Instruction/ Arguments randInt( lower,upper [,numtrials]) randM(rows,columns) Result Generates and displays a random integer within a range specified by lower and upper integer bounds for a specified number of trials numtrials. Returns a random matrix of rows (1–99) × columns (1–99).
Function or Instruction/ Arguments :Repeat condition :commands :End :commands Return Result Executes commands until condition is true. Key or Keys/ Menu or Screen/Item † CTL 6:Repeat Returns to the calling program. † CTL E:Return round(value[,#decimals]) ärow(value,matrix,row) row+(matrix,rowA,rowB) ärow+(value,matrix, rowA,rowB) rowSwap(matrix,rowA, rowB) rref(matrix) R4Pr(x,y) R4Pq(x,y) 16-11 Returns a number, expression, list, or matrix rounded to #decimals ( 9).
Function or Instruction/ Arguments 2.SampÜTest [listname1, listname2,freqlist1, freqlist2,alternative, drawflag] (Data list input) 2.SampÜTest Sx1,n1, Sx2,n2[,alternative, drawflag] (Summary stats input) 2.SampTInt [listname1, listname2, freqlist1,freqlist2, confidence level,pooled] (Data list input) 2.SampTInt v1,Sx1,n1, v2,Sx2,n2 [,confidence level,pooled] (Summary stats input) 2.
Function or Instruction/ Arguments 2.SampTTest v1,Sx1,n1, v2,Sx2,n2[,alternative, pooled,drawflag] (Summary stats input) 2.SampZInt(s1,s2 [,listname1,listname2, freqlist1,freqlist2, confidence level]) (Data list input) 2.SampZInt(s1,s2, v1,n1,v2,n2 [,confidence level]) (Summary stats input) 2.SampZTest(s1,s2 [,listname1,listname2, freqlist1,freqlist2, alternative,drawflag]) (Data list input) 2.
Function or Instruction/ Arguments Send(variable) Key or Keys/ Result Menu or Screen/Item Sends contents of variable to † the CBL 2/CBL System or CBR. I/O seq(expression,variable, begin,end[,increment]) Returns list created by evaluating expression with regard to variable, from begin to end by increment. Sets sequence graphing mode. y [LIST] Sets mode to graph functions sequentially. Removes all list names from the stat list editor, and then restores list names L1 through L6 to columns 1 through 6.
Function or Instruction/ Arguments ShadeÜ(lowerbound, upperbound, numerator df, denominator df) ShadeNorm(lowerbound, upperbound[,m,s]) Shade_t(lowerbound, upperbound,df) Simul sin(value) sinL1(value) sinh(value) sinhL1(value) Result Draws the density function for the Û distribution specified by numerator df and denominator df and shades the area between lowerbound and upperbound. Draws the normal density function specified by m and s and shades the area between lowerbound and upperbound.
Function or Instruction/ Arguments SinReg [iterations, Xlistname,Ylistname, period,regequ] Result Attempts iterations times to fit a sinusoidal regression model to Xlistname and Ylistname using a period guess, and stores the regression equation to regequ. solve(expression,variable, Solves expression for variable, guess,{lower,upper}) given an initial guess and lower and upper bounds within which the solution is sought. Sorts elements of listname in SortA(listname) ascending order.
Function or Instruction/ Arguments StorePic n String4Equ(string,Y= var) sub(string,begin,length) sum(list[,start,end]) Result Stores current picture in picture Picn. Converts string into an equation and stores it in Y= var. Returns a string that is a subset of another string, from begin to length. Returns the sum of elements of list from start to end. Returns the tangent of a real number, expression, or list. Returns the arctangent of a tanL1(value) real number, expression, or list.
Function or Instruction/ Arguments Time TInterval [listname, freqlist,confidence level] (Data list input) TInterval v,Sx,n [,confidence level] (Summary stats input) tpdf(x,df) Trace T-Test m0[,listname, freqlist,alternative, drawflag] (Data list input) T-Test m0, v,Sx,n [,alternative,drawflag] (Summary stats input) Result Sets sequence graphs to plot with respect to time. Computes a t confidence interval.
