TI-84 Plus C Silver Edition Guidebook This guidebook applies to software version 4.0. To obtain the latest version of the documentation, go to education.ti.com/go/download.
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Contents Important Information .................................................................................................................... ii Chapter 1: Getting Started with the TI-84 Plus C Silver Edition ............................................... 1 Documentation Conventions .......................................................................................................... 1 Using the TI-84 Plus C in the Classroom .......................................................................
Setting the Graph Format ............................................................................................................. 81 Displaying Graphs .......................................................................................................................... 82 Exploring Graphs with the Free-Moving Cursor .......................................................................... 84 Exploring Graphs with TRACE ...............................................................................
Background Menu and Image Vars ............................................................................................ 139 Chapter 9: Split Screen ........................................................................................................... 140 Getting Started: Exploring the Unit Circle ................................................................................. 140 Using Split Screen ...................................................................................................
Distribution Functions ................................................................................................................. 246 Distribution Shading ................................................................................................................... 252 Chapter 14: Applications .......................................................................................................... 255 The Applications Menu .......................................................................
Chapter 18: Memory and Variable Management .................................................................... 325 Checking Available Memory ....................................................................................................... 325 Deleting Items from Memory ..................................................................................................... 327 Clearing Entries (Home Screen) and List Editor Elements .........................................................
Chapter 1: Getting Started with the TI-84 Plus C Silver Edition Documentation Conventions In the body of this guidebook, TI-84 Plus refers to the TI-84 Plus, TI-84 Plus Silver Edition, and TI-84 Plus C Silver Edition. The names of the calculators may be used interchangeably. If any of the instructions, examples, and functions in this guidebook differ for each calculator, those differences are pointed out.
Using Color on the Graph Screen The examples below show how to set line color on the Y= editor using the spinner, and how to set a Background Image for a graph. Enter an equation in the Y= editor. 1. Press o. 2. Press k „ ¡ Ã 6. To set the line color in the Y= editor: 3. Press y | | | to select the color/line box to the left of Y=, and then press Í. The spinner dialog box becomes active. 4. Press ~ ~ ~ to select magenta. 5. Press †. Note: The thick line style is the default.
To set a Background Image: 7. Press y .. Set grid color, axes, and border color as desired. 8. Press } or † as necessary to highlight Background. The spinner dialog box becomes active. 9. Press ~ as necessary to select the desired Background Image or color. Note: Your pre-loaded Image Var may be different than the one displayed. Note: To create Background Image Vars, use the free TI Connect™ software to convert and send images to your TI-84 Plus C graphing calculator. 10.
TI-84 Plus C Silver Edition TI-84 Plus C Silver Edition Graphing Keys Editing Keys Advanced Function Keys Scientific Calculator Keys Using the Color.Coded Keyboard The keys on the TI-84 Plus C are color-coded to help you easily locate the key you need. The light colored keys are the number keys. The keys along the right side of the keyboard are the common math functions. The keys across the top set up and display graphs.
Many keys also have a third function. These functions are printed above the keys in the same color as the ƒ key. The third functions enter alphabetic characters and special symbols, as well as access SOLVE and shortcut menus. For example, when you press ƒ and then , the letter A is entered. This guidebook describes this keystroke combination as ƒ [A].
• If Automatic Power Down™ (APD™) had previously turned off the graphing calculator, the TI-84 Plus C will return exactly as you left it, including the display, cursor, and any error. • If the TI-84 Plus C is turned off and connected to another graphing calculator or personal computer, any communication activity will “wake up” the TI-84 Plus C. To prolong the life of the battery, APD™ turns off the TI-84 Plus C automatically after about five minutes without any activity.
Enter a calculation. 1. Press y 5 to return to the home screen, if needed. 2. Press y C 3 ¡ Ã 4 ¡ ~ Ã 6 Í. Note: When you are in a MathPrint™ template, the cursor turns to a right arrow to indicate that you must press ~ to get out of the template before you continue entering the calculation. Displaying Entries and Answers • When text is displayed, the TI-84 Plus C screen can display a maximum of 10 lines with a maximum of 26 characters per line in Classic mode.
MathPrint™ (default) Entry Answer Entry Answer Classic Entry Answer Entry Answer Scrolling Through Previous Entries on the Home Screen If all lines of the display are full, text scrolls off the top of the display. You can scroll up through previous entries and answers on the home screen, even if you have cleared the screen. When you find an entry or answer that you want to use, you can select it and paste it (press Í) on the current entry line.
Status Bar The status bar displays on all screens, and gives information about the selected calculator mode settings, any context help available for the item you currently have selected, and battery status. The status bar may also show a busy indicator if the calculator is performing an operation, Ø to indicate the calculator is in alpha status, and Þ to indicate the secondary function is active.
• Templates to enter fractions, and to toggle between whole and mixed fractions, and fractions and decimals. • Selected functions from the MATH MATH and MATH NUM menus as you would see them in a textbook, when in MathPrint™ mode. Functions include absolute value, numeric differentiation, numeric integration, summation, log base n, square root, permutations, combinations, and factorials. • Quick MathPrint™ matrix entry, when available. • Names of function variables from the VARS Y-VARS menu.
Busy Indicator 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. Note: The second cursor and alpha cursor may appear on the status bar, depending on the context. Cursor Appearance Effect of Next Keystroke Entry Solid rectangle $ A character is entered at the cursor; any existing character is overwritten.
Note: When you press z, the cursor is on NORMAL by default. Press } to switch between the MathPrint™ and Classic modes.
MATHPRINT, CLASSIC MathPrint™ mode displays most inputs and outputs the way they are shown in textbooks, such as 2 1 3 --- + --- and x 2 dx . 2 4 1 Classic mode displays expressions and answers as if written on one line, such as 1/2 + 3/4. Note: If you switch between these modes, most entries will be preserved; however matrix calculations will not be preserved. NORMAL, SCI, ENG Notation modes only affect the way an answer is displayed on the home screen.
Par (parametric) graphing mode plots relations, where X and Y are functions of T (Chapter 4). Pol (polar) graphing mode plots functions, where r is a function of q (Chapter 5). Seq (sequence) graphing mode plots sequences (Chapter 6). THICK, DOT-THICK, THIN, DOT-THIN THICK plotting mode is a quick way to reset all Y= line styles to a thick line connecting each point calculated for the selected functions. You can change individual line styles in the Y= editor.
FULL, HORIZONTAL, GRAPH-TABLE Full screen mode uses the entire screen to display a graph or edit screen. Each split-screen mode displays two screens simultaneously. • Horiz (horizontal) mode displays the current graph on the top half of the screen; it displays the home screen or an editor on the bottom half (Chapter 9 in the guidebook). • G-T (graph-table) mode displays the current graph on the left half of the screen; it displays the table screen on the right half (Chapter 9 in the guidebook).
SET CLOCK Use the clock to set the time, date, and clock display formats. Using the Clock Use the clock to set the time and date, select the clock display format, and turn the clock on and off. The clock is turned on by default and is accessed from the mode screen. Displaying the Clock Settings 1. 2. Press z. Press } } to move the cursor to SET CLOCK. 3. Press Í. Changing the Clock Settings 1. 2. Press ~ or | to highlight each field. • Press Í to select the date and time format.
EOS™ evaluates the functions in an expression in this order.
Example: MX2, evaluates to a negative number (or 0). Use parentheses to square a negative number. Note: Use the ¹ key for subtraction and the Ì key for negation. If you press ¹ to enter a negative number, as in 9 ¯ ¹ 7, or if you press Ì to indicate subtraction, as in 9 Ì 7, an error occurs. If you press ƒ A Ì ƒ B, it is interpreted as implied multiplication (A…MB).
Multiple Entries on a Line To enter two or more expressions or instructions on a line, separate them with colons (ƒ [:]). All instructions are stored together in last entry (ENTRY). Entering a Number in Scientific Notation 1. Enter the part of the number that precedes the exponent. This value can be an expression. 2. Press y D. â is pasted to the cursor location. 3. Enter the exponent, which can be one or two digits. Note: If the exponent is negative, press Ì, and then enter the exponent.
TI-84 Plus C 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. Moves the cursor from term to term within an expression in MathPrint™ mode; these keys repeat. On the home screen, scrolls through the history of entries and answers. y| Moves the cursor to the beginning of an expression. y~ Moves the cursor to the end of an expression.
Keystrokes Result „ Pastes an X in Func mode, a T in Par mode, a q in Pol mode, or an n in Seq mode with one keystroke. Pictures and Backgrounds The TI-84 Plus C uses both pictures and background images. They are both stored in Flash archive, but they are used in different ways: • Image Vars (Image1 - Image9, and Image0) are variables stored in archive memory. An Image Var is used as a Background Image in the graph area. Several images are pre-loaded on the TI-84 Plus C.
Variable Type Names Background images Image1, Image2, ... , Image9, Image0 Pictures Pic1, Pic2, ... , Pic9, Pic0 Strings Str1, Str2, ... , Str9, Str0 Apps Applications AppVars Application variables Groups Grouped variables System variables Xmin, Xmax, and others Notes about Variables • You can create as many list names as memory will allow (Chapter 11 in the guidebook). • Programs have user-defined names and share memory with variables (Chapter 16 in the guidebook).
Archiving Variables (Archive, Unarchive) You can archive data, programs, or other variables in a section of memory called user data archive where they cannot be edited or deleted inadvertently. These archived variables are indicated by asterisks (ä) to the left of the variable names. These archived variables cannot be edited or executed. They can only be seen and unarchived.
QuickPlot and Fit Equation QuickPlot and Fit Equation allows you to drop points on a graph screen and model a curve to those points using regression functions. You can select color and line style, draw points on a graph, and choose an equation to fit the drawn points. You can then store the results of the plot and equation. For details, refer to Chapter 12 in the guidebook. QuickPlot and Fit Equation is an option in the … / menu.
Using Ans in an Expression When an expression is evaluated successfully from the home screen or from a program, the TI-84 Plus C 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-84 Plus C, the value in Ans is retained in memory. You can use the variable Ans to represent the last answer in most places. Press y Z to copy the variable name Ans to the cursor location.
• When a menu item ends in an ellipsis (...), the item displays a secondary menu or editor when you select it. • When an asterisk (ä) appears to the left of a menu item, that item is stored in user data archive (Chapter 18 in the guidebook). Displaying a Menu While using your TI-84 Plus C, 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.
To page down six menu items at a time, press ƒ †. To page up six menu items at a time, press ƒ }. To go to the last menu item directly from the first menu item, press }. To go to the first menu item directly from the last menu item, press †. Selecting an Item from a Menu You can select an item from a menu in three 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 does not need to be displayed on the screen.
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, 4:Picture&Background, and 5:Statistics each access more than one secondary menu. VARS Y-VARS COLOR 1:Window... 2:Zoom... 3:GDB... 4:Picture & Background... X/Y, T/q, and U/V/W variables 5:Statistics... 6:Table... 7:String...
VARS Y-VARS COLOR 3: 4: 5: 6: 7: 8: 9: 0: A: B: C: D: E: BLACK MAGENTA GREEN ORANGE BROWN NAVY LTBLUE YELLOW WHITE LTGRAY MEDGRAY GRAY DARKGRAY To select an argument from the VARS COLOR menu, follow these steps. 1. Press ~ ~ to display the VARS COLOR menu. 2. Select the color argument, such as 2:RED. It is pasted to the cursor location. Note: Although the menu numbers for COLOR are 1-9, 0, A-E, colors are represented by the numbers 10-24 for selected programming commands.
3. Press 3 to select Overwrite All. The files in the selected group are ungrouped. Special Features of the TI-84 Plus C 3.5 Megabytes of Available Memory 3.5 MB of available memory is built into the TI-84 Plus C Silver Edition. About 21 kilobytes (K) of RAM (random access memory) are available for you to compute and store functions, programs, and data. About 3.
Matrices You can enter and save up to 10 matrices and perform standard matrix operations on them. For details, refer to Chapter 10 in the guidebook. Lists You can enter and save as many lists as memory allows for use in statistical analyses. You can attach formulas to lists for automatic computation. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves. For details, refer to Chapter 11 in the guidebook.
Removing a Faceplate 1. Lift the tab at the bottom edge of the faceplate away from the TI-84 Plus C Silver Edition case. 2. Carefully lift the faceplate away from the unit until it releases. Be careful not to damage the faceplate or the keyboard. Installing New Faceplates 1. Align the top of the faceplate in the corresponding grooves of the TI-84 Plus C Silver Edition case. 2. Gently click the faceplate into place. Do not force. 3.
Battery is 5% to 25% charged. Battery is charging. Warning: RAM memory will be lost if the battery charge is lost. You should back up or archive your variables if your battery power gets low. Displays this message when you turn on the unit. Message A Recharging the TI Rechargeable Battery You should make sure the TI-84 Plus C battery is charged for classroom use and before exams.
• Use of the battery in other devices may result in personal injury or damage to equipment or property. • There is a risk of explosion if a battery is replaced by the wrong type. Replacing the Battery Use only the TI Rechargeable Battery to replace the TI-84 Plus C battery. To replace the battery, follow these steps. 1. Use a small screwdriver to release the panel from the back of the handheld. 2. Remove the panel. 3. Remove the old battery. 4.
6. Replace the back panel and fasten the screws with a screwdriver. Disposing of Used Batteries Safely and Properly Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals. Discard used batteries according to local regulations. TI-84 Plus C Charging Station The TI-84 Plus C Charging Station is used to charge the TI Rechargeable Battery in the TI-84 Plus C Silver Edition graphing calculator.
Place the charging station on a flat, stable surface such as a table. You can also use a wheeled cart if you need to move the charging station from classroom to classroom. When deciding on a location, it is important to consider proximity to a power source such as a power strip or wall outlet.
Troubleshooting If the recharge fails: • Make sure the graphing calculator is seated properly in the slot. Batteries are not charged if the connector on the graphing calculator and the connector in the slot are not aligned. • Check the connector on the graphing calculator to ensure that it is clean. If there is build-up on the graphing calculator’s connector, you can remove it with a clean, dry cloth or a pencil eraser. Never use wet cloths or solutions of any kind.
• If you select 1:Quit (or press y 5 or ‘), then the home screen is displayed. • If you select 2:Goto, then the previous screen is displayed with the cursor at or near the error location. Note: If a syntax error occurs in the contents of a Y= function during program execution, then the Goto option returns to the Y= editor, not to the program. Correcting an Error To correct an error, follow these steps. 1. Note the error type (ERROR:error type). 2. Select 2:Goto, if it is available.
Table Yes Yes Function file Yes Yes GDB** Yes Yes List Yes Yes Matrix Yes Yes Number Yes Yes Complex Yes Yes Window Setup Yes Yes Certificate No No Backup No No * Programs created using commands available only in the latest OS version will not transfer to graphing calculators with an earlier OS version. * App Vars and Programs should be reviewed for use after the transfer between the TI-84 Plus Family and TI-84 Plus C graphing calculators.
Chapter 2: Math, Angle, and Test 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.
Addition, Subtraction, Multiplication, Division You can use + (addition, Ã), N (subtraction, ¹), … (multiplication, ¯), and à (division, ¥) with real and complex numbers, expressions, lists, and matrices. You cannot use à with matrices. If you need to input A/2, enter this as A †1/2 or A †.5. valueA N valueB valueA à valueB valueA+valueB valueA…valueB Note: For negation use Ì. You will get an error if you use Ì and ¹ incorrectly.
log(, 10^(, ln( You can use log( (logarithm, «), 10^( (power of 10, y G), and ln( (natural log, μ) with real or complex numbers, expressions, and lists. log(value) MathPrint™: 10power ln(value) Classic: 10^(power) Exponential e^( (exponential, y J) returns the constant e raised to a power. You can use e^( with real or complex numbers, expressions, and lists. MathPrint™: epower Classic: e^(power) Constant e (constant, y [e]) is stored as a constant. Press y [e] to copy e to the cursor location.
Negation Negation (Ì) returns the negative of value. You can use M with real or complex numbers, expressions, lists, and matrices. For subtraction, use ¹. Mvalue EOS™ rules (Chapter 1) determine when negation is evaluated. For example, L42 returns a negative number, because squaring is evaluated before negation. Use parentheses to square a negated number, as in (L4)2. Note: The negation symbol (M) is shorter and higher than the subtraction sign (N), which is displayed when you press ¹.
MATH NUM CMPLX PROB FRAC Displays the equation solver. B: Solver... * FUNC shortcut menu ALPHA F2. Note: Use Catalog Help for more syntax help when needed.Select a menu item and then press à to go to a syntax help editor (if the menu item is supported). 4Frac, 4Dec 4Frac (display as a fraction) displays an answer as its rational equivalent. You can use 4Frac with real or complex numbers, expressions, lists, and matrices.