Function or Instruction/ Arguments tvm_FV[(Ú,æ,PV,PMT, P/Y,C/Y)] Result Computes the future value. tvm_æ[(Ú,PV,PMT,FV, P/Y,C/Y)] Computes the annual interest rate. y [FINANCE] tvm_Ú[(æ,PV,PMT,FV, P/Y,C/Y)] Computes the number of payment periods. y [FINANCE] tvm_Pmt[(Ú,æ,PV,FV, P/Y,C/Y)] Computes the amount of each payment. y [FINANCE] tvm_PV[(Ú,æ,PMT,FV, P/Y,C/Y)] Computes the present value. y [FINANCE] uvAxes Sets sequence graphs to plot u(n) on the x-axis and v(n) on the y-axis.
Function or Instruction/ Arguments :While condition :commands :End :command valueA xor valueB ZBox ZDecimal ZInteger Result Executes commands while condition is true. Returns 1 if only valueA or valueB = 0. valueA and valueB can be real numbers, expressions, or lists. Displays a graph, lets you draw a box that defines a new viewing window, and updates the window. Adjusts the viewing window so that @X=0.1 and @Y=0.1, and displays the graph screen with the origin centered on the screen.
Function or Instruction/ Arguments ZoomFit ZoomRcl ZoomStat ZoomSto ZPrevious ZSquare ZStandard Result Recalculates Ymin and Ymax to include the minimum and maximum Y values, between Xmin and Xmax, of the selected functions and replots the functions. Graphs the selected functions in a user-defined viewing window. Redefines the viewing window so that all statistical data points are displayed. Immediately stores the current viewing window.
Function or Instruction/ Arguments ZNTest(m0,s[,listname, freqlist,alternative, drawflag]) (Data list input) ZNTest(m0,s,v,n [,alternative,drawflag]) (Summary stats input) ZTrig Factorial: value! Result Performs a z test with frequency freqlist. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Performs a z test. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
Function or Instruction/ Arguments x throotx‡value Result Returns x throot of value. Key or Keys/ Menu or Screen/Item MATH 5:x‡ x throotx‡list listx‡value Returns x throot of list elements. Returns list roots of value. MATH 5:x‡ MATH 5:x‡ listAx‡listB Returns listA roots of listB.
Function or Instruction/ Arguments Greater than: valueA>valueB Less than or equal: valueAvalueB Greater than or equal: valueA‚valueB Inverse: valueL1 Inverse: listL1 Inverse: matrixL1 Square: value2 Square: list2 Result Returns 1 if valueA > valueB. Returns 0 if valueA valueB. valueA and valueB can be real or complex numbers, expressions, or lists. Returns 1 if valueA valueB. Returns 0 if valueA > valueB. valueA and valueB can be real or complex numbers, expressions, or lists.
Function or Instruction/ Arguments Powers: matrix^power Negation: Lvalue Power of ten: 10^(value) Power of ten: 10^(list) Square root: ‡(value) Multiplication: valueAävalueB Multiplication: valueälist Multiplication: listävalue Multiplication: listAälistB Multiplication: valueämatrix Multiplication: matrixAämatrixB Division: valueAàvalueB Division: listàvalue Division: valueàlist Division: listAàlistB Result Returns matrix elements raised to power.
Function or Instruction/ Arguments Addition: valueA+valueB Addition: list+value Addition: listA+listB Addition: matrixA+matrixB Concatenation: string1+string2 Subtraction: valueANvalueB Subtraction: valueNlist Subtraction: listNvalue Subtraction: listANlistB Subtraction: matrixANmatrixB Minutes notation: degrees¡minutes' seconds" Seconds notation: degrees¡minutes' seconds" Result Returns valueA plus valueB. Returns list in which value is added to each list element.
TI-83 Menu Map The TI.83 Menu Map begins at the top-left corner of the keyboard and follows the keyboard layout from left to right. Default values and settings are shown. o ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ (Func mode) Plot1 Plot2 Plot3 çY1= çY2= çY3= çY4= ... çY9= çY0= y [STAT PLOT] ÚÄÄÄÄÄÙ STAT PLOTS 1:Plot1…Off " L1 L2 › 2:Plot2…Off " L1 L2 › 3:Plot3…Off " L1 L2 › 4:PlotsOff 5:PlotsOn (Par mode) Plot1 Plot2 Plot3 çX1T= Y1T= çX2T= Y2T= ...
q ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ZOOM 1:ZBox 2:Zoom In 3:Zoom Out 4:ZDecimal 5:ZSquare 6:ZStandard 7:ZTrig 8:ZInteger 9:ZoomStat 0:ZoomFit MEMORY 1:ZPrevious 2:ZoomSto 3:ZoomRcl 4:SetFactors… MEMORY (Set Factors...
y [LINK] ÚÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ SEND 1:All+… 2:AllN… 3:Prgm… 4:List… 5:Lists to TI82… 6:GDB… 7:Pic… 8:Matrix… 9:Real… 0:Complex… A:Y-Vars… B:String… C:Back Up… RECEIVE 1:Receive … ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ EDIT 1:Edit… 2:SortA( 3:SortD( 4:ClrList 5:SetUpEditor CALC 1:1-Var Stats 2:2-Var Stats 3:Med-Med 4:LinReg(ax+b) 5:QuadReg 6:CubicReg 7:QuartReg 8:LinReg(a+bx) 9:LnReg 0:ExpReg A:PwrReg B:Logistic C:SinReg TESTS 1:Z-Test… 2:T-Test… 3:2-SampZTest… 4:2-SampTTest… 5:1-PropZTest… 6:2-PropZTest…
y [LIST] ÚÄÄÁÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿ NAMES 1:listname 2:listname 3:listname ...
y [ANGLE] ÚÁÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿ NAMES 1:[A] 2:[B] 3:[C] 4:[D] 5:[E] 6:[F] 7:[G] 8:[H] 9:[I] 0:[J] MATH 1:det( 2: T 3:dim( 4:Fill( 5:identity( 6:randM( 7:augment( 8:Matr4list( 9:List4matr( 0:cumSum( A:ref( B:rref( C:rowSwap( D:row+( E:…row( F:…row+( ÚÄÄÄÙ EDIT 1:[A] 2:[B] 3:[C] 4:[D] 5:[E] 6:[F] 7:[G] 8:[H] 9:[I] 0:[J] ANGLE 1:¡ 2:' 3: r 4:4DMS 5:R4Pr( 6:R4Pq( 7:P4Rx( 8:P4Ry( ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ EXEC 1:name 2:name ... EDIT 1:name 2:name ...
y [DRAW] ÚÄÄÄÄÁÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ DRAW 1:ClrDraw 2:Line( 3:Horizontal 4:Vertical 5:Tangent( 6:DrawF 7:Shade( 8:DrawInv 9:Circle( 0:Text( A:Pen POINTS 1:Pt-On( 2:Pt-Off( 3:Pt-Change( 4:Pxl-On( 5:Pxl-Off( 6:Pxl-Change( 7:pxl-Test( STO 1:StorePic 2:RecallPic 3:StoreGDB 4:RecallGDB ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ VARS 1:Window… 2:Zoom… 3:GDB… 4:Picture… 5:Statistics… 6:Table… 7:String… Y-VARS 1:Function… 2:Parametric… 3:Polar… 4:On/Off… VARS ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄ (Window…) X/Y 1:Xmin 2:Xmax 3:Xscl
VARS ÄÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄ (Zoom…) ZX/ZY 1:ZXmin 2:ZXmax 3:ZXscl 4:ZYmin 5:ZYmax 6:ZYscl 7:ZXres (Zoom…) ZT/Zq 1:ZTmin 2:ZTmax 3:ZTstep 4:Zqmin 5:Zqmax 6:Zqstep (Zoom…) ZU 1:Zu(nMin) 2:Zv(nMin) 3:Zw(nMin) 4:ZnMin 5:ZnMax 6:ZPlotStart 7:ZPlotStep VARS ÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄ (GDB…) GRAPH DATABASE 1:GDB1 2:GDB2 ... 9:GDB9 0:GDB0 (Picture…) PICTURE 1:Pic1 2:Pic2 ...