Cube, Cube Root 3 (cube) returns the cube of value. You can use 3 with real or complex numbers, expressions, lists, and square matrices. value3 (cube root) returns the cube root of value. You can use 3‡( with real or complex numbers, expressions, and lists. 3‡( 3 ‡(value) x ‡ (Root) (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. MathPrint™: Classic: 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.
Classic: fnInt(expression,variable,lower,upper[,tolerance]) In MathPrint™ mode, the default H is 1EM3. You can switch to Classic mode to change H for investigations. Note: To speed the drawing of integration graphs (when fnInt( is used in a Y= equation), increase the value of the Xres window variable before you press s or set “Detect Asymptotes” off in FORMAT. Using the Equation Solver Solver Solver displays the equation solver, in which you can solve for any variable in an equation.
2. Enter the expression in any of three ways. • Enter the expression directly into the equation solver. • Paste a Y= variable name from the YVARS shortcut menu (t a) to the equation solver. • Press y K, paste a Y= variable name from the YVARS shortcut menu, and press Í. The expression is pasted to the equation solver. The expression is stored to variables E1, E2 (MathPrint™ mode) or eqn (Classic mode) as you enter it. 3. Press † (MathPrint™ mode) or Í (Classic mode).
Solving for a Variable in the Equation Solver To solve for a variable using the equation solver after the equation has been stored on the equation entry screen, follow these steps. 1. Select B: 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.
upper + lower 2 The default guess is calculated as ----------------------------------------- . 4. Edit bound={lower,upper}. lower and upper are the bounds between which a solution is searched. This is optional, but it may help find the solution more quickly. The default is bound={L1â99,1â99}. 5. Move the cursor to the variable for which you want to solve and press ƒ \. The solution is displayed next to the variable for which you solved..
Equations with Multiple Roots Some equations have more than one solution. You can enter a new initial guess or new bounds to look for additional solutions. Use the graph or a table of values to locate a guess as the starting value for the solver routine. Further Solutions After you solve for a variable, you can continue to explore solutions from the interactive solver editor. Edit the values of one or more variables.
MATH NUM CMPLX PROB FRAC Fractional part 4: fPart( 5: 6: 7: 8: 9: 0: int( min( max( lcm( gcd( remainder( ** A: 4n/d3 4Un/d ** B: ** 4F3 4D C: Un/d ** D: n/d Greatest integer Minimum value Maximum value Least common multiple Greatest common divisor Reports the remainder as a whole number from a division of two whole numbers where the divisor is not zero. Converts an improper fraction to a mixed number or a mixed number to an improper fraction.
round(value[,#decimals]) 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) Note: The way the fractional result is displayed depends on the Answers mode setting. To convert from one format to another, use 4F3 4D on the FRAC shortcut menu (t ^ 4).
int( int( (greatest integer) returns the largest integer real or complex numbers, expressions, lists, and matrices. int(value) Note: For a given value, the result of int( is the same as the result of iPart( for nonnegative numbers and negative integers, but one integer less than the result of iPart( for negative non-integer numbers. min(, max( min( (minimum value) returns the smaller of valueA and valueB or the smallest element in list.
lcm(, gcd( lcm( returns the least common multiple of valueA and valueB, both of which must be nonnegative integers. When listA and listB are specified, lcm( returns a list of the least common multiple of each pair of elements. If list and value are specified, lcm( finds the least common multiple of each element in list and value. gcd( returns the greatest common divisor of valueA and valueB, both of which must be nonnegative integers.
remainder(dividend, list) remainder(list, list) 4n/d3 4Un/d 4n/d3 4Un/d converts an improper fraction to a mixed number or a mixed number to an improper fraction. You can also access 4n/d3 4Un/d from MATH FRAC and the FRAC shortcut menu (t ^ 3). 4F3 4D 4F3 4D converts a fraction to a decimal or a decimal to a fraction. You can also access 4F3 4D from the MATH FRAC and the FRAC shortcut menu (t ^ 4). For complex number conversion, use 4Frac or 4Dec only ( 1 or 2).
Un/d Un/d displays the mixed number template. You can also access Un/d from MATH FRAC and the FRAC shortcut menu (t ^ 2). In the fraction, n and d must be non-negative integers. U, n, and d must all be integers. If U is a non-integer, the result may be converted U … n/d. If n or d is a non-integer, a syntax error is displayed. The whole number, numerator, and denominator may each contain a maximum of three digits..
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. For example, in Real mode ln(L1) returns an error; in a+bi mode ln(L1) returns an answer. Real mode a+bi mode Entering Complex Numbers Complex numbers are stored in rectangular form, but you can enter a complex number in rectangular form or polar form, regardless of the mode setting.
When you use the n/d template, a fraction cannot contain a complex number. " You can use division to compute the answer: Note about Radian Versus Degree Mode Radian mode is recommended for complex number calculations. Internally, the calculator converts all entered trigonometric values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic functions.
To enter a complex number in rectangular form, enter the value of a (real component), press à or ¹, enter the value of b (imaginary component), and press y V (constant). real component(+ or N)imaginary component i Polar-Complex Mode Polar-complex mode recognizes and displays a complex number in the form re^ (qi), where r is the magnitude, e is the base of the natural log, q is the angle, and i is a constant equal to –1 .
MATH CMPLX (Complex) Operations MATH CMPLX Menu To display the MATH CMPLX menu, press ~ ~. MATH NUM CMPLX PROB FRAC Returns the complex conjugate. 1: conj( 2: 3: 4: 5: 6: 7: real( imag( angle( abs( 4Rect 4Polar Returns the real part. Returns the imaginary part. Returns the polar angle. Returns the magnitude (modulus). Displays the result in rectangular form. Displays the result in polar form. Note: Use Catalog Help for more syntax help when needed.
Classic imag( imag( (imaginary part) returns the imaginary (nonreal) part of a complex number or list of complex numbers. imag(a+bi) returns b. imag(re^(qi)) returns r†sin(q) MathPrint™ Classic 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).
abs(a+bi) returns . abs(re^(qi)) returns r (magnitude) MathPrint™ Classic 4Rect 4Rect (display as rectangular) displays a complex result in rectangular form. It is valid only at the end of an expression. It is not valid if the result is real. complex result8Rect returns a+bi. 4Polar 4Polar (display as polar) displays a complex result in polar form. It is valid only at the end of an expression. It is not valid if the result is real. complex result8Polar returns re^(qi).
MATH PROB (Probability) Operations MATH PROB Menu To display the MATH PROB menu, press |. MATH NUM CMPLX PROB FRAC Random-number generator 1: rand * * * 2: 3: 4: 5: 6: 7: 8: * FUNC nPr nCr ! randInt( randNorm( randBin( randIntNoRep( shortcut menu Number of permutations Number of combinations Factorial Random-integer generator Random # from Normal distribution Random # from Binomial distribution Random ordered list of integers in a range ALPHA F2.
MathPrint™: Classic: items nCr number MathPrint™ Classic Factorial ! (factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorials for each integer or multiple of .5. value must be ‚ L.5 and 69. value! Note: The factorial is computed recursively using the relationship (n+1)! = n…n!, until n is reduced to either 0 or L1/2. At that point, the definition 0!=1 or the definition (L1à2)!=‡p is used to complete the calculation. Hence: n!=n…(nN1)…(nN2)… ...
randInt(lower,upper [numtrials]). " randNorm( randNorm( (random Normal) generates and displays a random real number from a specified Normal distribution. Each generated value could be any real number, but most will be within the interval [mN3(s), m+3(s)]. To generate a list of random numbers, specify an integer > 1 for numtrials (number of trials); if not specified, the default is 1. randNorm(m,s[,numtrials]).
randIntNoRep( randIntNoRep( returns a random ordered list of integers from a lower integer to an upper integer. The list of integers may include the lower integer and the upper integer. Numtrials is optional and lists the first numtrials in the output. randIntNoRep(lowerint, upperint, [numtrials]) " ANGLE Operations ANGLE Menu To display the ANGLE menu, press y ;. The ANGLE menu displays angle indicators and instructions. The Radian/Degree mode setting affects the interpretation of ANGLE menu entries.
Degree ¡ (degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In Radian mode, you can use ¡ to convert degrees to radians. value¡ {value1,value2,value3,value4,...,value n}¡ ¡ also designates degrees (D) in DMS format. ' (minutes) designates minutes (M) in DMS format. " (seconds) designates seconds (S) in DMS format. Note: " is not on the ANGLE menu. To enter ", press ƒ [ã].
R8Pr( converts rectangular coordinates to polar coordinates and returns r. R8Pq( converts rectangular coordinates to polar coordinates and returns q. x and y can be lists. R8Pr(x,y), R8Pq(x,y) Note: Radian mode is set. P8Rx( converts polar coordinates to rectangular coordinates and returns x. P8Ry( converts polar coordinates to rectangular coordinates and returns y. r and q can be lists. P8Rx(r,q), P8Ry(r,q) Note: Radian mode is set.
Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values. valueAƒvalueB valueA‚valueB valueAvalueB valueA=valueB valueA>valueB valueA
and, or, xor and, or, and xor (exclusive or) return a value of 1 if an expression is true or 0 if an expression is false, according to the table below. valueA and valueB can be real numbers, expressions, or lists. valueA and valueB valueA or valueB valueA xor valueB valueA valueB and or xor ƒ0 ƒ0 returns 1 1 0 ƒ0 0 returns 0 1 1 0 ƒ0 returns 0 1 1 0 0 returns 0 0 0 not( not( returns 1 if value (which can be an expression) is 0.
Chapter 3: Function Graphing Getting Started: Graphing a Circle Getting Started is a fast-paced introduction. Read the chapter for details. Graph a parabola in the standard viewing window. Then translate this parabola to see a family of curves. Use ZDecimal to adjust the display to trace by 0.1. 1. In Func mode, press o to display the Y= editor. Press Ë 2 „ ¡ Í to enter the function Y=.2X 2, which defines a parabola. You can define one function in terms of another.
4. To trace the family of parabolas by 0.1 step size, press q 4:ZDecimal. Press r and use | ~ to trace along a graph. Use } † to switch functions. Defining Graphs Graphing Mode Similarities Chapter 3 specifically describes function graphing, but the steps shown here are similar for each 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.
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-84 Plus C has four graphing modes.
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. To erase a function, press ‘. 3. Enter or edit the expression to define the function. • You may use functions and variables (including matrices and lists) in the expression. When the expression evaluates to a nonreal number, the value is not plotted; no error is returned.
"expression"!Yn When the instruction is executed, the TI-84 Plus C stores the expression to the designated variable Yn, selects the function, and displays the message Done. Evaluating Y= Functions in Expressions You can calculate the value of a Y= function Yn at a specified value of X. A list of values returns a list. Yn(value) Yn({value1,value2,value3, . . .
Plot1 is turned on. Plot2 and Plot3 are turned off. 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.
Icon ì í Style Description Animate A circular cursor traces the leading edge of the graph without drawing a path Dot-Thick A dot (3 x 3 pixel) enhances the view around the actual plotted point; this is the default in Dot mode. Dot-Thin A small dot (1 x1 pixel) represents each plotted point. Note: Some graph styles are not available in all graphing modes. Chapters 4, 5, and 6 list the styles for Par, Pol, and Seq modes.
Note: When é or ê is selected for a Y= function that graphs a family of curves, such as Y1={1,2,3}X, the four shading patterns rotate for each member of the family of curves. In this case, all three graphs of Y1={1,2,3}X will be the same color. Setting a Graph Style from a Program To set the graph style from a program, select H:GraphStyle( from the PRGM CTL menu. To display this menu, press while in the program editor. function# is the number of the Y= function name in the current graphing mode.
Displaying the Window Variables To display the current window variable values, press p. The window editor above and to the right shows the default values in Func graphing mode and Radian angle mode. The window variables differ from one graphing mode to another. Xres sets pixel resolution (1 through 8) for function graphs only. The default is 1. • At Xres=1, functions are evaluated and graphed at each graphed pixel on the x-axis.
FULL HORIZONTAL GRAPH-TABLE Xmax – Xmin X = --------------------------------------264 Xmax – Xmin X = --------------------------------------264 Xmax – Xmin X = --------------------------------------184 Ymax – Ymin Y = -------------------------------------164 Ymax – Ymin Y = -------------------------------------80 Ymax – Ymin Y = -------------------------------------144 TraceStep = 2@X (Function graphing only) TraceStep = 2@X (Function graphing only) TraceStep = 2@X (
3. Press | and ~ to scroll the available options. Note: There is no need to press Enter to choose the menu options. The last option displayed will be the setting. 4. Press † to go to the next setting. The options displayed on the format screen are the settings that will be applied to the graph. RectGC, PolarGC RectGC (rectangular graphing coordinates) displays the cursor location as rectangular coordinates X and Y.
Smart Graph Smart Graph is a TI-84 Plus C feature that re-displays the last graph immediately when you press s, but only if all graphing factors that would cause replotting have remained the same since the graph was last displayed. If you performed any of the following actions since the graph was last displayed, the TI-84 Plus C will replot the graph based on new values when you press s.
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.
Trace cursor on the curve If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately. Moving the Trace Cursor from Function to Function To move the trace cursor from function to function, press † and }. The cursor follows the order of the selected functions in the Y= editor. The trace cursor moves to each function at the same X value. If ExprOn format is selected, the expression is updated.
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 A: ZQuadrant1 B: ZFrac1/2 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.
4. When you have defined the box, press Í to replot the graph. To use ZBox to define another box within the new graph, repeat steps 2 through 4. To cancel ZBox, press ‘. 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; change as needed. 2.
ZStandard ZStandard replots the functions immediately. It updates the window variables to the standard values shown below. [Xmin, Xmax] @X @Y TraceStep 1 .07575... .12195 .151515... 1 1 .07575... .25 .151515... 1 1 .1086956... .1388888889... .21739130... Xscl [Ymin, Ymax] Yscl Xres FULL [-10, 10] 1 [-10, 10] 1 HORIZONTAL [-10, 10] 1 [-10, 10] GRAPH-TABLE [-10, 10] 1 [-10, 10] ZTrig ZTrig replots the functions immediately.
ZFrac1/2 ZFrac1/2 replots the functions immediately. It updates the window variables to preset values, as shown below.. [Xmin, Xmax] Xscl [Ymin, Ymax] Yscl Xres @X @Y TraceStep FULL [-33, 33] 1 [-41/2, 41/2] 1 1 1/4 1/4 1/2 HORIZONTAL [-33, 33] 1 [-10, 10] 1 1 1/4 1/4 1/2 GRAPH-TABLE [-23, 23] 1 [-18, 18] 1 1 1/4 1/4 1/2 ZFrac1/3 ZFrac1/3 replots the functions immediately. It updates the window variables to preset values, as shown below.
[Xmin, Xmax] Xscl [Ymin, Ymax] Yscl Xres @X @Y TraceStep FULL [-33/4, 33/4] 1 [-41/8, 41/8] 1 1 1/16 1/16 1/8 HORIZONTAL [-33/4, 33/4] 1 [-5/2, 5/2] 1 1 1/16 1/16 1/8 GRAPH-TABLE [-23/4, 23/4] 1 [-9/2, 9/2] 1 1 1/16 1/16 1/8 ZFrac1/10 ZFrac1/10 replots the functions immediately. It updates the window variables to preset values, as shown below.
Changing XFact and YFact You can change XFact and YFact in either of two ways. • Enter a new value. The original value is cleared automatically when you enter the first digit. • Place the cursor on the digit you want to change, and then enter a value or press { to delete it. Using ZOOM MEMORY Menu Items from the Home Screen or a Program From the home screen or a program, you can store directly to any of the user-defined ZOOM variables.
To move the cursor from function to function at the entered X value, press } or †. To restore the freemoving cursor, press | or ~. 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 an intersection, follow these steps. 1. Select 5:intersect from the CALCULATE menu. The current graph is displayed with First curve? in the bottom-left corner. 2. Press † or }, if necessary, to move the cursor to the first function, and then press Í. Second curve? is displayed in the bottom-left corner. 3. Press † or }, if necessary, to move the cursor to the second function, and then press Í. 4.
3. Set lower and upper limits as you would set left and right bounds for zero. The integral value is displayed, and the integrated area is shaded. Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or any action that invokes Smart Graph to clear the shaded area.
Chapter 4: Parametric Graphing 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 vertical component vector is defined by X2T and Y2T. 5. Press 0 Í to define X2T. 6. Press t a † Í Í to define Y2T. The horizontal component vector is defined by X3T and Y3T. 7. Press t a Í Í to define X3T. 8. Press 0 to define Y3T. 9. Press Í. Note: The cursor moves to X4T. 10. Change the graph line styles. • Press } } | | Í †. Press ~ as necessary to change the graph style to ë (Path) for X3T and Y3T. Press Í twice to select the graph style. • Press } Í †.