VARS ÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ (Table…) TABLE 1:TblStart 2:@Tbl 3:TblInput (String…) STRING 1:Str1 2:Str2 3:Str3 4:Str4 ... 9:Str9 0:Str0 Y-VARS ÚÄÁÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄ¿ (Function…) FUNCTION 1:Y1 2:Y2 3:Y3 4:Y4 ... 9:Y9 0:Y0 (Parametric…) PARAMETRIC 1:X1T 2:Y1T 3:X2T 4:Y2T ... A:X6T B:Y6T (Polar…) POLAR 1:r1 2:r2 3:r3 4:r4 5:r5 6:r6 (On/Off…) ON/OFF 1:FnOn 2:FnOff A-46 Tables and Reference Information 8399APXA.
y [DISTR] ÚÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ DISTR 1:normalpdf( 2:normalcdf( 3:invNorm( 4:tpdf( 5:tcdf( 6:c 2 pdf( 7:c 2 cdf( 8:Ûpdf( 9:Ûcdf( 0:binompdf( A:binomcdf( B:poissonpdf( C:poissoncdf( D:geometpdf( E:geometcdf( DRAW 1:ShadeNorm( 2:Shade_t( 3:Shadec 2 ( 4:ShadeÛ( y [FINANCE] ÚÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄ¿ CALC 1:TVM Solver… 2:tvm_Pmt 3:tvm_æ 4:tvm_PV 5:tvm_Ú 6:tvm_FV 7:npv( 8:irr( 9:bal( 0:GPrn( A:GInt( B:4Nom( C:4Eff( D:dbd( E:Pmt_End F:Pmt_Bgn VARS 1:Ú 2:æ 3:PV 4:PMT 5:FV 6:P/Y 7:C/Y Tables and Reference Information A-47
y [MEM] ÚÄÄÙ MEMORY 1:Check RAM… 2:Delete… 3:Clear Entries 4:ClrAllLists 5:Reset… MEMORY ÚÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿ (Check RAM…) MEM FREE 27225 Real 15 Complex 0 List 0 Matrix 0 Y-Vars 240 Prgm 14 Pic 0 GDB 0 String 0 (Delete…) DELETE FROM… 1:All… 2:Real… 3:Complex… 4:List… 5:Matrix… 6:Y-Vars… 7:Prgm… 8:Pic… 9:GDB… 0:String… y [CATALOG] MEMORY (Reset...
Variables User Variables The TI.83 uses the variables listed below in various ways. Some variables are restricted to specific data types. The variables A through Z and q are defined as real or complex numbers. You may store to them. The TI.83 can update X, Y, R, q, and T during graphing, so you may want to avoid using these variables to store nongraphing data. The variables (list names) L1 through L6 are restricted to lists; you cannot store another type of data to them.
Statistics Formulas This section contains statistics formulas for the Logistic and SinReg regressions, ANOVA, 2.SampÜTest, and 2.SampTTest.
ANOVA( The ANOVA Û statistic is: Û= Factor MS Error MS The mean squares (MS) that make up Û are: Factor SS Factor df Factor MS = Error SS Error df Error MS = The sum of squares (SS) that make up the mean squares are: I Factor SS = ∑ n (x − x) i 2 i i =1 I Error SS = ∑ (n − 1)Sx 2 i i i =1 The degrees of freedom df that make up the mean squares are: Factor df = I − 1 = numerator df for Û I Error df = ∑ (n − 1) = denominator df for Û i i =1 where: I xi Sxi ni x = = = = = number of pop
2-SampÜTest Below is the definition for the 2.SampÜTest. Sx1, Sx2 = Sample standard deviations having n1-1 and n2-1 degrees of freedom df, respectively. Sx1 2 Û = Û-statistic = Sx 2 df(x, n1-1, n2-1) = Ûpdf( ) with degrees of freedom df, n1-1, and n2-1 p = reported p value 2.SampÜTest for the alternative hypothesis s 1 > s 2. ∞ p= ∫ f (x, n − 1, n 1 2 − 1)dx F 2.SampÜTest for the alternative hypothesis s 1 < s 2. F p= ∫ f (x, n − 1, n 1 2 − 1)dx 0 2.
2-SampTTest The following is the definition for the 2.SampTTest. The two-sample t statistic with degrees of freedom df is: t= x1 − x 2 S where the computation of S and df are dependent on whether the variances are pooled. If the variances are not pooled: S= Sx12 Sx22 + n1 n2 Sx12 Sx22 2 + n1 n2 df = 1 Sx12 2 1 Sx 22 2 + n1 − 1 n1 n2 − 1 n2 otherwise: Sxp = ( n1 − 1) Sx12 + ( n2 − 1) Sx22 df S= 1 1 Sxp + n1 n2 df = n1 + n2 − 2 and Sxp is the pooled variance.
Financial Formulas This section contains financial formulas for computing time value of money, amortization, cash flow, interest-rate conversions, and days between dates. Time Value of Money i = [e ( y × ln( x + 1))] − 1 where: PMT y x C/Y P/Y I% ƒ0 = C/Y ÷ P/Y = (.
PMT = PV + FV × PV + Gi (1 + i) N − 1 where: i ƒ0 −i PMT = −( PV + FV ) ÷ N where: i = 0 PMT × Gi 1 PMT × Gi PV = − FV × − N i i i ( 1 + ) where: i ƒ0 PV = −( FV + PMT × N ) where: FV = i = 0 PMT × Gi PMT × Gi − ( 1 + i )N × PV + i i where: i ƒ0 FV = −( PV + PMT × N ) where: i = 0 Tables and Reference Information A-55 8399APXA.
Amortization If computing bal( ), pmt2 = npmt Let bal(0) = RND(PV) Iterate from m = 1 to pmt2 Im = RND[ RND12(− i × bal( m − 1))] bal( m) = bal (m − 1) − Im + RND( PMT ) then: bal( ) = bal( pmt 2) Σ Pr n ( ) = bal( pmt 2) − bal( pmt1) Σ Int( ) = ( pmt 2 − pmt1 + 1) × RND( PMT ) − Σ Pr n ( ) where: RND = round the display to the number of decimal places selected RND12 = round to 12 decimal places Balance, principal, and interest are dependent on the values of PMT, PV, æ, and pmt1 and pmt2.
Cash Flow N npv( ) = CF0 + ∑ CF (1 + i) j − Sj − 1 j =1 j ni where: Sj = i 1 = 0 ∑ (1 − (1 + i) i −n j ) j ≥1 j=0 Net present value is dependent on the values of the initial cash flow (CF0), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i). irr( ) = 100 × i, where i satisfies npv( ) = 0 Internal rate of return is dependent on the values of the initial cash flow (CF0) and subsequent cash flows (CFj).
Days between Dates With the dbd( function, you can enter or compute a date within the range Jan. 1, 1950, through Dec. 31, 2049.
B Contents General Information Battery Information ...................................... B-2 In Case of Difficulty ..................................... B-4 Error Conditions ......................................... B-5 Accuracy Information.................................... B-10 Support and Service Information......................... B-12 Warranty Information .................................... B-13 General Information B-1 8399APXB.
Battery Information When to Replace the Batteries The TI.83 uses five batteries: four AAA alkaline batteries and one lithium battery. The lithium battery provides auxiliary power to retain memory while you replace the AAA batteries. When the battery voltage level drops below a usable level, the TI.83 displays this message when you turn on the unit. After this message is first displayed, you can expect the batteries to function for about one or two weeks, depending on usage.
Replacing the Batteries To replace the batteries, follow these steps. 1. Turn off the calculator. Replace the slide cover over the keyboard to avoid inadvertently turning on the calculator. Turn the back of the calculator toward you. 2. Hold the calculator upright. Place your thumb on the oval indentation on the battery cover. Push down and toward you to slide the cover about ¼ inch (6 mm). Lift off the cover to expose the battery compartment.
In Case of Difficulty Handling a Difficulty To handle a difficulty, follow these steps. 1. If you cannot see anything on the screen, the contrast may need to be adjusted. To darken the screen, press and release y, and then press and hold } until the display is sufficiently dark. To lighten the screen, press and release y, and then press and hold † until the display is sufficiently light. 2. If an error menu is displayed, follow the steps in Chapter 1. Refer to pages B.5 through B.
Error Conditions When the TI.83 detects an error, it displays ERR:message and an error menu. Chapter 1 describes the general steps for correcting errors. This table contains each error type, possible causes, and suggestions for correction. Error Type Possible Causes and Suggested Remedies ARCHIVED VAR A function or instruction is archived and therefore cannot be executed or edited. Use the unarchive command to unarchive the variable before using it.
Error Type Possible Causes and Suggested Remedies DOMAIN ¦ You specified an argument to a function or instruction outside the valid range. This error is not returned during graphing. The TI.83 allows for undefined values on a graph. See Appendix A and the appropriate chapter. ¦ You attempted a logarithmic or power regression with a LX or an exponential or power regression with a LY. ¦ You attempted to compute GPrn( or GInt( with pmt2 < pmt1.