12. Press s. The plotting action simultaneously shows the ball in flight and the vertical and horizontal component vectors of the motion. Note: To simulate the ball flying through the air, set graph style to ì (animate) for X1T and Y1T. 13. Press r to obtain numerical results and answer the questions at the beginning of this section. Tracing begins at Tmin on the first parametric equation (X1T and Y1T). As you press ~ to trace the curve, the cursor follows the path of the ball over time.
Icon Style Description è Thick A thick solid line connects plotted points. é Above Shading covers the area above the graph ê Below Shading covers the area below the graph ë Path A circular cursor traces the leading edge of the graph and draws a path ì Animate A circular cursor traces the leading edge of the graph without drawing a path Dot-Thick A dot (3 x 3 pixel) enhances the view around the actual plotted point; this is the default in Dot mode.
Displaying a Graph When you press s, the TI-84 Plus C 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. The window variables define the viewing window. As the graph is plotted, X, Y, and T are updated. Smart Graph (see Chapter 3) applies to parametric graphs. Window Variables and Y.VARS Menus You can perform these actions from the home screen or a program.
In RectGC format, TRACE updates and displays the values of X, Y, and T if CoordOn format is on. In PolarGC format, X, Y, R, q and T are updated; if CoordOn format is selected, R, q, and T are displayed. The X and Y (or R and q) values are calculated from T. To move five plotted points at a time on a function, press y | or y ~. If you move the cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.
Chapter 5: Polar Graphing 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.
Defining and Displaying Polar Graphs 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.
Selecting and Deselecting Polar Equations The TI-84 Plus C graphs only the selected polar equations. In the Y= editor, a polar equation is selected when the = sign is highlighted. You may select any or all of the equations. To change the selection status, move the cursor onto the = sign, and then press Í. Setting Window Variables To display the window variable values, press p. These variables define the viewing window. The values below are defaults for Pol graphing in Radian angle mode.
• Store polar equations. • Select or deselect polar equations. • Store values directly to window variables. 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.
ZOOM ZOOM operations in Pol 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. The q window variables (qmin, qmax, and qstep) are not affected, except when you select ZStandard. The VARS ZOOM secondary menu ZT/Zq items 4:Zqmin, 5:Zqmax, and 6:Zqstep are zoom memory variables for Pol graphing. CALC CALC operations in Pol graphing work the same as in Func graphing.
Chapter 6: Sequence Graphing Getting Started: Forest and Trees Note: 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. Press y .
5. Press p 0 to set nMin=0. Press † 50 to set nMax=50. nMin and nMax evaluate forest size over 50 years. Set the other window variables. PlotStart=1 Xmin=0 Ymin=0 PlotStep=1 Xmax=50 Ymax=6000 Xscl=10 Yscl=1000 6. Press r. Tracing begins at nMin (the start of the forestry plan). Press ~ to trace the sequence year by year. The sequence is displayed at the top of the screen. The values for n (number of years), X (X=n, because n is plotted on the x-axis), and Y (tree count) are displayed at the bottom.
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. nMin in the Y= editor is the same as nMin in the window editor.
You can enter the function name from the keyboard (y [u], y [v], y [w]) or use the shortcut menu t a. Generally, sequences are either nonrecursive or recursive. Sequences are evaluated only at consecutive integer values. n is always a series of consecutive integers, starting at zero or any positive integer. Nonrecursive Sequences In a nonrecursive sequence, the nth term is a function of the independent variable n. Each term is independent of all other terms.
• If each term in the sequence is defined in relation to the previous term, as in u(nN1), you must specify an initial value for the first term. Note: Use q 0: ZoomFit to display the graph. • If each term in the sequence is defined in relation to the term that precedes the previous term, as in u(nN2), you must specify initial values for the first two terms. Enter the initial values as a list enclosed in brackets { } with commas separating the values.
Selecting Axes Combinations Setting the Graph Format To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings. The axes setting on the top line of the screen is available only in Seq mode. Time Web uv vw uw RectGC PolarGC CoordOn CoordOff GridOff GridDot GridLine GridColor Axes Type of sequence plot (axes) Sets cursor coordinates. Sets coordinates display on or off.
• Quick Zoom applies to all directions. To center the viewing window on the current cursor location after you have moved the trace cursor, pressÍÍ. The trace cursor returns to nMin. In Web format, the trail of the cursor helps identify points with attracting and repelling behavior in the sequence. When you begin a trace, the cursor is on the x-axis at the initial value of the first selected function. Note: To move the cursor to a specified n during a trace, enter a value for n, and press Í.
Graphing Web Plots Graphing a Web Plot To select Web axes format, press y . ~ 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.
2. Press y . 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 4. Press s to graph the sequence. 5. Press y . and select the Web axes setting. 6. Press p and change the variables below. Xmin=L10 Ymin=L10 Ymax=10 Yscl=1 Xmax=10 7. Press s to graph the sequence. 8. Press r, and then press ~ to draw the web. The displayed cursor coordinates n, X (u(nN1)), and Y (u(n)) change accordingly.
Graphing Phase Plots Graphing with uv, vw, and uw The phase-plot axes settings uv, vw, and uw show relationships between two sequences. To select a phase-plot axes setting, press y ., press ~ until the cursor is on uv, vw, or uw, and then press Í. Axes Setting x-axis y-axis uv u(n) v(n) vw v(n) w(n) uw u(n) w(n) Example: Predator-Prey Model Use the predator-prey model to determine the regional populations of a predator and its prey that would maintain population equilibrium for the two species.
3. Press p and set the variables as shown below. nMin=0 nMax=400 PlotStart=1 PlotStep=1 Ymin=0 Ymax=300 Yscl=100 Xmin=0 Xmax=400 Xscl=100 4. Press s to graph the sequence. 5. Press r ~ to individually trace the number of rabbits (u(n)) and foxes (v(n)) over time (n). Note: Press a number, and then press Í to jump to a specific n value (month) while in TRACE. 6. Press y . ~ ~ Í to select uv axes format. 7. Press p and change these variables as shown below. Xmin=84 Xmax=237 Xscl=50 8.
Chapter 7: Tables 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 - to display the TABLE SETUP screen: 4. • Press Ì 10 Í to set TblStart= L10. • Press 1 Í to set @Tbl= 1.
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). You can adjust TblStart and @Tbl while in the Table screen. Independent and dependent variables vary with Func mode settings (X, T, q,n). For example, select an X value in the X column, press + and edit the @Tbl value. The table will update and the cursor will be on the new TblStart X value.
1. Press y 0 to display the table, and then press ~ or | to move the cursor to a dependentvariable column. 2. Press } until the cursor is on the function name at the top of the column. The function is displayed on the bottom line. 3. Press Í. The cursor moves to the bottom line. Edit the function. 4. Press Í or †. The new values are calculated. The table and the Y= function are updated automatically.
Current cell Dependent-variable values in the second and third columns Independent-variable values in the first column Current cell’s full value Note: When the table first displays, the message “Press + for @Tbl” is on the status bar. This message reminds you that you can select an independent variable for a new TblStart and press à to change @Tbl at any time. Independent and Dependent Variables The current graphing mode determines which independent and dependent variables are displayed in the table.
Changing Table Settings from the Table View You can change table settings from the table view by first highlighting an x value for the new TblStart, then pressing Ã, and entering a new @ value. 1. Press o and then press 1 t ^ 1 2 ~ „ to enter the function Y1=1/2x. 2. Press y - to display the TABLE SETUP screen: • Press 3 Í to set TblStart= 3. • Press 1 Í to set @Tbl= 1. • Press Í to select Indpnt: Auto (automatically generated independent values). 3.
7. Press Í. Displaying Other Dependent Variables All selected Y= functions will display in a table. To see functions not in view, press ~ or |. The independent variable always remains in the left column, except during a trace with parametric graphing mode and G-T split-screen mode set. Note: To select an ordering of the Y= functions (Y-vars) to display, pick only the Y= functions you wish to view. For example, to simultaneously display Y4 and Y7 on the table, go to the Y= editor and deselect Y5 and Y6.
Chapter 8: Draw Instructions Getting Started: Drawing a Tangent Line Getting Started is a fast-paced introduction. Read the chapter for details. 2 2 Suppose you want to find the equation of the tangent line at X = ------- for the function Y=sin(X). 1. Before you begin, press z and set the decimal setting to 4 places. Select Radian and Function (if necessary). 2. Press o to display the Y= editor. Press ˜ „ ¤ to store sin(X) in Y1. 3.
5. Press y C 2 ¤ ¥ 2. 6. Press Í. The tangent line is drawn; the X value and the tangent-line equation are displayed on the graph. Consider repeating this activity with the mode set to the number of decimal places desired. The first screen shows four decimal places. The second screen shows the decimal setting at Float. Using the DRAW Menu DRAW Menu To display the DRAW menu, press y <.
Before Drawing on a Graph The DRAW instructions draw on top of graphs. Therefore, before you use the DRAW instructions, consider whether you want to perform one or more of the following actions. Note: DRAW will not change the Background Image Vars. • Change the mode settings on the mode screen. • Change the format settings on the format screen. You can press y . or use the shortcut on the mode screen to go to the format graph screen. • Enter or edit functions in the Y= editor.
Drawing Line Segments Setting Graph Styles This table describes the graph styles available for drawing line segments. Use the styles to visually differentiate line segments. You can also set the line color. Icon Style Description ç Thin A solid line connects plotted points è Thick A thick solid line connects plotted points; this is the default.
Drawing a Line Segment from the Home Screen or a Program Line( also draws a line segment between the coordinates (X1,Y1) and (X2,Y2). The values may be entered as expressions. Line(X1,Y1,X2,Y2[,erase#,[color#,linestyle#]]) To erase a line segment, enter Line(X1,Y1,X2,Y2,0) Note: DRAW commands can erase parts of graphs and the axes. DRAW commands will not erase a Background Image.
To cancel Horizontal or Vertical, press ‘. Drawing a Line from the Home Screen or a Program Horizontal (horizontal line) draws a horizontal line at Y=y. y, which can be an expression but not a list. Horizontal y [,color#, line style#] Vertical (vertical line) draws a vertical line at X=x. x, which can be an expression but not a list. Vertical x [,color#, line style#] To instruct the TI-84 Plus C to draw more than one horizontal or vertical line, separate each instruction with a colon ( : ).
5. Press Í. In Func mode, the X value at which the tangent line was drawn is displayed on the bottom of the screen, along with the equation of the tangent line. In all other modes, the dy/dx value is displayed. 6. Change the fixed decimal setting on the mode screen if you want to see fewer digits displayed for X and the equation for Y. Drawing a Tangent Line from the Home Screen or a Program Tangent( (tangent line) draws a line tangent to expression in terms of X, such as Y1 or X2, at point X=value.
DrawF expression [,color#]) 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. When you select 8:DrawInv from the DRAW menu, the TI-84 Plus C returns to the home screen or the program editor. DrawInv is not interactive. DrawInv works in Func mode only. DrawInv expression [,color#]) Note: You cannot use a list of expressions with DrawInv.
Xleft and Xright, if included, specify left and right boundaries for the shading. Xleft and Xright must be numbers between Xmin and Xmax, which are the defaults. pattern specifies one of four shading patterns. pattern=1 pattern=2 pattern=3 pattern=4 vertical (default) horizontal negative—slope 45¡ positive—slope 45¡ patres specifies one of eight shading resolutions.
You can also choose a color name in the menu (color sub-menu). 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. Press t b to change the color and line style using spinner menus. 3. Place the cursor at the center of the circle you want to draw. Press Í. 4. Move the cursor to a point on the circumference. Press Í to draw the circle on the graph.
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. Press t b to change the color. 3. Place the cursor where you want the text to begin. 4. Enter the characters. Press ƒ or y 7 to enter letters and q. You may enter TI-84 Plus C functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies.
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. Pen is also not included in Catalog Help. You can capture the screen you created using TI-Connect™ software and save it to your computer for homework or teaching material or store it as a picture file (Pic Var) on your TI-84 Plus C. To draw on a displayed graph, follow these steps. 1. Select A:Pen from the DRAW menu. 2. Press t b to change the color. 3.
4. Press Í to draw the point. To continue drawing points, repeat steps 2,3 and 4. To cancel Pt-On(, press ‘. 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. Press t b to change the color and mark (as required). 3. Move the cursor to the point you want to erase. 4. Press Í to erase the point. To continue erasing points, repeat steps 2 and 3. To cancel Pt-Off(, press ‘.
Note: If you specified mark to turn on a point with Pt-On(, you must specify mark when you turn off the point with Pt-Off(. Pt-Change( does not have the mark option. Drawing Pixels TI-84 Plus C Pixels A pixel is a square dot on the TI-84 Plus C display. The Pxl- (pixel) instructions let you turn on, turn off, or reverse a pixel (1x1 pixel) on the graph using the cursor. When you select a pixel instruction from the DRAW POINTS menu, the TI-84 Plus C returns to the home screen or the program editor.
Storing Graph Pictures (Pic) DRAW STO Menu To display the DRAW STO menu, press y < | |. You can use the DRAW STO menu items to store and recall Pic Vars. When you select an instruction from the DRAW STO menu, the TI-84 Plus C returns to the home screen or the program editor. DRAW POINTS STO BACKGROUND Stores the current picture. 1: StorePic Recalls a saved picture. 2: RecallPic Stores the current graph database. 3: StoreGDB Recalls a saved graph database.
Note: You also can select a variable from the PICTURE secondary menu ( 4). The variable is pasted next to RecallPic. 3. Press Í to display the current graph with the picture superimposed on it. Note: Pictures are drawings. You cannot trace a curve that is part of a picture. Recalling a Pic from the Graph Screen To recall a picture from the graph screen: 1. Press s. 2. Select 2:RecallPic from the DRAW STO menu. 3. Press ~ in the spinner menu to preview Pic Vars and select a picture. 4. Press Í .
Note: You also can select a variable from the GDB secondary menu ( 3). The variable is pasted next to StoreGDB. 3. Press Í to store the current database to the specified GDB variable. Recalling Graph Databases (GDB) 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.
Chapter 9: Split Screen Getting Started: Exploring the Unit Circle Getting Started is a fast-paced introduction. Read the chapter for details. Use 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 Parametric graphing mode. Press † † † † ~ ~ Í to select Graph-Table split-screen mode.
7. Press y 0 to make the table portion of the split screen active. Using Split Screen Setting a Split-Screen Mode To set a split-screen mode, press z, and then move the cursor to Horizontal (Horiz) or Graph-Table (G-T) and press Í. • Select Horizontal to display the graph screen and another screen split horizontally. • Select Graph-Table to display the graph screen and table screen split vertically. Note: Classic mode is used in this example.
Some screens are never displayed as split screens. For example, if you press z in Horizontal or Graph-Table mode, the mode screen is displayed as a full screen. If you then press a key that displays either half of a split screen, such as r, the split screen returns. When you press a key or key combination in either Horizontal or Graph-Table mode, the cursor is placed in the half of the display to which that key applies.
Graph-Table Split Screen Graph-Table Mode In Graph-Table split-screen mode, a vertical line splits the screen into left and right halves. The left half displays all active graphs and plots. The right half displays either table data corresponding to the graph at the left or list data corresponding to the plot at the left. Moving from Graph View to Table View in Graph-Table Mode To use the graph view (left side) of the split screen: • Press s or r.
TI-84 Plus C Pixels in Horizontal and Graph-Table Modes TI-84 Plus C Pixels in Horizontal and Graph-Table Modes Note: Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on. Graph Area Pixel Rows Pixel Columns FULL 0-164 0-264 HORIZ 0-80 0-264 G-T 0-144 0-184 DRAW POINTS Menu Pixel Instructions See Chapter 8 “Draw Instructions” for more information. DRAW Menu Text( Instruction See Chapter 8 “Draw Instructions” for more information.
Chapter 10: Matrices Getting Started: Using the MTRX Shortcut Menu Getting Started is a fast-paced introduction. Read the chapter for details. You can use the MTRX shortcut menu (t `) to enter a quick matrix calculation on the home screen or in the Y= editor. Note: To input a fraction in a matrix, delete the pre-populated zero first. Example: Add the following matrices: and store the result to matrix C. 1. Press t ` to display the quick matrix editor.
5. Press v y Q and select 3:[C]. 6. Press Í to store the matrix to [C]. In the matrix editor (y Q), you can see that matrix [C] has a dimension of 2x2. You can press ~ ~ to display the EDIT screen and then select [C] to edit it.
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-84 Plus, 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 y . 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. You can also define a matrix using the MTRX shortcut menu (t `).The TI-84 Plus C 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-84 Plus matrices. Fractions are stored as real numbers and can be used in matrices.