Error Type Possible Causes and Suggested Remedies INVALID (cont.) ¦ In Seq mode, you attempted to graph a recursive sequence without having input the correct number of initial conditions. ¦ In Seq mode, you attempted to reference terms other than (nN1) or (nN2). ¦ You attempted to designate a graph style that is invalid within the current graph mode. ¦ You attempted to use Select( without having selected (turned on) at least one xyLine or scatter plot.
Error Type Possible Causes and Suggested Remedies MemoryFull ¦ You are unable to transmit an item because the receiving unit’s available memory is insufficient. You may skip the item or exit receive mode. ¦ During a memory backup, the receiving unit’s available memory is insufficient to receive all items in the sending unit’s memory. A message indicates the number of bytes the sending unit must delete to do the memory backup. Delete items and try again.
Error Type Possible Causes and Suggested Remedies SINGULARITY expression in the solve( function or the equation solver contains a singularity (a point at which the function is not defined). Examine a graph of the function. If the equation has a solution, change the bounds or the initial guess or both. STAT You attempted a stat calculation with lists that are not appropriate. ¦ Statistical analyses must have at least two data points. ¦ Med.Med must have at least three points in each partition.
Accuracy Information Computational Accuracy To maximize accuracy, the TI.83 carries more digits internally than it displays. Values are stored in memory using up to 14 digits with a two-digit exponent. • You can store a value in the window variables using up to 10 digits (12 for Xscl, Yscl, Tstep, and qstep). • Displayed values are rounded as specified by the mode setting with a maximum of 10 digits and a two-digit exponent. • RegEQ displays up to 14 digits in Float mode.
Cursor coordinates are displayed as eight-character numbers (which may include a negative sign, decimal point, and exponent) when Float mode is selected. X and Y are updated with a maximum accuracy of eight digits. minimum and maximum on the CALCULATE menu are calculated with a tolerance of 1EL5; ‰f(x)dx is calculated at 1EL3. Therefore, the result displayed may not be accurate to all eight displayed digits. For most functions, at least five accurate digits exist.
Support and Service Information Product Support Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands For general questions, contact Texas Instruments Customer Support: phone: e-mail: 1.800.TI.CARES (1.800.842.2737) ti-cares@ti.com For technical questions, call the Programming Assistance Group of Customer Support: phone: 1.972.917.8324 Customers outside the U.S., Canada, Puerto Rico, and the Virgin Islands Contact TI by e-mail or visit the TI calculator home page on the World Wide Web.
Warranty Information Customers in the U.S. and Canada Only One-Year Limited Warranty for Electronic Product This Texas Instruments (“TI”) electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This TI electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This TI electronic product is warranted against defective materials and construction.
Australia & New Zealand Customers only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction.
Index + (addition), 2-3, A-38 c2cdf( (chi-square cdf), 13-31, A-3 c2pdf( (chi-square pdf), 13-31, A-4 c2.
.B. backing up calculator memory, 19-4, 19-10 bal( (amortization balance), 14-9, A-3 batteries, 1-2, B-2 below graph style (ê), 3-9 binomcdf(, 13-33, A-3 binompdf(, 13-33, A-3 Boolean logic, 2-26 box pixel mark (›), 8-15, 12-34 Boxplot plot type ( Ö), 12-33 busy indicator, 1-4 .C.
. D (continued) . coshM1( (hyperbolic arccosine), 15-10, A-5 cosine (cos(), 2-3, A-5 cross pixel mark (+), 8-15, 12-34 cube ( 3) , 2-6, A-35 cube root (3‡(), 2-6, A-35 CubicReg (cubic regression), 12-26, A-5 cubic regression (CubicReg), 12-26, A-5 cumulative sum (cumSum(), 10-15, 11-12, A-5 cumSum( (cumulative sum), 10-15, 11-12, A-5 cursors, 1-5, 1-8 C/Y (compounding-periods-per-year variable), 14-4, 14-14 .D.
. D (continued) . drawing on a graph circles (Circle(), 8-11 functions and inverses (DrawF, DrawInv), 8-9 lines (Horizontal, Line(, Vertical), 8-6, 8-7 line segments (Line(), 8-5 pixels (Pxl.Change, Pxl.Off, Pxl.On, pxl.Test), 8-16 points (Pt.Change, Pt.Off, Pt.On), 8-14 tangents (Tangent), 8-8 text (Text), 8-12 using Pen, 8-13 DrawInv (draw inverse), 8-9, A-7 DRAW menu, 8-3 DRAW instructions, 8-3 N 8.16 Draw output option, 13-6 N 13.
. E (continued) .
. F (continued) . . G (continued) .
. I (continued) . inferential statistics. See also stat tests; confidence intervals alternative hypotheses, 13-7 bypassing editors, 13-8 calculating test results (Calculate), 13-8 confidence interval calculations, 13-8, 13-16 N 13.
. L (continued) . . M (continued) . lists, 11-1 to 11-18 accessing an element, 11-5 attaching formulas, 11-7, 12-14 clearing all elements, 12-12, 12-20 copying, 11-5 creating, 11-3, 12-12 deleting from memory, 11-5, 18-3 detaching formulas, 11-8, 12-16 dimension, 11-4, 11-11 entering list names, 11-6, 12-11 indicator ({ }), 11-4 naming lists, 11-3 storing and displaying, 11-4 transmitting to and from TI.
. M (continued) . modified box plot type (Õ), 12-32 mode settings, 1-9 a+bi (complex rectangular), 1-12, 2-16, A-3 re^qi (complex polar), 1-12, 2-16, A-22 Connected (plotting), 1-11, A-4 Degree (angle), 1-11, 2-24, A-6 Dot (plotting), 1-11, A-7 Eng (notation), 1-10, A-8 Fix (decimal), 1-10, A-8 Float (decimal), 1-10, A-8 Full (screen), 1-12, A-10 Func (graphing), 1-11, A-10 G.
. P (continued) . Pause, 16-12, A-18 pausing a graph, 3-15 Pen, 8-13 permutations (nPr), 2-21, A-17 phase plots, 6-13 Pi (p), 2-4 Pic (pictures), 8-17, 8-18 pictures (Pic), 8-17, 8-18 pixel, 8-16 pixels in Horiz/G.
. P (continued) . . R (continued) . PV (present value variable), 14-4, RegEQ (regression equation variable), 14-14 p-value, 13-28 PwrReg (power regression), 12-27, A-20 Pxl.Change(, 8-16, A-21 Pxl.Off(, 8-16, A-21 Pxl.On(, 8-16, A-21 pxl.
. S (continued) . seconds DMS notation ( ") , 2-23 Select(, 11-12, A-25 selecting data points from a plot, 11-13 functions from the home screen or a program, 3-8 functions in the Y= editor, 3-7 items from menus, 4 stat plots from the Y= editor, 3-7 Send( (send to CBL 2/CBL or CBR), 16-21, A-26 sending.
. S (continued) . stat list editor (continued) editing elements of formulagenerated lists, 12-16 editing list elements, 12-13 enter-names context, 12-19 entering list names, 12-11 formula-generated list names, 12-15 removing lists, 12-12 restoring list names L1–L6, 12-12, 12-21 switching contexts, 12-17 view-elements context, 12-18 view-names context, 12-19 STAT PLOTS menu, 12-34 stat tests and confidence intervals ANOVA( (one-way analysis of variance), 13-25 c².
.T.
. T (continued) . turning on and off axes, 3-14 calculator, 1-2 coordinates, 3-14 expressions, 3-14 functions, 3-7 grid, 3-14 labels, 3-14 pixels, 8-16 points, 8-14 stat plots, 3-7, 12-35 tvm_FV (future value), 14-7, A-31 tvm_I% (interest rate), 14-7, A-31 tvm_Ú (# payment periods), 14-7, A-31 tvm_Pmt (payment amount), 14-6, A-31 tvm_PV (present value), 14-7, A-31 two-proportion z confidence interval (2.PropZInt), 13-21, A-20 two-proportion z test (2.
.X. XFact zoom factor, 3-24 x-intercept of a root, 3-26 . Z (continued) . ZoomSto (store zoom window), 3-23, A-33 xor (Boolean) exclusive or operator, ZPrevious (use previous window), 2-26, A-32 x th root (x‡), 2-6 xyLine (Ó) plot type, 12-31 @X window variable, 3-12 ZSquare (set square pixels), 3-21, A-33 ZStandard (use standard window), .Y. YFact zoom factor, 3-24 Y= editor 3-23, A-33 3-22, A-33 Z.
TI83CALC.
TI83CALC.