Select the matrix from the MATRX EDIT menu and enter or accept the dimensions. The center portion of the matrix editor displays up to ten rows and five columns of a matrix, showing the values of the elements in abbreviated form if necessary. The full value of the current element, which is indicated by the rectangular cursor, is displayed on the bottom line. In MathPrint™ mode: • An arrow at the left or right indicates additional columns. • An arrow at the top or bottom indicates additional rows.
Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions.
Using Editing-Context Keys Key Function | or ~ Moves the edit cursor within the value † or } Stores the value displayed on the edit line to the matrix element; switches to viewing context and moves the cursor within the column Í Stores the value displayed on the edit line to the matrix element; switches to viewing context and moves the cursor to the next row element ‘ Clears the value on the bottom line Any entry character Copies the character to the location of the edit cursor on the bottom line
• Press y [ ] ] to indicate the end of the matrix. The resulting matrix is displayed in the form: [[element1,1,...,element1,n],...,[elementm,1,...,elementm,n]] Any expressions are evaluated when the entry is executed. Note: • The commas that you must enter to separate elements are not displayed on output. • Closing brackets are required when you enter a matrix directly on the home screen or in an expression. • When you define a matrix using the matrix editor, it is automatically stored.
Note: You cannot copy a matrix output from the history. Accessing a Matrix Element On the home screen or from within a program, you can store a value to, or recall a value from, a matrix element. The element must be within the currently defined matrix dimensions. Select matrix from the MATRX NAMES menu.
Multiplying a matrix by a value or a value by a matrix returns a matrix in which each element of matrix is multiplied by value. matrix…value value…matrix Negation Negating a matrix returns a matrix in which the sign of every element is changed. Lmatrix Note: For negation use Ì. You get an error message if you use Ì and ¹ incorrectly. abs( abs( (absolute value, MATH NUM menu or ALPHA F2) returns a matrix containing the absolute value of each element of matrix.
Inverse Use the L1 function (œ) or › L1 to invert a matrix. matrice must be square. The determinant cannot equal zero. 1 matrixL Powers To raise a matrix to a power, matrix must be square. You can use 2 (¡), 3 (MATH menu), or ^power (›) for integer power between 0 and 255.
MathPrint™ Classic 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-by-element 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.
iPart(matrix) fPart(matrix) int(matrix) Using the MATRX MATH Operations MATRX MATH Menu To display the MATRX MATH menu, press y ~. NAMES 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+( EDIT Calculates the determinant. Transposes the matrix. Returns the matrix dimensions. Fills all elements with a constant. Returns the identity matrix. Returns a random matrix. Appends two matrices.
det( det( (determinant) returns the determinant (a real number) of a square matrix. det(matrix) Transpose T (transpose) returns a matrix in which each element (row, column) is swapped with the corresponding element (column, row) of matrix. matrixT Accessing Matrix Dimensions with dim( dim( (dimension) returns a list containing the dimensions ({rows columns}) of matrix. dim(matrix) Note: dim(matrix)"Ln:Ln(1) returns the number of rows. dim(matrix)"Ln:Ln(2) returns the number of columns.
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. {rows,columns}"dim(matrixname) Fill( Fill( stores value to every element in matrixname. Fill(value,matrixname) identity( identity( returns the identity matrix of dimension rows × dimension columns.
randM(rows,columns) 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.
Matr4list(matrix,column#,listname) List4matr( List4matr( (lists stored to matrix) fills matrixname column by column with the elements from each list. If dimensions of all lists are not equal, List4matr( fills each extra matrixname row with 0. Complex lists are not valid. List4matr(listA,...,list n,matrixname) 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.
rref( (reduced row-echelon form) returns the reduced row-echelon form of a real matrix. The number of columns must be greater than or equal to the number of rows. rref(matrix) 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) …row( …row( (row multiplication) returns a matrix.
…row+(value,matrix,rowA,rowB) Chapter 10: Matrices 163
Chapter 11: Lists 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 user-created list. Then display the results in fraction form. Begin this example on a blank line on the home screen. 1. Press y 9 ~ to display the LIST OPS menu. 2. Press 5 to select 5:seq(, which opens a wizard to assist in the entry of the syntax. 3.
4. Press ¿, and then press y 7 to turn on alpha-lock. Press [S] [E] [Q], and then press ƒ to turn off alpha-lock. Press 1 to complete the list name. Note: Since the seq( command creates a list, you can name give the list a name up to five characters long. 5. Press Í to generate the list and store it in SEQ1. The list is displayed on the home screen. Note: An ellipsis (...) in Classic mode indicates that the list continues beyond the viewing window.
Creating a List Name on the Home Screen To create a list name on the home screen, follow these steps. 1. Press y E, enter one or more list elements, and then press y F. Separate list elements with commas. List elements can be real numbers, complex numbers, or expressions. 2. Press ¿. 3. Press ƒ [letter from A to Z or q] to enter the first letter of the name. 4. Enter zero to four letters, q, or numbers to complete the name. 5. Press Í. The list is displayed on the next line.
Storing and Displaying Lists Storing Elements to a List You can store list elements in either of two ways. • Use brackets and ¿ on the home screen. • Use the stat list editor (Chapter 12). The maximum dimension of a list is 999 elements. Note: 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.
listname(element) Deleting a List from Memory To delete lists from memory, including L1 through L6, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18). Use the SetUpEditor command to restore L1 through L6 names and to set up list data. Note: Removing a list from the stat list editor does not delete list names and data from memory, only from view. Using Lists in Graphing To graph a family of curves, you can use lists (Chapter 3) or the Transformation Graphing App.
• The Ù symbol does not precede a list name when the name is pasted where a list name is the only valid input, such as the stat list editor’s Name= prompt or the stat plot editor’s XList: and YList: prompts. Entering a User-Created List Name Directly To enter an existing list name directly, follow these steps. 1. Press y 9 ~ to display the LIST OPS menu. 2. Select B:Ù, which pastes Ù to the current cursor location. Ù is not always necessary.
For example, the first screen below shows that elements are stored to L3, and the formula L3+10 is attached to the list name ÙADD10. The quotation marks designate the formula to be attached to ÙADD10. Each element of ÙADD10 is the sum of an element in L3 and 10. The next screen shows another list, L4. The elements of L4 are the sum of the same formula that is attached to L3. However, quotation marks are not entered, so the formula is not attached to L4.
• 4. Enter a user.created list name directly using Ù. Press Í. Note: The stat list editor displays a formula-lock symbol next to each list name that has an attached formula. Chapter 12 describes how to use the stat list editor to attach formulas to lists, edit attached formulas, and detach formulas from lists. Detaching a Formula from a List You can detach (clear) an attached formula from a list in several ways. For example: • Enter ã ã !listname on the home screen.
• Use y K to recall the contents of the list into an expression at the cursor location (Chapter 1). Note: You must paste user-created list names to the Rcl prompt by selecting them from the LIST NAMES menu. You cannot enter them directly using Ù. Using Lists with Math Functions You can use a list to input several values for some math functions. The function is evaluated for each list element, and a list is displayed.
LIST OPS Menu LIST OPS Menu To display the LIST OPS menu, press y 9 ~. 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 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.
SortA(keylistname,dependlist1[,dependlist2,...,dependlist n]) SortD(keylistname,dependlist1[,dependlist2,...,dependlist n]) Note: • In the example, 5 is the first element in L4, and 1 is the first element in L5. After SortA(L4,L5), 5 becomes the second element of L4, and likewise, 1 becomes the second element of L5. • SortA( and SortD( are the same as SortA( and SortD( on the STAT EDIT menu (Chapter 12). • You cannot sort a locked list.
length!dim(listname) Fill( Fill( replaces each element in listname with value. Fill(value,listname) Note: dim( and Fill( are the same as dim( and Fill( on the MATRIX MATH menu (Chapter 10). 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.
cumSum(list) @List( @List( returns a list containing the differences between consecutive elements in list. @List subtracts the first element in list from the second element, subtracts the second element from the third, and so on. The list of differences is always one element shorter than the original list. list elements can be a real or complex numbers.
3. Use ZoomStat to plot the data (Chapter 3). MathPrint™ Classic 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 9 ~ 8 to select 8:Select( from the LIST OPS menu. Select( is pasted to the home screen. 2. Enter xlistname, press ¢, enter ylistname, and then press ¤ to designate list names into which you want the selected data to be stored. 3. Press Í.
6. Press Í. A 4 indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottom-left 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.
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) Matr4list( Matr4list( (matrix stored to lists) fills each listname with elements from each column in matrix.
Matr4list(matrix,column#,listname) Ù preceding one to five characters identifies those characters as a user-created listname. listname may comprise letters, q, and numbers, but it must begin with a letter from A to Z or q. Ùlistname Generally, Ù must precede a user-created list name when you enter a user-created list name where other input is valid, for example, on the home screen. Without the Ù, the TI-84 Plus C may misinterpret a usercreated list name as implied multiplication of two or more characters.
min(listA[,listB]) max(listA[,listB]) Note: min( and max( are the same as min( and max( on the MATH NUM menu. mean(, median( mean( returns the mean value of list. median( returns the median value of list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid. mean(list[,freqlist]) median(list[,freqlist]) sum(, prod( sum( (summation) returns the sum of the elements in list.
Sums and Products of Numeric Sequences You can combine sum( or prod( with seq( to obtain: upper upper G expression(x) x=lower x=lower expression(x) To evaluate G 2 (N–1) from N=1 to 4 and then p 2 (N–1) from N=1 to 4: stdDev(, variance( stdDev( returns the standard deviation of the elements in list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid.
Chapter 12: Statistics 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.
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. 6. Press o to display the Y= editor. If necessary, press ‘ to clear the function Y1. As necessary, press }, Í, and ~ to turn off Plot1, Plot2, and Plot3 from the top line of the Y= editor (Chapter 3). As necessary, press †, |, and Í to deselect functions. 7.
10. Press … ~ 4 to select 4:LinReg(ax+b) (linear regression model) from the STAT CALC menu. 11. Fill in each argument in the stat wizard displayed. Press y d (for Xlist:), and † y e (for Ylist:), Press † † (to Store ReqEQ:)and then press t a Í to paste Y1. Press † (to select Calculate). 12. Press Í to execute LinReg(ax+b). The linear regression for the data in L1 and L2 is calculated. Values for a and b are displayed in a temporary result screen. The linear regression equation is stored in Y1.
14. Press s. The regression line and the scatter plot are displayed. 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. 15. Press … 1 to select 1:Edit. The stat list editor is displayed. Press ~ and } to move the cursor onto L3. Press y 6. 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. 16.
Notice that the first three residuals are negative. They correspond to the shortest pendulum string lengths in L1. The next five residuals are positive, and three of the last four are negative. The latter correspond to the longer string lengths in L1. Plotting the residuals will show this pattern more clearly. 19. Press y , 2 to select 2: Plot2 from the STAT PLOTS menu. The stat plot editor is displayed for Plot 2. 20. Press Í to select On, which turns on Plot 2. Press † Í to select " (scatter plot).
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 … xb. 23. 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. 24.
The new function y=.192x.522 appears to fit the data well. To get more information, examine a residual plot. 28. 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). 29. 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.
33. Press y [ to recall the Last Entry. Press | | | 5 to change the string length to 50 cm. 34. Press Í to calculate the predicted time of about 1.48 seconds. Since a string length of 50 cm exceeds the lengths in the data set, and since residuals appear to be increasing as string length increases, we would expect more error with this estimate. Note: You also can make predictions using the table with the TABLE SETUP settings Indpnt:Ask and Depend:Auto (Chapter 7).
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 6. 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.
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. Press y 7 to lock the alpha key in the on position and enter several alpha characters as needed. To unlock, press the ƒ key. 4. 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. 5. Press Í or † to store the list name in the current column of the stat list editor.
Thin-bar fraction on the home screen (regular division): Note: Order of operations applies to fractions. For example, evaluates to because the order of operations dictates that division is performed before addition. To evaluate , enter with parentheses around the numerator. • Press ~ to move the cursor to the character before which you want to insert, press y 6, and then enter one or more characters.
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 Formula-Generated Lists Are Displayed When you edit an element of a list referenced in an attached formula, the TI-84 Plus C 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-84 Plus C takes slightly longer to accept each edit or entry than when no lists with formulas attached are in view.
Notes: • If an error menu is returned when you attempt to display a formula-generated list in the stat list editor, you can select 2:Goto, write down the formula that is attached to the list, and then press ‘ Í to detach (clear) the formula. You then can use the stat list editor to find the source of the error. After making the appropriate changes, you can reattach the formula to a list.
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 and switch to viewnames context. Press ~ and | to view list names stored in other stat list editor columns. 2. Press Í to switch to edit-elements context. You may edit any element in a list. All elements of the current list are displayed in braces ( { } ) in the entry line.
6. Press ‘ to switch to view-names context. 7. Press † to switch back to view-elements 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 20 characters at a time. An ellipsis (...) indicates that the element continues beyond 20 characters. To page down ten elements, press ƒ †. To page up ten elements, press ƒ }.
• When you switch to edit-elements context from view-names context, the full values of all elements in the list are displayed. An ellipsis indicates that list elements continue beyond the screen. You can press ~ and | to edit any element in the list. Note: In edit-elements context, you can attach a formula to a list name only if you switched to it from view-names context. View-Names Context In view-names context, the entry line displays the list name and the list elements.
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 specified lists in the stat list editor. Note: Use Catalog Help for more syntax help when needed.Select a menu item and then press à to go to a syntax help editor (if the menu item is supported).
SetUpEditor [listname1,listname2,...,listname n] SetUpEditor displays the specified lists beginning in column 1. Previous lists displayed are removed from the editor view. MathPrint™ Classic If you enter a listname that is not stored in memory already, then listname is created and stored in memory; it becomes an item on the LIST NAMES menu.
The TI-84 Plus C uses the formula below to compute RESID list elements. The next section describes the variable RegEQ. RESID = Ylistname N RegEQ(Xlistname) Automatic Regression Equation Each regression model has an optional argument, regequ, for which you can specify a Y= variable such as Y1. Upon execution, the regression equation is stored automatically to the specified Y= variable and the Y= function is selected.
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. QuadReg CubicReg QuartReg The r and r2 that are computed for LnReg, ExpReg, and PwrReg are based on the linearly transformed data. For example, for ExpReg (y=ab^x), r and r2 are computed on ln y=ln a+x(ln b). By default, these values are not displayed with the results of a regression model when you execute it.
MathPrint™ Classic 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 D: Manual Linear Fit E: Quick Plot & Fit E-Q Menu items have a wizard. Calculates 1-variable statistics. Calculates 2-variable statistics. Calculates a median-median line. Fits a linear model to data.
The following screens demonstrate the STAT WIZARDS flow for a STAT CALC menu command. 1. Press press … ~ to select the STAT CALC menu. Select 1 Í to select the 1-Var Stats menu. 2. The 1 -Var Stats wizard opens. Enter the values in the wizard. Scroll down to Calculate and press Í. Note: In this example, data has been entered in L1. FreqList is an optional argument. 3. The STAT CALC results are displayed. 4. Press † to scroll down through the data. Note: This is a temporary view.
Frequency of Occurrence for Data Points For most STAT CALC menu items, you can specify a list of data occurrences, or frequencies (freqlist). Each element in freqlist indicates how many times the corresponding data point or data pair occurs in the data set you are analyzing. For example, if L1={15,12,9,14} and ÙFREQ={1,4,1,3}, then the TI-84 Plus C interprets the instruction 1-Var Stats L1, ÙFREQ to mean that 15 occurs once, 12 occurs four times, 9 occurs once, and 14 occurs three times.
Med-Med (ax+b) Med-Med (median-median) fits the model equation y=ax+b to the data using the median-median line (resistant line) technique, calculating the summary points x1, y1, x2, y2, x3, and y3. Med-Med displays values for a (slope) and b (y-intercept). Med-Med [Xlistname,Ylistname,freqlist,regequ] LinReg (ax+b) LinReg(ax+b) (linear regression) fits the model equation y=ax+b to the data using a least-squares fit.
QuartReg—(ax 4+bx 3+cx 2+ dx+e) QuartReg (quartic regression) fits the fourth-degree polynomial y=ax 4+bx 3+cx 2+dx+e to the data. It displays values for a, b, c, d, and e; when DiagnosticOn is set, it also displays a value for R2. For five points, the equation is a polynomial fit; for six or more, it is a polynomial regression. At least five 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+a…e-bx) Logistic fits the model equation y=c/(1+a…eLbx) 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. MathPrint™ Classic 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.
After entering List data and viewing the StatPlot, select the Manual-Fit function. 1. 2. Press … to display the Stat menu. Press ~ to select CALC. Press } } to scroll up and select D:Manual-Fit. Presst a † † Í to store the equation to Y3. Press † to highlight Calculate and then press Í. This displays a free-floating cursor at the center of the display screen. 3. Press t [F5] to open the STYLE menu. Choose your color and line style, press † to highlight OK, and then press Í. 4.
Modify parameter values Press the cursor navigation keys (| ~) to move from the first parameter (m) or (b) the second parameter. You can press Í and type a new parameter value. Press Í to display the new parameter value. When you edit the value of the selected parameter, the edit can include insert, delete, type over, or a mathematical expression. The screen dynamically displays the revised parameter value.
3. Press t [F5] to open the STYLE menu. 4. Choose your color and line style, press † to highlight OK, and then press Í. 5. Use the arrow keys to move the cursor, and press Í at the desired spot to draw a point. After you draw at least two points, the FitEQ menu appears. Note: Once you start to drop points, the points are saved to lists QPX and QPY even if you do not complete the entire Quick Plot and EQ activity. 6. Press t [F5] to open the FitEQ menu. 7. Choose your desired equation and press Í.
Press t [F5] to store the results. 8. Note: If you do not want to store the results, use ClrDraw to clear your work. 9. Choose your options from the menu and then press OK. Note: You can store up to three unique Quick Plot sessions on one image.
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.
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.
xyLine xyLine (Ó)is a scatter plot in which the data points are plotted and connected in order of appearance in Xlist and Ylist. You may want to use SortA( or SortD( to sort the lists before you plot them. Histogram Histogram (Ò) 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 131 must be true.
Boxplot Boxplot (Ö)(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. 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.
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. 5.
Turning On and Turning Off Stat Plots PlotsOn and PlotsOff allow you to turn on or turn off stat plots from the home screen or a program. With no plot number, PlotsOn turns on all plots and PlotsOff turns off all plots. With one or more plot numbers (1, 2, and 3), PlotsOn turns on specified plots, and PlotsOff turns off specified plots. PlotsOff [1,2,3] PlotsOn [1,2,3] Note: You also can turn on and turn off stat plots in the top line of the Y= editor (Chapter 3).
2. Select the plot to define, which pastes Plot1(, Plot2(, or Plot3( to the cursor location. 3. Press y , ~ to display the STAT TYPE menu. 4. Select the type of plot, which pastes the name of the plot type to the cursor location. 5. Press ¢. Enter the list names, separated by commas. 6. Press ¢ y , | 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.
Chapter 13: Inferential Statistics and Distributions 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.
7. Press … | to display the STAT TESTS menu, and then press † until 8:TInterval is highlighted. 8. 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. 9. Press † y 9 and press † until HGHT is highlighted and then press Í. 10. Press † † Ë 99 to enter a 99 percent confidence level at the C-Level: prompt. 11. Press † to move the cursor onto Calculate, and then press Í.
3. Press † to move the cursor onto Calculate, and then press Í to calculate the new 99 percent confidence interval. The results are displayed on the home screen. If the height distribution among a population of women is normally distributed with a mean m of 165.1 centimeters and a standard deviation s of 6.35 centimeters, what height is exceeded by only 5 percent of the women (the 95th percentile)? 4. Press ‘ to clear the home screen. Press y = to display the DISTR (distributions) menu. 5.
9. Press Í to open a wizard for the input of the ShadeNorm( parameters. 10. Enter 175 Ë 5448205 for the lower bound and press †. Enter 1 y D 99 for the upper bound and press †. Enter the mean m of 165 Ë 1 for the normal curve and press †. Enter a standard deviation s of 6 Ë 35. 11. Press † to select Draw and then press Í to plot and shade the normal curve. Area is the area above the 95th percentile. low is the lower bound. up is the upper bound.
4. Select the alternative hypothesis (ƒÄ, <, or >) against which to test, if the selection is available. 5. Select No or Yes for the Pooled option, if the selection is available. 6. Select the color option using a spinner menu. Press | and ~ to scroll through the color options to set a color. 7. Select Calculate or Draw (when Draw is available) to execute the instruction. • When you select Calculate, the results are displayed on the home screen.
• 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. Selecting Color Color spinner menu offers a color graph for Draw. Press | and ~ to scroll through the color options to set a color.
EDIT CALC TESTS 0: 2-SampTInt... A: 1-PropZInt... B: 2-PropZInt... C: c2-Test... D: c2-GOF Test... E: 2-SampÛTest... F: LinRegTTest... G: LinRegTInt...
Data Stats Calculated results: Drawn results: Note: All STAT TESTS examples assume a fixed-decimal mode setting of 4 (Chapter 1). If you set the decimal mode to Float or a different fixed-decimal setting, your output may differ from the output in the examples. T-Test T-Test (one-sample t test; item 2) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is unknown. It tests the null hypothesis H0: m=m0 against one of the alternatives below.
Data Stats Calculated results: Drawn results: Chapter 13: Inferential Statistics and Distributions 230
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 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.
• Ha: p1>p2 (p1:>p2) Input: Calculated results: Drawn results: ZInterval 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. In the example: L1={299.4, 297.7, 301, 298.9, 300.
Data Stats Calculated results: TInterval 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. In the example: L6={1.6, 1.7, 1.8, 1.
Data Stats Calculated results: 2-SampTInt 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 user-specified confidence level. 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 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 user-specified confidence level.
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]. At the Expected: prompt, enter the matrix variable name to which you want the computed expected counts to be stored; default=[B]. Matrix editor: Note: Press y ú ~ ~ 1 to select 1:[A] from the MATRX EDIT menu. Input: Note: Press y ú †] Í to display matrix [B].
c2GOF-Test c2GOF-Test (Chi Square Goodness of Fit; item D) performs a test to confirm that sample data is from a population that conforms to a specified distribution. For example, c2 GOF can confirm that the sample data came from a normal distribution. In the example: list 1={16, 25, 22, 8, 10} list 2={16.2, 21.6, 16.2, 14.4, 12.6} The Chi-square Goodness of Fit input screen: Note: Press … ~ ~ to select TESTS. Press † several times to select D:X2GOF-Test... Press Í.
2-SampFTest 2-SampÜTest (two-sample Ü-test; item E) computes an Ü-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 LinRegTTest (linear regression t test; item F) computes a 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:ă0) • 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).
In the example: list 1={4, 5, 6, 7, 8} list 2={1, 2, 3, 3.5, 4.5} LinRegTInt input screen: Note: Press … ~ ~ to select TESTS. Press † several times to select G:LinRegTint... Press Í. Press † several times to select Calculate. Press Í. Calculated results: Xlist, Ylist is the list of independent and dependent variables. The list containing the Freq (frequency) values for the data is stored in List. The default is 1. All elements must be real numbers.
ANOVA( ANOVA( (one-way analysis of variance; item H) 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=...=mk is tested against the alternative Ha: not all m1...mk are equal. 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 n1 The count of observations in sample one for the 2-PropZTest and 2-PropZInt. Must be an integer > 0. n2 The count of observations in sample two for the 2-PropZTest and 2-PropZInt. Must be an integer > 0. C-Level The confidence level for the interval instructions. Must be ‚ 0 and < 100. If it is ‚ 1, it is assumed to be given as a percent and is divided by 100. Default=0.95.
Variables LinRegTTest, ANOVA VARS Menu Tests Intervals ‚Ç2 ‚Ç2 TEST lower, upper TEST v v XY sample standard deviation of x Sx Sx XY number of data points n n XY estimated sample proportion for population 2 confidence interval pair mean of x values standard error about the line s TEST a, b EQ r EQ r2 EQ RegEQ EQ regression/fit coefficients correlation coefficient coefficient of determination regression equation Note: The variables listed above cannot be archived.
normalpdf( normalpdf( computes the probability density function (pdf) for the normal distribution at a specified x value. The defaults are mean m=0 and standard deviation s=1. To plot the normal distribution, paste normalpdf( to the Y= editor. The probability density function (pdf) is: 1 f x = -------------- e 2 – x – 2 – -----------------2 2 , 0 normalpdf(x[,m,s]) Note: For this example, Xmin = 28 Xmax = 42 Xscl = 1 Ymin = 0 Ymax = .2 Yscl = .
invT( invT( computes the inverse cumulative Student-t probability function specified by Degree of Freedom, df for a given Area under the curve. invT(area,df) tpdf( tpdf( computes the probability density function (pdf) for the Student-t distribution at a specified x value. df (degrees of freedom) must be > 0. To plot the Student-t distribution, paste tpdf( to the Y= editor.
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. The probability density function (pdf) is: 1 df/2 df 2 – 1 – x/2 f x = -------------------- 1/2 x e ,x 0 df 2 c2pdf(x,df) Note: For this example, Xmin = 0 Xmax = 30 Ymin = L.02 Ymax = .
Fpdf( Üpdf( computes the probability density function (pdf) for the Ü distribution at a specified x value. numerator df (degrees of freedom) and denominator df must be integers > 0. To plot the Ü distribution, paste Üpdf( to the Y= editor.
binompdf(numtrials,p[,x]) binomcdf( binomcdf( computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial. x can be a real number or a list of real numbers. 0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a list of cumulative probabilities is returned.
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. The probability density function (pdf) is: fx = p1 – p x–1 ,x = 1,2,...
Note: Use Catalog Help for more syntax help when needed.Select a menu item and then press à to go to a syntax help editor (if the menu item is supported). L1â99 and 1â99 specify infinity. If you want to view the area left of upperbound, for example, specify lowerbound=L1â99. ShadeNorm( ShadeNorm( draws the normal density function specified by mean m and standard deviation s and shades the area between lowerbound and upperbound. The defaults are m=0 and s=1.
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. Shadec2(lowerbound,upperbound,df) Note: For this example, Xmin = 0 Xmax = 35 Ymin = L.025 Ymax = .1 ShadeF( ShadeÜ( draws the density function for the Ü distribution specified by numerator df (degrees of freedom) and denominator df and shades the area between lowerbound and upperbound.
Chapter 14: Applications The Applications Menu The TI-84 Plus C comes with several applications already installed and listed on the APPLICATIONS menu, such as: CellSheet™ Inequality Graphing Vernier EasyData™ Polynomial Root Finder and Simultaneous Equation Solver Except for the Finance application, you can add and remove applications as space permits. The Finance application is built into the TI-84 Plus C code and cannot be deleted. Check education.ti.
You have found a car you would like to buy. You can afford payments of 250 per month for four years. The car costs 9,000. Your bank offers an interest rate of 5%. What will your payments be? Can you afford it? 1. 2. Press z † ~ ~ ~ Í to set the fixed-decimal mode setting to 2. Press Œ Í to select 1:Finance from the APPLICATIONS menu. 3. Press Í to select 1:TVM Solver from the CALC VARS menu. The TVM Solver is displayed. 4.
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 Œ Í to select 1:Finance from the APPLICATIONS menu. 2. Press Í to select 1:TVM Solver from the CALC VARS menu. The TVM Solver is displayed. 3. Enter the data: N=7 PV= M1250 PMT=0 FV=2000 P/Y=1 C/Y=12 4. Move the cursor to æ and press ƒ \. YYou need to look for an interest rate of 6.73% to grow 1250 to 2000 in 7 years.
4. Select END or BEGIN to specify the payment method. 5. Place the cursor on the TVM variable for which you want to solve. 6. Press ƒ \. The answer is computed, displayed in the TVM Solver, and stored to the appropriate TVM variable. An indicator square in the left column designates the solution variable.
Each TVM function takes zero to six arguments, which must be real numbers. The values that you specify as arguments for TVM functions are not stored to the TVM variables. Note: To store a value to a TVM variable, use the TVM Solver or use ¿ and any TVM variable on the FINANCE VARS menu. If you enter less than six arguments, the graphing calculator substitutes a previously stored TVM variable value for each unspecified argument.
tvm_PV[(Ú,¾æ,PMT,FV,P/Y,C/Y)] MathPrint™ Classic tvm_N tvm_Ú computes the number of payment periods. tvm_Ú[(æ¾,PV,PMT,FV,P/Y,C/Y)] tvm_FV tvm_FV computes the future value. tvm_FV[(Ú,¾æ,PV,PMT,P/Y,C/Y)] 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.
2000 2000 2000 4000 4000 -3000 CF0 = 2000 CFList = {2000,L3000,4000} CFFreq = {2,1,2} npv(, irr( npv( (net present value) is the sum of the present values for the cash inflows and outflows. A positive result for npv indicates a profitable investment. npv(interest rate,CF0,CFList[,CFFreq]) irr( (internal rate of return) is the interest rate at which the net present value of the cash flows is equal to zero.
bal(npmt[,roundvalue]) GPrn(, GInt( GPrn( computes the sum of the principal during a specified period for an amortization schedule using stored values for ¾æ, PV, and PMT. pmt1 is the starting payment. pmt2 is the ending payment in the range. pmt1 and pmt2 must be positive integers < 10,000. roundvalue specifies the internal precision the calculator uses to calculate the principal; if you do not specify roundvalue, the graphing calculator uses the current Float/Fix decimal-mode setting.
3. Press 360 to enter number of payments. Press † 8 to enter the interest rate. Press † † Ì 800 to enter the payment amount. Press † 0 to enter the future value of the mortgage. Press † 12 to enter the payments per year, which also sets the compounding periods per year to 12. Press † † Í to select PMT:END. 4. Move the cursor to the PV prompt and then press ƒ \ to solve for the present value. 5. Press o to display the parametric Y= editor. Turn off all stat plots. Press „ to define X1T as T.
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.
Pmt_End Pmt_End (payment end) specifies an ordinary annuity, where payments occur at the end of each payment period. Most loans are in this category. Pmt_End is the default. Pmt_End On the TVM Solver’s PMT:END BEGIN line, select END to set PMT to ordinary annuity. Pmt_Bgn Pmt_Bgn (payment beginning) specifies an annuity due, where payments occur at the beginning of each payment period. Most leases are in this category.
• • Graph Scaling support – Preset y-axis scaling for live graphs – Turn off auto scaling after data collection completes – Manually scale graphs within the application Support for additional sensor calibration types – Quadratic (allows support for Wide-Range Temperature Probe & Melt Station) – Power (allows support for Ethanol Sensor) Steps for Running the EasyData™ App Follow these basic steps when using the EasyData™ App. Starting the EasyData™ App 1.
Starting and Stopping Data Collection Starting Data Collection To start sampling, select Start (press q). Sampling will automatically stop when the number of samples set in the Time Graph Settings menu is reached. The graphing calculator will then display a graph of the sampled data. Stopping Data Collection To stop sampling before it automatically stops, select Stop (press and hold q) at any time during the sampling process. When sampling stops, a graph of the sampled data is displayed.
Chapter 15: CATALOG, Strings, Hyperbolic Functions Browsing the TI-84 Plus C Catalog Help What Is the CATALOG? The CATALOG is an alphabetical list of all functions and instructions on the TI-84 Plus C.
Using Catalog Help Displaying Catalog Help You can display Catalog Help arguments for functions in two ways: • Using an alpha/numeric function listing in the catalog (e.g, y N). • Using the functions listed in certain menus (e.g, ). Catalog Help lists the valid arguments for the function under the edit line. Arguments in brackets are optional. Arguments for this function. Function edit line. Optional argument for this function. Catalog Help commands available for this function. 1.
• Enter your argument values on the function edit line, and then select PASTE to paste the function and the argument values you entered. Note: You can paste to most cursor locations. • Select ESC to exit the Catalog Help screen. Entering and Using Strings What Is a String? A string is a sequence of characters that you enclose within quotation marks. On the TI-84 Plus C, a string has two primary applications. • It defines text to be displayed in a program.
Note: A string must be enclosed in quotation marks. The quotation marks do not count as string characters. Storing Strings to String Variables String Variables The TI-84 Plus C 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.
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( ... Converts an equation to a string.
expr( expr( converts the character string contained in string to an expression and executes it. string can be a string or a string variable. expr(string) inString( inString( returns the character position in string of the first character of substring. string can be a string or a string variable. start is an optional character position at which to start the search; the default is 1.
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( Hyperbolic cosine cosh-1( ... sinh( Hyperbolic arccosine sinh-1( ... tanh( Hyperbolic arcsine -1 tanh ( ...
Chapter 16: Programming 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-84 Plus C 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.
8. Press Í to paste prgmCYLINDER to the current cursor location. (If CYLINDER is not item 1 on your PRGM EXEC menu, move the cursor to CYLINDER before you press Í.) 9. Press Í to execute the program. Enter 1.5 for the radius, and then press Í. Enter 3 for the height, and then press Í. The text VOLUME IS, the value of V, and Done are displayed. Repeat steps 7 through 9 and enter different values for R and H.
5. Press Í. The program editor is displayed. 6. Enter one or more program commands. 7. Press y 5 to leave the program editor and return to the home screen. Managing Memory and Deleting a Program To check whether adequate memory is available for a program you want to enter: 1. Press y L to display the MEMORY menu. 2. Select 2:Mem Management/Delete to display the MEMORY MANAGEMENT/DELETE menu (Chapter 18). 3. Select 7:Prgm to display the PRGM editor.
4. Press Í to archive the program. An asterisk will appear to the left of the program to indicate it is an archived program. To unarchive a program in this screen, put the cursor next to the archived program and press Í. The asterisk will disappear. Note: Archive programs cannot be edited or executed. In order to edit or execute an archived program, you must first unarchive it.
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. 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.
PRGM CTL (Control) Instructions PRGM CTL Menu To display the PRGM CTL (program control) menu, press from the program editor only. CTL 1: 2: 3: 4: 5: 6: 7: 8: 9: 0: A: B: C: D: E: F: G: H: I: J: K: I/O EXEC If Then Else For( While Repeat End Pause Lbl Goto IS>( DS<( Menu( prgm Return Stop DelVar GraphStyle( GraphColor( OpenLib( ExecLib( Creates a conditional test. Executes commands when If is true. Executes commands when If is false. Creates an incrementing loop. Creates a conditional loop.
:If condition :command (if true) :command Program Output If-Then Then following an If executes a group of commands if condition is true (nonzero). End identifies the end of the group of commands. :If condition :Then :command (if true) :command (if true) :End :command Program Output 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.
:End :command Program Output Note: In OS 2.55MP and higher and TI-84 Plus C 4.0 and higher, the program name displays again when you press Í to repeat the program. For( For( loops and increments. It increments variable from begin to end by increment. increment is optional (default is 1) and can be negative (end
Repeat Repeat repeats a group of commands until condition is true (nonzero). It is similar to While, but condition is tested when End is encountered; therefore, the group of commands is always executed at least once. Repeat instructions can be nested. :Repeat condition :command (until condition is true) :command (until condition is true) :End :command Program Output 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.
Goto label Program Output IS>( 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. variable cannot be a system variable. :IS>(variable,value) :command (if answer value) :command (if answer > value) Program Output Note: IS>( is not a looping instruction. DS<( DS<( (decrement and skip) subtracts 1 from variable.
Menu("title","text1",label1,"text2",label2, . . .) Program Output The program above pauses until you select 1 or 2. If you select 2, for example, the menu disappears and the program continues execution at Lbl B. prgm Use prgm to execute other programs as subroutines. When you select prgm, it is pasted to the cursor location. Enter characters to spell a program name.
GraphColor( designates the color of the graph to be drawn. function# is the number of the Y= function name in the current graphing mode. color# is a number from 10 to 24 that corresponds to the graph color, as shown in the table below: Color Number Color Name 10 BLUE 11 RED 12 BLACK 13 MAGENTA 14 GREEN 15 ORANGE 16 BROWN 17 NAVY 18 LTBLUE 19 YELLOW 20 WHITE 21 LTGRAY 22 MEDGRAY 23 GRAY 24 DARKGRAY You can also choose a color name in the menu (color sub-menu).
CTL 6: 7: 8: 9: 0: A: B: I/O EXEC Displays text at a specified position. Output( Checks the keyboard for a keystroke. getKey Clears the display. ClrHome Clears the current table. ClrTable Gets a variable from another TI-84 Plus C. GetCalc( Gets a variable from CBL 2™ or CBR™ data collection device. Get( Sends a variable to CBL 2 or CBR data collection device. Send( Note: Press à (plus) to run the catalog help application and to use syntax help for programming.
Input ["text",variable] Input [Strn,variable] Program Output Note: When a program prompts for input of lists and Yn functions during execution, you must include the braces ( { } ) around the list elements and quotation marks ( " ) around the expressions. 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.
Note: If a matrix or list is too large to display in its entirety, ellipses (...) are displayed in the last column, but the matrix or list cannot be scrolled. To scroll, use Pause value. 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.
TI-84 Plus C Key Code Diagram ClrHome, ClrTable ClrHome (clear home screen) clears the home screen during program execution. ClrTable (clear table) clears the values in the table during program execution. GetCalc( GetCalc( gets the contents of variable on another TI-84 Plus C and stores it to variable on the receiving TI-84 Plus C. variable can be a real or complex number, list element, list name, matrix element, matrix name, string, Y= variable, graph database, or picture.
Note: You can access Get(, Send(, and GetCalc( from the CATALOG to execute them from the home screen (Chapter 15). Calling Other Programs as Subroutines Calling a Program from Another Program On the TI-84 Plus C, 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.
If you write an assembly language program, use the two instructions below from the CATALOG to identify and compile the program. Instructions Comments AsmComp(prgmASM1, Compiles an assembly language program written in ASCII and stores the hex version prgmASM2) Asm84CPrgm Identifies an assembly language program; must be entered as the first line of an assembly language program To compile an assembly program that you have written: 1.
Chapter 17: Activities The Quadratic Formula Note: Each activity in this chapter assumes a default setting. This example uses MathPrint™ mode for real answers and a classic format entry using division for nonreal (complex) results. You can also use the Polynomial Root Finder/Simultaneous Equation Solver application to solve these types of problems with a quick set-up. This application comes pre-loaded on your TI-84 Plus C and can be downloaded from education.ti.com.
Entering a Calculation Begin with the equation 2x2 N 11x + 14 = 0. 1. Press 2 ¿ ƒ A to store the coefficient of the x2 term. 2. Press ƒ [:]. The colon allows you to enter more than one instruction on a line. 3. Press Ì 11 ¿ ƒ B to store the coefficient of the X term. Press ƒ [:] to enter a new instruction on the same line. Press 14 ¿ ƒ C to store the constant. 4. Press Í to store the values to the variables A, B, and C. The last value you stored is shown on the right side of the display.
To save keystrokes, you can scroll up to find an expression you entered, copy it, and then edit it for a new calculation. 3. 4. and Press } to highlight then press Í to paste it to the entry line. Press | until the cursor is on the + sign in the formula. Press ¹ to edit the quadraticformula expression to become . 5. Press Í to find the other solution for the quadratic equation 2x2 N 11x + 14 = 0. Displaying Complex Results Now solve the equation 2x2 N 6x + 5 = 0.
3. Press 2 ¿ ƒ A ƒ [:] Ì 6 ¿ ƒ B ƒ [:] 5 ¿ ƒ C Í. The coefficient of the x2 term, the coefficient of the X term, and the constant for the new equation are stored to A, B, and C, respectively. 4. Enter the quadratic formula using Classic entry: £ Ì ƒ B Ã y C ƒ B ¡ ¹ 4 ƒ A ƒ C ~ ¤ ¥ £ 2 ƒ A ¤. Because the solution is a complex number, you have to enter the formula using the division operation instead of using the n/d shortcut template.
Begin by defining a function that describes the volume of the box. From the diagram: 2X + A = 20 2X + 2B = 25 V = A…B…X Substituting: V = (20 N 2X) (25à2 N X) X X 20 A X X B B 25 1. 2. Press o to display the Y= editor. Press £ 20 ¹ 2 „ ¤ ä £ t ^ 1 25 ~ 2 ¹ „ ¤ „ Í to define the volume function as Y1 in terms of X. „ lets you enter X quickly, without having to press ƒ. The highlighted = sign indicates that Y1 is selected.
5. Press and hold † to scroll the table until a negative result for Y1 is displayed. Notice that the maximum length of X for this problem occurs where the sign of Y1 (box’s volume) changes from positive to negative, between 10 and 11. Zooming In on the Table 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.
7. Press † or } to move the cursor to 3.67. Press ~ to move the cursor into the Y1 column. The value of Y1 at X=3.67 is displayed on the bottom line in full precision as 410.261226. 8. Press † to display the other maximum. The value of Y1 at X=3.68 in full precision is 410.264064, at X=3.69 is 410.262318 and at X=3.7 is 410.256. The maximum volume of the box would occur at 3.68 if you could measure and cut the paper at 01-centimeter increments.
4. Press Í. The expression is evaluated, and 10 is stored in Xmax. Press Í to accept Xscl as 1. 5. Press 0 Í 500 Í 100 Í 1 Í to define the remaining window variables. Displaying and Tracing the Graph 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.
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. Press | and ~ until you are on the maximum Y value. This is the maximum of Y1(X) for the X pixel values. The actual, precise maximum may lie between pixel values.
3. The graph is displayed again. The cursor has changed to indicate that you are using a ZOOM instruction. 4. With the cursor near the maximum value of the function, press Í. The new viewing window is displayed. Both XmaxNXmin and YmaxNYmin have been adjusted by factors of 4, the default values for the zoom factors. 5. Press | and ~ to search for the maximum value. 6. Press p to display the new window settings. Note: To return to the previous graph, press q ~ 1:ZPrevious.
3. Press ~ to trace along the curve to a point to the right of the maximum, and then press Í. A 3 at the top of the screen indicates the selected bound. A Guess? prompt is displayed. 4. Press | to trace to a point near the maximum, and then press Í. Or, press 3 Ë 8, and then press Í to enter a guess for the maximum. When you press a number key in TRACE, the X= prompt is displayed in the bottomleft corner.
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.
4. Likewise, enter each man’s correct guesses in MLEFT (Men Left) and MRGHT (Men Right). 5. Press y ,. Select 1:Plot1. Turn on plot 1; define it as a modified box plot Õ that uses Xlist as WLEFT. Move the cursor to the top line and select Plot2. Turn on plot 2; define it as a modified box plot that uses Xlist as WRGHT. (See Chapter 12: Statistics for detailed information on using Stat Plots.) 6. Press o. Turn off all functions. 7. Press p. Set Xscl=1 and Yscl=0. Press q 9 to select 9:ZoomStat.
The fine (Y) as a function of kilometers per hour (X) is: which simplifies to: Procedure 1. Press z. Select Func and Classic. 2. Press o. Turn off all functions and stat plots. Enter the Y= function to describe the fine. Use the TEST menu operations to define the piecewise function. Set the graph style for Y1 to í (Dot-Thick). 3. Press p and set Xmin=L2, Xscl=10, Ymin=L5, Yscl=10, @X=.5 and TraceStep=1. Ignore Xmax and Ymax; they are set in step 4. 4. Press y 5 to return to the home screen.
Graphing Inequalities Problem Graph the inequality 0.4x3 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. Note: You can also investigate graphing inequalities using the Inequality Graphing application. The application is pre-loaded on your TI-84 Plus C and can be downloaded from education.ti.com. Procedure 1. Press z. Select Dot-Thick, Simul, and the default settings.
7. Press r. Notice that the values of Y7 and Y8 are zero where the inequality is false. You only see the intervals of the graph where Y4
5. Press Í to zoom in. Move the cursor over the intersection. 6. Press Í to zoom in again. Move the free-moving cursor onto a point exactly on the intersection. Notice the number of decimal places. 7. Press y / 5 to select 5:intersect. Press Í to select the first curve and Í to select the second curve. To guess, move the trace cursor near the intersection. Press Í. What are the coordinates of the intersection point? 8. Press q 4 to select 4:ZDecimal to redisplay the original graph. 9. Press q.
Note: This program uses the default BLUE color (# = 10). See the Draw chapter for available color options. After you execute the program above, you can recall and display the picture with the instruction RecallPic 6. Note: After you run this program, press y . † † † † ~ ~ ~ † Í to turn on the axes in the graph screen. Graphing Cobweb Attractors Problem Using Web format, you can identify points with attracting and repelling behavior in sequence graphing. Procedure 1. Press z.
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. Note: This program changes the graph window and graph styles. After you run the program, you can change individual settings as needed or you can press y L 7 2 2 to return to default settings.
:DispGraph :Pause Display graph. :FnOn 2 :Lbl Z :Prompt C,D Prompt for guess. :DispGraph :Pause Display graph. :If C=A :Text(1,1,"C IS OK") :If CƒA :Text(1,1,"C IS WRONG") :If D=B :Text(1,150,"D IS OK") :If DƒB :Text(1,150,"D IS WRONG") :DispGraph :Pause Display results. Display graph. :If C=A and D=B :Stop :Goto Z Quit if guesses are correct.
4. Enter the expressions to define the sine curve. 5. Press r. As the graph is plotting, you may press Í to pause and Í again to resume graphing as you watch the sine function “unwrap” from the unit circle. Note: • You can generalize the unwrapping. Replace sin(T) in Y2T with any other trig function to unwrap that function. • You can graph the functions again by turning the functions off and then turning them back on on the Y= editor or by using the FnOff and FnOn commands on the home screen.
4. Press y / 5 to select 5:Intersect. The graph is displayed. Select a first curve, second curve, and guess for the intersection toward the left side of the display. The solution is displayed, and the value of X at the intersection, which is the lower limit of the integral, is stored in Ans and X. 5. Press y 5 to go to the home screen. Press y < 7 and use Shade( to see the area graphically. Shade(Y2,Y1,Ans,75, 4, 4, 18) 6. Press y 5 to return to the home screen.
A person standing on the ground throws a ball to the ferris wheel passenger. The thrower’s arm is at the same height as the bottom of the ferris wheel, but 25 meters (b) to the right of the ferris wheel’s lowest point (25,0). The person throws the ball with velocity (v0) of 22 meters per second at an angle (q) of 66¡ from the horizontal. The parametric equations below describe the location of the ball at time T. X(T) = b N Tv 0 cosq Y(T) = Tv 0 sinq N (gà2) T 2 where g = 9.8 m/sec2 Procedure 1. Press z.
7. Press † to move to the path of the ball. Notice the values of X and Y (T is unchanged). Notice where the cursor is located. This is the position of the ball when the ferris wheel passenger passes the intersection. Did the ball or the passenger reach the intersection first? You can use r to, in effect, take snapshots in time and explore the relative behavior of two objects in motion.
4. Press r. Press |, }, ~, and † to compare the values of Y1 and Y2. 5. Press o. Turn off Y1 and Y2, and then enter the numerical derivative of the integral of 1àX and the function 1àX. Set the graph style for Y3 to ç (line) and Y4 to è (thick). 6. Press r. Again, use the cursor keys to compare the values of the two graphed functions, Y3 and Y4. Problem 2 Explore the functions defined by y = x – 2 2 t dt, x 0 2 t dt , and x 2 t dt 2 Procedure 2 1. Press o.
2. The graphs are displayed as each calculation of the integral and derivative occurs at the pixel point, which may take some time. 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. Notice that although the three graphs defined by Y5 are different, they share the same derivative.
Procedure 1. Press } B to select B:Solver from the MATH menu. Either the equation editor or the interactive solver editor is displayed. If the interactive solver editor is displayed, press } to display the equation editor. 2. Enter the formula as A=NB2sin(p / N)cos(p / N), and then press Í. The interactive solver editor is displayed. 3. Enter N=4 and B=6 to find the area (A) of a square with a distance (B) from center to vertex of 6 centimeters. 4.
Enter N=8. To find the distance B, move the cursor onto B, and then press ƒ \. Find B for N=9, and then for N=10. 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. 6. Enter B=6. To find the area A, move the cursor onto A, and then press ƒ \. 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.
10. Press r. After the graph is plotted, press 100 Í to trace to X=100. Press 150 Í. Press 188 Í. Notice that as X increases, the value of Y converges to p62, which is approximately 113.097. Y2=pB2 (the area of the circle) is a horizontal asymptote to Y1. The area of an N-sided regular polygon, with r as the distance from the center to a vertex, approaches the area of a circle with radius r (pr 2) as N gets large.
Note: Enter a positive number (800) to show PMT as a cash inflow. Payment values will be displayed as positive numbers on the graph. Enter 0 for FV, since the future value of a loan is 0 once it is paid in full. Enter PMT: END, since payment is due at the end of a period. 3. Move the cursor onto the PV= prompt, and then press ƒ \. The present value, or mortgage amount, of the house is displayed at the PV= prompt.
The graph shows that for the 240th payment (X=240), 358.03 of the 800 payment is applied to principal (Y=358.03). Note: The sum of the payments (Y3T=Y1T+Y2T) is always 800. 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 5 Œ Í 9 to paste 9:bal( to the home screen. Check the figures from the graph.
Chapter 18: Memory and Variable Management Checking Available Memory MEMORY Menu At any time you can check available memory or manage existing memory by selecting items from the MEMORY menu. To access this menu, press y L. MEMORY 1: About... 2: Mem Management/Delete... 3: 4: 5: 6: 7: 8: Clear Entries ClrAllLists Archive UnArchive Reset... Group... Displays information about the graphing calculator including current OS version number. Reports memory availability and variable usage.
Displays the type of graphing calculator. Displays the Product ID. Each Flash-based graphing calculator has a unique product ID, which you may need if you contact technical support. You can also use this ID to register your calculator at education.ti.com, or identify your calculator in the event that it is lost or stolen. Displays the OS version. As new software upgrades become available, you can electronically upgrade your unit.
3. Select variable types from the list to display memory usage. Notes: Real, List, Y-Vars, and Prgm variable types never reset to zero, even after memory is cleared. Apps are independent applications which are stored in Flash ROM. AppVars is a variable holder used to store variables created by Apps. You cannot edit or change variables in AppVars unless you do so through the application which created them. To leave the MEMORY MANAGEMENT/DELETE menu, press either y 5 or ‘.
To cancel Clear Entries, press ‘. Note: If you select 3:Clear Entries from within a program, the Clear Entries instruction is pasted to the program editor, and the Entry (last entry) is cleared when the program is executed. ClrAllLists ClrAllLists sets the dimension of each list in RAM to 0. To clear all elements from all lists, follow these steps. 1. Press y L to display the MEMORY menu. 2. Select 4:ClrAllLists to paste the instruction to the home screen. 3.
Variable Type Names Archive? (yes/no) UnArchive? (yes/no) Polar functions r1, r2, r3, r4, r5, r6 no not applicable Sequence functions u, v, w no not applicable Stat plots Plot1, Plot2, Plot3 no not applicable Graph databases GDB1, GDB2,... yes yes Pictures (Pic Vars) Pic1, Pic2, ... , Pic9, Pic0 yes no Background Images (Image Vars) Image1, Image2, ... , Image9, Image0 yes no Strings Str1, Str2, . . .
To archive or unarchive a list variable (L1) using the Archive/UnArchive options from the MEMORY menu: 1. Press y L to display the MEMORY menu. 2. Select 5:Archive or 6:UnArchive to place the command in the Home screen. 3. Press y d to place the L1 variable in the Home screen. 4. Press Í to complete the archive process. An asterisk (*) is displayed to the left of the Archived variable name to indicate it is archived. Note: Pic Vars that are stored always run from and remain in archive memory (*Pic).
5. Press y 5 to leave the LIST menu. Note: You can access an archived variable for the purpose of linking, deleting, or unarchiving it, but you cannot edit it. Resetting the TI-84 Plus C RAM ARCHIVE ALL Menu Reset displays the RAM ARCHIVE ALL menu. This menu gives you the option of resetting all memory (including default settings) or resetting selected portions of memory while preserving other data stored in memory, such as programs and Y= functions.
To reset all RAM memory or RAM defaults on the TI-84 Plus C, follow these steps. 1. From the RAM ARCHIVE ALL menu, select 1:All RAM to display the RESET RAM menu or 2:Defaults to display the RESET DEFAULTS menu. 2. If you are resetting RAM, read the message below the RESET RAM menu. • To cancel the reset and return to the HOME screen, press Í. • To erase RAM memory or reset defaults, select 2:Reset. Depending on your choice, the message RAM cleared or Defaults set is displayed on the home screen.
Note: Resetting the archive includes resetting Pic and Image Vars. 3. Read the message below the menu. • To cancel the reset and return to the HOME screen, press Í. • To continue with the reset, select 2:Reset. A message indicating the type of archive memory cleared will be displayed on the HOME screen. Resetting All Memory When resetting memory, consider backing up your data to another calculator unit. You can also backup existing data to a computer using the TI-Connect™ software.
1. Press y L to display the MEMORY menu. 2. Select 8:Group to display GROUP UNGROUP menu. 3. Press Í to display the GROUP menu. 4. Enter a name for the new group and press Í. Note: A group name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q. 5. Select the type of data you want to group. You can select 1:All+ which shows all variables of all types available and selected.
7. Press Í to complete the grouping process. Note: You can only group variables in RAM. You cannot group some system variables, such as the lastanswer variable Ans and the statistical variable RegEQ. Ungrouping Variables Ungrouping allows you to make a copy of variables in a group stored in user data archive and place them ungrouped in RAM. DuplicateName Menu During the ungrouping action, if a duplicate variable name is detected in RAM, the DUPLICATE NAME menu is displayed.
4. Press } and † to move the selection cursor (4) next to the group variable you want to ungroup, and then press Í. The ungroup action is completed. Note: Ungrouping does not remove the group from user data archive. You must delete the group in user data archive to remove it. Garbage Collection Garbage Collection Message If you use the user data archive extensively, you may see a Garbage Collect? message.
variable D variable A Sector 1 variable B Empty block variable C Sector 2 Depending on its size, variable D is stored in one of these locations. Sector 3 Each variable that you archive is stored in the first empty block large enough to hold it. This process continues to the end of the last sector. Depending on the size of individual variables, the empty blocks may account for a significant amount of space. Garbage collection occurs when the variable you are archiving is larger than any empty block.
Note: Power loss during garbage collection may cause all memory (RAM and Archive) to be deleted. Using the GarbageCollect Command You can reduce the number of automatic garbage collections by periodically optimizing memory. This is done by using the GarbageCollect command. To use the GarbageCollect command, follow these steps. 1. From the HOME screen, press y N to display the CATALOG. 2.
Chapter 19: Communication Link Getting Started: Sending Variables Getting Started is a fast-paced introduction. Read the chapter for details. Create and store a variable and store a matrix to an archive; then transfer them to another TI-84 Plus C. 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 t ` to display the quick matrix editor. The default size of the matrix is two rows by two columns. Press Í. Press 1 ~ 2 ~ 3 ~ 4 ~ to enter the values.
6. On the sending unit, press Í to archive [A]. An asterisk (ä) will appear, signifying that [A] is now archived. 7. Connect the graphing calculators with the USB unit-to-unit cable. Push both ends in firmly. 8. On the receiving unit, press y 8 ~ to display the RECEIVE menu. Press 1 to select 1:Receive. The message Waiting... is displayed and the busy indicator is on. 9. On the sending unit, press y 8 to display the SEND menu. 10. Press 2 to select 2:AllN. The AllN SELECT screen is displayed. 11.
14. On the sending unit, press 1 to select 1:Transmit and begin transmission. The receiving unit displays the message Receiving....When the items are transmitted, both units display the name and type of each transmitted variable. TI-84 Plus C LINK The TI-84 Plus C Silver Edition has a USB port using a USB unit-to-unit cable to connect and communicate with another TI-84 Plus C Silver Edition, TI-84 Plus Silver Edition, or TI-84 Plus.
GDB** Yes Yes List Yes Yes Matrix Yes Yes Number Yes Yes Complex Yes Yes Window Setup Yes Yes Certificate No No Backup No No * Programs created using commands available only in the latest OS version will not transfer to graphing calculators with an earlier OS version. * App Vars and Programs should be reviewed for use after the transfer between the TI-84 Plus Family and TI-84 Plus C graphing calculators. Some App Vars may not set up an App as expected.
TI-84 Plus C to a TI-83 Plus using I/O Unit-to-Unit Cable The TI-84 Plus C I/O link port is located at the top left edge of the graphing calculator. The TI-83 Plus I/O link port is located at the bottom edge of the graphing calculator. 1. Firmly insert either end of the I/O unit-to-unit cable into the port. 2. Insert the other end of the cable into the other graphing calculator’s I/O port.
2. Select the menu item that describes the data type to send. The corresponding SELECT screen is displayed. 3. Press } and † to move the selection cursor ( 4 ) to an item you want to select or deselect. 4. Press Í to select or deselect the item. Selected names are marked with a 0. Note: An asterisk (ä) to the left of an item indicates the item is archived. 5. Repeat steps 3 and 4 to select or deselect additional items.
2. On the sending unit press y 8 and select a data type and items to SEND. 3. Press ~ on the sending unit to display the TRANSMIT menu. 4. On the other unit, press y 8 ~ to display the RECEIVE menu. 5. Press Í on the receiving unit. 6. Press Í on the sending unit. A copy of the selected item(s) is sent to the receiving unit. 7. Disconnect the link cable only from the receiving unit and connect it to another unit. 8. Press y 8 on the sending unit. 9. Select only the data type.
When you select 4:Quit, transmission stops, and the receiving unit exits receive mode. Receiving from a TI-84 Plus Silver Edition or TI-84 Plus C The TI-84 Plus Silver Edition and the TI-84 Plus share most file types with the TI-84 Plus C. The notable exceptions are the operating system, Apps, Image Vars and Pic Vars. See table under section “Linking Compatibility” for more information. You cannot send memory backups between the TI-84 Plus C Silver Edition and the TI-84 Plus or TI-84 Plus Silver Editions.
• You attempt a backup between a TI-73 Explorer, TI-82, TI-83, TI-83 Plus, or TI-83 Plus Silver Edition. • You attempt a data transfer from a TI-84 Plus C to a TI-84 Plus Silver Edition, TI-84 Plus, TI-83 Plus Silver Edition, TI-83 Plus, TI-83, TI-82, or TI-73 Explorer with variables or features not recognized by the receiving graphing calculator.
Appendix A: 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 ( [ ] ). From the CATALOG, you can paste any function or instruction to the home screen or to a command line in the program editor. However, some functions and instructions are not valid on the home screen.
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item AxesOff Turns off the graph axes. † y. AxesOff AxesOn[color#] a+bi BackgroundOff Turns on the graph axes with color. The color option allows the color of the axes to be specified. Color #: 10-24 or color name. † y. Sets the mode to rectangular complex number mode (a+bi). †z Turns off background image in the graph area.
Function or Instruction/Arguments CLASSIC Clear Entries Key or Keys/Menu or Screen/Item Result z Displays inputs and outputs on a single line, such as 1/2+3/4. CLASSIC Clears the contents of the Last Entry storage area. yL MEMORY 3:Clear Entries ClockOff Turns off the clock display in the mode screen. yN ClockOff ClockOn Turns on the clock display in the mode screen. yN ClockOn ClrAllLists Sets to 0 the dimension of all lists in memory.
Function or Instruction/Arguments cumSum(matrix) dayOfWk(year,month, day) dbd(date1,date2) Key or Keys/Menu or Screen/Item Result Returns a matrix of the cumulative sums of matrix elements. Each element in the returned matrix is a cumulative sum of a matrix column from top to bottom. Returns an integer from 1 to 7, with each integer representing a day of the week. Use dayOfWk( to determine on which day of the week a particular date would occur.
Function or Instruction/Arguments length!dim(listname) Key or Keys/Menu or Screen/Item Result Assigns a new dimension (length) to a new or existing listname. {rows,columns}! dim(matrixname) Assigns new dimensions to a new or existing matrixname. Disp Displays the home screen. y9 OPS 3:dim( y> MATH 3:dim( † I/O 3:Disp Disp [valueA,valueB, valueC,...,value n] Displays each value. DispGraph Displays the graph. † I/O 3:Disp † I/O 4:DispGraph DispTable † Displays the table.
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item 4Eff(nominal rate, Computes the effective interest rate. Œ 1:Finance compounding periods) CALC C:4Eff( Else See If:Then:Else End Eng Identifies end of For(, If-Then-Else, Repeat, or While loop. Sets engineering display mode. † CTL 7:End †z Eng Equ4String(Y= var,Strn) Converts the contents of a Y= var to a string and stores y N Equ4String( it in Strn. expr(string) Converts string to an expression and executes it.
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item Float Sets floating decimal mode. †z Float fMax(expression, variable,lower,upper [,tolerance]) Returns the value of variable where the local maximum MATH of expression occurs, between lower and upper, with 7:fMax( specified tolerance. fMin(expression,variable, lower,upper[,tolerance]) Returns the value of variable where the local minimum MATH of expression occurs, between lower and upper, with 6:fMin( specified tolerance.
Function or Instruction/Arguments Key or Keys/Menu or Screen/Item Result geometcdf(p,x) Computes a cumulative probability at x, the number of y = DISTR the trial on which the first success occurs, for the F:geometcdf( discrete geometric distribution with the specified probability of success p. geometpdf(p,x) Computes a probability at x, the number of the trial on y = which the first success occurs, for the discrete geometric DISTR distribution with the specified probability of success p.
Function or Instruction/Arguments Result Goto label Transfers control to label. Key or Keys/Menu or Screen/Item † CTL 0:Goto GraphColor(function#, Sets the color for function#. Color #: 10-24. color#) GraphStyle(function#, † Sets a graphstyle for function#. graphstyle#) GridDot [color#] GridLine [color#] GridOff † CTL H:GraphColor( CTL H:GraphStyle( † y. Turns on grid dots in the graph area in the specified color. Color #: 10-24.
Function or Instruction/Arguments IndpntAuto Input Key or Keys/Menu or Screen/Item Result † y- Sets table to generate independent-variable values automatically. Indpnt: Auto Displays graph. † I/O 2:Input Input [variable] Prompts for value to store to variable. I/O 2:Input Input ["text",variable] Input [Strn,variable] † Displays Strn and stores entered value to variable.
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item Lbl label Creates a label of one or two characters. † CTL 9:Lbl lcm(valueA,valueB) length(string) Returns the least common multiple of valueA and valueB, which can be real numbers or lists. Returns the number of characters in string.
Function or Instruction/Arguments Logistic [Xlistname, Ylistname,freqlist, regequ] Manual-Fit [equname,color#, line style#] MATHPRINT Key or Keys/Menu or Screen/Item Result Fits a logistic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. Fits a linear equation to a scatter plot with specified color and line style (color #: 10-24, line style #: 1-4).
Function or Instruction/Arguments min(listA,listB) Key or Keys/Menu or Screen/Item Result Returns real or complex list of the smaller of each pair y 9 MATH of elements in listA and listB. 1:min( min(value,list) Returns a real or complex list of the smaller of value or y 9 MATH each list element. 1:min( valueA nCr valueB value nCr list list nCr value listA nCr listB n/d Returns the number of combinations of valueA taken valueB at a time.
Key or Keys/Menu or Screen/Item Function or Instruction/Arguments Result normalcdf(lowerbound, upperbound[,m,s]) Computes the normal distribution probability between y = DISTR lowerbound and upperbound for the specified m and s. 2:normalcdf( normalpdf(x[,m,s]) not(value) valueA nPr valueB value nPr list list nPr value 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.
Key or Keys/Menu or Screen/Item Function or Instruction/Arguments Result Plot#(type,Xlist, [,freqlist,color#]) Defines Plot# (1, 2, or 3) of type Histogram or Boxplot † y , STAT PLOTS for Xlist with frequency freqlist and color #: 10-24. Note: Xlist represents the Xlist name. Plot#(type,Xlist, [,freqlist,mark,color#]) Defines Plot# (1, 2, or 3) of type ModBoxplot for Xlist with frequency freqlist using mark and color #: 10-24. Note: Xlist represents the Xlist name.
Key or Keys/Menu or Screen/Item Function or Instruction/Arguments Result prod(list[,start,end]) Returns product of list elements between start and end. y 9 MATH 6:prod( Prompt variableA [,variableB,...,variable n] Prompts for value for variableA, then variableB, and so † I/O on. 2:Prompt 1-PropZInt(x,n Computes a one-proportion z confidence interval. [,confidence level]) 2-PropZInt(x1,n1,x2,n2 Computes a two-proportion z confidence interval.
Function or Instruction/Arguments P4Rx(r,q) P4Ry(r,q) QuadReg [Xlistname, Ylistname,freqlist, Key or Keys/Menu or Screen/Item Result Returns X, given polar coordinates r and q or a list of polar coordinates. Returns Y, given polar coordinates r and q or a list of polar coordinates. y; ANGLE 7:P4Rx( y; ANGLE 8:P4Ry( … regequ] Fits a quadratic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
Key or Keys/Menu or Screen/Item Function or Instruction/Arguments Result RecallPic n Displays the graph and adds the picture stored in Picn. y < STO 2:RecallPic complex value 4Rect Displays complex value or list in rectangular format. CMPLX 6:4Rect RectGC Sets rectangular graphing coordinates format. † y. RectGC ref(matrix) Returns the row-echelon form of a matrix.
Key or Keys/Menu or Screen/Item Function or Instruction/Arguments Result rowSwap(matrix,rowA, rowB) Returns a matrix with rowA of matrix swapped with rowB. y> rref(matrix) Returns the reduced row-echelon form of a matrix. y> MATH C:rowSwap( MATH B:rref( Returns R, given rectangular coordinates x and y or a list of rectangular coordinates. y; Returns q, given rectangular coordinates x and y or a list of rectangular coordinates.
Key or Keys/Menu or Screen/Item Function or Instruction/Arguments Result 2-SampZInt(s1,s2, Computes a two-sample z confidence interval. †… TESTS 9:2-SampZInt( v1,n1,v2,n2 [,confidence level]) (Summary stats input) Computes a two-sample z test. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Color #: 10-24. †… Computes a two-sample z test. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >.
Function or Instruction/Arguments SetUpEditor listname1 [,listname2,..., listname20] Key or Keys/Menu or Screen/Item Result Removes all list names from the stat list editor, then sets it up to display one or more listnames in the specified order, starting with column 1.
Function or Instruction/Arguments Key or Keys/Menu or Screen/Item Result SortA(keylistname, dependlist1[,dependlist2, ...,dependlist n]) Sorts elements of keylistname in ascending order, then sorts each dependlist as a dependent list. SortD(listname) Sorts elements of listname in descending order. y9 OPS 1:SortA( y9 OPS 2:SortD( SortD(keylistname, dependlist1[,dependlist2, ..., dependlist n]) Sorts elements of keylistname in descending order, then y 9 OPS sorts each dependlist as a dependent list.
Function or Instruction/Arguments Tangent(expression, value[,color#,linestyle#]) tanh(value) Key or Keys/Menu or Screen/Item Result Draws a line tangent to expression at X=value with specified color #: 10-24 and line style linestyle #: 1-2. y< DRAW 5:Tangent( yN Returns hyperbolic tangent of a real number, expression, or list. tanh( tanhL1(value) Returns the hyperbolic arctangent of a real number, expression, or list.
Function or Instruction/Arguments T-Test m0[,listname, freqlist,alternative, drawflag,color#]) Key or Keys/Menu or Screen/Item Result Performs a t test with frequency freqlist. alternative=L1 † … TESTS is <; alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Color #: 10- 2:T-Test 24. (Data list input) T-Test m0, v,Sx,n Performs a t test with frequency freqlist.
Function or Instruction/Arguments Key or Keys/Menu or Screen/Item Result Returns the variance of the elements in list with frequency freqlist. y9 Vertical x[,color#, linestyle#]) Draws a vertical line at x with specified color and line style. Color #: 10-24; line style #: 1-4. y< vwAxes Sets sequence graphs to plot v(n) on the x-axis and w(n) on the y-axis. variance(list[,freqlist]) Web MATH 8:variance( DRAW 4:Vertical † y. vw † y. Sets sequence graphs to trace as webs.
Key or Keys/Menu or Screen/Item Function or Instruction/Arguments Result ZFrac 1/10 Sets the window variables so that you can trace in increments of @X and @Y to ZInteger ZInterval s[,listname, freqlist,confidence level] 1 ----- , 10 1 ----- . 20 if possible. Sets TraceStep to 1 ----10 and Redefines the viewing window using the following dimensions: TraceStep=1, @X=0.5, Xscl=10, @Y=1, Computes a z confidence interval. †… TESTS 7:ZInterval Computes a z confidence interval.
Function or Instruction/Arguments Z-Test(m0,s[,listname, freqlist,alternative, drawflag,color#]) Key or Keys/Menu or Screen/Item Result Performs a z test with frequency freqlist. alternative= L1 † … TESTS is <; alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Color #: 10- 1:Z-Test( 24. (Data list input) Z-Test(m0,s,v,n [,alternative,drawflag, color#]) (Summary stats input) Performs a z test. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >.
Function or Instruction/Arguments Cube root: 3‡(value) Key or Keys/Menu or Screen/Item Result Returns the cube root of a real or complex number, expression, or list. MATH 4:3‡( Equal: valueA=valueB y: Returns 1 if valueA = valueB. Returns 0 if valueA ƒ valueB. valueA and valueB can be real or complex numbers, expressions, lists, or matrices. TEST 1:= Not equal: valueAƒvalueB Returns 1 if valueA ƒ valueB. Returns 0 if valueA = valueB.
Function or Instruction/Arguments Key or Keys/Menu or Screen/Item Result Square root: ‡(value) Returns square root of a real or complex number, expression, or list. yC Multiplication: valueAävalueB Returns valueA times valueB. ¯ Multiplication: valueälist Returns value times each list element. ¯ Multiplication: listävalue Returns each list element times value. ¯ Multiplication: listAälistB Returns listA elements times listB elements.
Appendix A: Functions and Instructions 377
Appendix B: Reference Information Variables User Variables The TI-84 Plus C 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-84 Plus C can update X, Y, R, q, and T during graphing, so you may want to avoid using these variables to store nongraphing data.
Logistic The logistic regression algorithm applies nonlinear recursive least-squares techniques to optimize the following cost function: N J = c - – y i ---------------------– bx 1 + ae 2 i i=1 which is the sum of the squares of the residual errors, where: x = the independent variable list y = the dependent variable list N = the dimension of the lists This technique attempts to estimate the constants a, b, and c recursively to make J as small as possible.
The degrees of freedom df that make up the mean squares are: Factordf = I – 1 = numeratordf forÜ I Errordf = ni – 1 = denominatordf for Ü i=1 where: I = = = = = xi Sxi ni x number of populations the mean of each list the standard deviation of each list the length of each list the mean of all lists 2-SampFTest Below is the definition for the 2-SampÜTest. Sx1, Sx2 = Sample standard deviations having n 1 – 1 and n 2 – 1 degrees of freedom df, respectively.
2-SampTTest The following is the definition for the 2-SampTTest. The two-sample t statistic with degrees of freedom df is: x1 – x2 t = ---------------S where the computation of S and df are dependent on whether the variances are pooled.
The iteration used to compute i: –N 1 – 1 + i –N 0 = PV + PMT G i ------------------------------ + FV 1 + i i I% = 100 C Y e where: x = i y = P/Y C/Y y ln x + 1 – 1 Gi = 1 + i k where: k = 0 for end-of-period payments k = 1 for beginning-of-period payments PMT G i – FV i ln --------------------------------------------- PMT G i + PV i N = ---------------------------------------------------------ln 1 + i where: i ƒ 0 N = – PV + FV PMT whe
Iterate from m = 1 to pmt2 I m = RND RND12 – i bal m – 1 bal m = bal m – 1 – I m + RND PMT then: bal( ) = bal pmt2 Prn( ) = bal pmt2 – bal pmt1 Int( ) = pmt2 – pmt1 + 1 RND PMT – Prn( ) 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.
Days between Dates With the dbd( function, you can enter or compute a date within the range Jan. 1, 1950, through Dec. 31, 2049.
Remember that EOS™ evaluates from left to right and calculations within parentheses are evaluated first. You should use parentheses where the rules of algebra may not be clear. In MathPrint™ mode, parentheses may be pasted in an expression to indicate how the input is interpreted. If you are using trigonometric functions or performing polar and rectangular conversions, the unexpected results may be caused by an angle mode setting.
4. Select TRANSMIT to send the file. Brightness Feature If the brightness setting is too dark (set to 9) or too dim (set to 0) the unit may appear as if it is malfunctioning or turned off. To adjust the brightness, press and release y, and then press and hold } or †. The TI-84 Plus C retains the brightness setting in memory when it is turned off. Automatic Dimming The TI-84 Plus C has an automatic dimming feature. To help prolong battery life, the screen dims after 90 seconds of no activity.
TI-Cares KnowledgeBase The TI-Cares KnowledgeBase provides 24-hour access through the Web to find answers to frequently asked questions. The TI-Cares KnowledgeBase searches its repository of known solutions and presents you with the solutions that are most likely to solve your problem. You can search the TI-Cares KnowledgeBase at education.ti.com/support.
Error Conditions When the TI-84 Plus C Silver Edition detects an error, it returns an error message as a menu title, such as ERR:SYNTAX or ERR:DOMAIN. This table contains each error type, possible causes, and suggestions for correction. The error types listed in this table are each preceded by ERR: on your graphing calculator display. For example, you will see ERR:ARCHIVED as a menu title when your graphing calculator detects an ARCHIVED error type.
Error Type Possible Causes and Suggested Remedies DIMENSION MISMATCH Your calculator displays the ERR:DIMENSION MISMATCH error if you are trying to perform an operation that references one or more lists or matrices whose dimensions do not match. For example, multiplying L1*L2, where L1={1,2,3,4,5} and L2={1,2} produces an ERR:DIMENSION MISMATCH error because the number of elements in L1 and L2 do not match. You may need to turn Plots Off to continue.
Error Type Possible Causes and Suggested Remedies INVALID DIMENSION • The ERR:INVALID DIMENSION error message may occur if you are trying to graph a function that does not involve the stat plot features. The error can be corrected by turning off the stat plots. To turn the stat plots off, press y , and then select 4:PlotsOff. • You specified a list dimension as something other than an integer between 1 and 999. • You specified a matrix dimension as something other than an integer between 1 and 99.
Error Type Possible Causes and Suggested Remedies NONREAL ANSWERS In Real mode, the result of a calculation yielded a complex result. This error is not returned during graphing. The TI-84 Plus C allows for undefined values on a graph. OVERFLOW You attempted to enter, or you have calculated, a number that is beyond the range of the graphing calculator. This error is not returned during graphing. The TI-84 Plus C allows for undefined values on a graph.
Error Type Possible Causes and Suggested Remedies VERSION You have attempted to receive an incompatible variable version from another graphing calculator. A program may contain commands not supported in the OS version on your graphing calculator. Always use the latest OS. TI-84 Plus C and TI-84 Plus share programs but a version error will be given if any new TI-84 Plus C programs may need to be adjusted for the high resolution graph area. WINDOW RANGE A problem exists with the window variables.
Screen MODE Horizontal (Xmax-Xmin) / 264 = @X (Ymax-Ymin) / 80 = @Y @X É… 2 = TraceStep (Function Mode) Entering a value for @X or @Y from the home screen on a program gives: Xmax = Xmin + @X * 264 Ymax = Ymin + @Y * 80 Graph-Table (Xmax-Xmin) / 184 = @X (Ymax-Ymin) / 144 = @Y @X É… 2 = TraceStep (Function Mode) Entering a value for @X or @Y from the home screen on a program gives: Xmax = Xmin + @X * 184 Ymax = Ymin + @Y * 144 Cursor coordinates are displayed as eight-character numbers (which may includ
Function Results Function Range of Result sinL1 x, tanL1 x L90¡ to 90¡ or Lp à 2 to p à 2 (radians) cosL1 x 0¡ to 180¡ or 0 to p (radians) Appendix B: Reference Information 394
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Index - (negation) 17 Symbols ! Store 22 !dim( (assign dimension) 174 (- (degrees notation) 374 (- (negation) 43, 375 (– (subtraction) 41, 376 ( ) (parentheses) 17 (^ (power) 41, 375 (: (colon) 279 (! (factorial) 374 (! Store 369 (!dim( (assign dimension) 158, 352 (' (minutes notation) 67, 376 (“ ” (string indicator) 270 () (plot type, normal probability) 218 ()Int( (sum of interest) 357 ()Prn( (sum of principal) 362 ([ ] (matrix indicator) 151 ({ (less than or equal to) 375 (* (multiplication) 41, 376 (*
addition (+) 41, 376 alpha cursor 11 alpha-lock 20 alternative hypothesis 226 amortization )Int( (sum of interest) 357 )Prn( (sum of principal) 362 bal( (amortization balance) 261, 349 calculating schedules 261 formula 382 and (Boolean operator) 71, 348 ANGLE menu 67 angle modes 13 angle( 62, 348 animate graph style 77 ANOVA( (one-way variance analysis) 243, 348, 379 Ans (last answer) 25, 327, 348 APD (Automatic Power Down) 5 applications See examples, applications 40 Apps 22, 327 AppVars 22, 327 arccosine
complex modes (a+bi, re^qi) 14, 57, 349, 364 numbers 14, 57, 364 compounding-periods-per-year variable (C/Y) 257, 265 concatenation (+) 272, 376 confidence intervals 40, 227 conj( (conjugate) 61, 350 connecting two calculators 342, 343, 345 contrast (display) 6 convergence, sequence graphing 113 conversions 4Dec (to decimal) 44, 351 4DMS (to degrees/minutes/ seconds) 68, 352 4Eff (to effective interest rate) 264 4F3 4D 56 4Frac (to fraction conversion) 44, 354 4n/d3 4Un/d 56 4Nom (to nominal interest rate c
drawing on a graph circles (Circle( ) 132 functions and inverses (DrawF, DrawInv) 129 line segments (Line( ) 126 lines (Horizontal, Line(, Vertical) 128 points (Pt-Change, Pt-Off, Pt-On) 134 tangents (Tangent) 128 text (Text) 133 using Pen 134 DrawInv (draw inverse) 130, 352 DS<( (decrement and skip) 285, 352 DuplicateName menu 345 dx/dt operation on a graph 93, 100 dy/dx operation on a graph 93, 100, 105 E E (exponent) 13, 19, 352 e^( (exponential) 42, 352 edit keys table 20 Else 282 End 283, 353 Eng (eng
cash flow 383 days between dates 384 interest rate conversions 383 logistic regression 379 sine regression 379 time value of money 381 two-sample F-Test 380 two-sample t test 381 fPart( (fractional part) 53, 156, 354 fractions n/d 15, 57 Un/d 15, 57 free-moving cursor 84 frequency 206 Full (full-screen mode) 15, 354 full-screen mode (Full) 15, 354 Func (function graphing mode) 13, 354 function graphing accuracy 84 CALC (calculate menu) 91 defining and displaying 73 defining in the Y= editor 74 defining on t
imaginary part (imag( ) 356 implied multiplication 17 increment and skip (IS>( ) 285 increment and skip (IS>( ) 357 independent variable 118, 120, 356 IndpntAsk 118, 120, 356 IndpntAuto 118, 120, 357 inferential stat editors 225 inferential statistics alternative hypotheses 226 bypassing editors 227 calculating test results (Calculate) 227 confidence interval calculations 227 data input or stats input 226 entering argument values 226 graphing test results (Draw) 227 input descriptions table 244 pooled optio
M Manual Linear Fit 204, 210 marked for deletion 336 MATH CPX (complex menu) 61 MATH menu 43 MATH NUM (number menu) 51 math operations 40 MATH PRB (probability menu) 64 Matr4list( (matrix-to-list conversion) 160, 179, 359 matrices accessing elements 153 copying 152 defined 148 deleting from memory 149 dimensions 148, 158 displaying a matrix 152 displaying matrix elements 148 editing matrix elements 150 indicator ([ ]) 151 math functions 153 matrix math functions (det(, T, dim(, Fill(, identity(, randM(, aug
or (Boolean) operator 71, 361 order of evaluating equations 16 Output( 144, 290, 361 Overwrite 335, 345 Overwrite All 335 P P/Y (number-of-payment-periods-per-year variable) 257, 265 P4Rx(, P4Ry( (polar-to-rectangular conversions) 68, 364 panning 85 Par/Param (parametric graphing mode) 13, 361 parametric equations 98 parametric graphing CALC (calculate operations on a graph) 100 defining and editing 98 free-moving cursor 99 graph format 98 graph styles 97 moving the cursor to a value 100 selecting and dese
R4Pr(, R4Pq( (rectangular-to-polar conversions) 366 Radian angle mode 13, 68, 364 radian notation (R) 68, 374 RAM ARCHIVE ALL menu 331 rand (random number) 64, 364 randBin( (random binomial) 66, 364 randInt( (random integer) 65, 364 randIntNoRep( 67 randM( (random matrix) 159, 364 randNorm( (random Normal) 66, 364 random seed 64 RCL (recall) 23 re^i) (polar complex mode) 14 re^i (polar complex mode) 57 re^qi (polar complex mode) 364 Real mode 14, 364 real( (real part) 61, 364 RecallGDB 139, 364 RecallPic
Solver 47 solving for variables in the equation solver 49 SortA( (sort ascending) 173, 200, 368 SortD( (sort descending) 173, 200, 369 spinner 1 split-screen modes G-T (graph-table) mode 143 Horiz (horizontal) mode 142 setting 141, 144 split-screen values 134, 144 square (²) 41, 375 square root ($( ) 41 square root ($( ) 376 startTmr, start timer 369 STAT CALC Stat Wizards 204 STAT CALC menu 204 STAT EDIT menu 200 stat list editor attaching formulas to list names 194 clearing elements from lists 192 creatin
tan( (tangent) 41, 369 tan/( (arctangent) 41, 369 tangent (tan( ) 41 tangent (tan( ) 369 tangent lines, drawing 128 Tangent( (draw line) 128, 370 tanh( (hyperbolic tangent) 275, 370 tanh/( (hyperbolic arctangent) 275, 370 TblStart (table start variable) 118 tcdf( (student-t distribution probability) 248, 370 TEST (relational menu) 69 TEST LOGIC (Boolean menu) 70 Text( instruction 133, 144, 370 placing on a graph 133, 144 Then 282, 356 thick graph style 77 TI Connect™ 343 TI Rechargeable Batteries charging 3
variance of a list (variance( ) 372 variance( (variance of a list) 182, 372 VARS menu GDB 28 Picture 28 Statistics 28 String 28 Table 28 Window 28 Zoom 28 Vertical (draw line) 128, 372 viewing window 79 vw/uvAxes (axes format) 111, 372 W w sequence function 107 Web (axes format) 111, 372 web plots 113 While 283, 372 window variables function graphing 80 parametric graphing 99 polar graphing 103 X x$ (root) 374 XFact zoom factor 90 x-intercept of a root 92 xor (Boolean) exclusive or operator 71, 372 xth ro
