### Summary of content (431 pages)

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TI-86 GRAPHING CALCULATOR GUIDEBOOK TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR, Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas Instruments Incorporated. Windows is a registered trademark of Microsoft Corporation. IBM is a registered trademark of International Business Machines Corporation Macintosh is a registered trademark of Apple Computer, Inc. Copyright © 1997, 2001 by Texas Instruments Incorporated $$FRONT.

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ii Important Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an “as-is” basis.

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iii Table of Contents TI-86 Quick Start 1 Preparing to Use Your New TI-86 ..................................................... 2 Installing the AAA Batteries ......................................................... 2 Turning On and Turning Off the TI-86.......................................... 2 Adjusting the Contrast ................................................................. 2 Resetting All Memory and Defaults.............................................. 3 Calculating on the Home Screen......

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iv TI-86 Table of Contents The ALPHA Key........................................................................... 21 ALPHA-lock and alpha-lock........................................................ 22 Common Cursors........................................................................ 22 Cursor Direction Keys ................................................................. 23 Inserting, Deleting, and Clearing Characters.............................. 23 Entering Expressions and Instructions .........

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TI-86 Table of Contents The CHAR (Character) Menu........................................................... 45 The CHAR MISC (Miscellaneous) Menu...................................... 46 The CHAR GREEK Menu ............................................................. 46 The CHAR INTL (International) Menu ......................................... 46 Adding a Modifier to a Vowel ....................................................

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vi TI-86 Table of Contents The BASE CONV (Conversion) Menu .......................................... 68 Converting Number Bases.......................................................... 68 The BASE BOOL (Boolean) Menu ............................................... 68 Results of Boolean Operations ................................................... 69 The BASE BIT Menu.................................................................... 69 Using Complex Numbers.............................................

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TI-86 Table of Contents Using ‰f(x), DIST, or ARC ............................................................ 98 Using dyàdx or TANLN............................................................... 99 Using ISECT .............................................................................. 100 Using YICPT.............................................................................. 100 Evaluating a Function for a Specified x......................................... 101 Drawing on a Graph...................

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viii TI-86 Table of Contents Chapter 9: Parametric Graphing 123 Preview: Parametric Graphing ...................................................... 124 Defining a Parametric Graph......................................................... 125 Setting Parametric Graphing Mode.......................................... 126 The GRAPH Menu..................................................................... 126 Displaying the Parametric Equation Editor...............................

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TI-86 Table of Contents Chapter 11: Lists 151 Lists on the TI-86 .......................................................................... 152 The LIST Menu.......................................................................... 152 The LIST NAMES Menu............................................................. 153 Creating, Storing, and Displaying Lists.......................................... 153 Entering a List Directly in an Expression...................................

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x TI-86 Table of Contents The MATRX (Matrix) Menu ...................................................... 178 The MATRX NAMES Menu ....................................................... 178 Creating a Matrix in the Matrix Editor ..................................... 178 The Matrix Editor Menu ........................................................... 179 Creating a Matrix on the Home Screen .................................... 180 Creating a Complex Matrix ................................................

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TI-86 Table of Contents Entering and Solving a Polynomial........................................... 211 Storing a Polynomial Coefficient or Root to a Variable ............ 212 Chapter 16: Programming 213 Writing a Program on the TI-86 .................................................... 214 The PRGM Menu ...................................................................... 214 Creating a Program in the Program Editor ............................... 214 The Program Editor Menu ..........................

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xii TI-86 Table of Contents The LINK SND85 (Send Data to TI-85) Menu ........................... 239 Preparing the Receiving Device..................................................... 240 Transmitting Data ......................................................................... 240 Receiving Transmitted Data .......................................................... 241 Repeating Transmission to Several Devices ............................. 242 Error Conditions ..........................................

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TI-86 Quick Start TI-86 Preparing to Use Your New TI-86 ........................................ 2 Calculating on the Home Screen.......................................... 3 Plotting Functions on the Graph Screen .............................. 9 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 00QWIKST.

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2 Quick Start Preparing to Use Your New TI-86 The brief examples in the TI-86 Quick Start demonstrate some common TI-86 features. Before you begin, you must install the batteries, turn on the calculator, adjust the contrast, and reset the memory and the defaults. Chapter 1 has more details on these topics. Installing the AAA Batteries Four AAA batteries are included in the TI-86 retail package. Remove the batteries from the package and install them in the battery compartment on the back of the calculator.

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Quick Start 3 Resetting All Memory and Defaults To reset all memory and defaults, press - ™ ( & ). The messages Mem cleared and Defaults set are displayed on the home screen, confirming that all memory and defaults are reset. You may need to adjust the contrast after memory and default reset. Calculating on the Home Screen To express - and 1 keystroke combinations, this guidebook places brackets ( ã and ä ) around the word above the key to press.

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4 Quick Start When ALPHA-lock is on and you press a key, the letters printed in blue above the keys are pasted to the screen. In the example, press Z to enter a V. Enter the variable name to which you want to store the last answer. ALPHA-lock is on. ãVä Store the last answer to the variable. The stored value is displayed on the next line. b Using a Variable in an Expression Enter the variable, and then square it. (:) 1 ãVä I Evaluate.

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Quick Start a negates a value, as in L2. T subtracts, as in 5N2=3. An ellipsis (...) indicates that the result continues beyond the screen. Displaying a Complex Number as a Result Enter the natural log function. (:) B Enter a negative number. Da2E Evaluate. The result is displayed as a complex number. b (press " to display more) Using a List with a Function Enter the exponential function. (:) - ‚ Display the LIST menu, and then select the open brace ( { ) from the LIST menu.

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6 Quick Start Displaying the Integer Part of Real Numbers in a List Display the MATH menu. (The MATH menu automatically replaces the LIST menu from the last activity.) -Œ Select NUM to display the MATH NUM menu. The MATH menu shifts up. & Select the iPart (integer part) function from the MATH NUM menu. iPart is pasted to the screen. (The previous entry was left on the screen to illustrate the effect of iPart on the previous answer.) ' Paste Ans to the cursor location.

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Quick Start Finding the Square Root Paste the square root function to the screen. (:) - ˆ Enter a value for which you want to find the square root. 144 Evaluate the expression. The square root of 144 is displayed. b Calculating Derivatives Display the CALC menu, and then select der1. (:) -† ( CALC menu Enter an expression ( x 2) with respect to a variable (x) at a given point (8). 2IP2 P8E Evaluate. The first derivative of x 2 with respect to x at 8 is displayed. b 00QWIKST.

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8 Quick Start Retrieving, Editing, and Re-evaluating the Previous Entry When you press b, the TI-86 stores the expression or instruction you entered to the built-in memory storage area called ENTRY. Retrieve the last entry from the previous example. (The last activity was not cleared.) -¢ Edit the retrieved entry. !!3 Evaluate. The first derivative of x 2 with respect to x at 3 is displayed.

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Quick Start Select ¡C to designate Celsius as the unit to which you want to convert. & Convert. The ¡C equivalent of L4¡F is displayed. b 9 Storing an Unevaluated Expression to an Equation Variable When storing to an equation variable using =, enter the equation variable first, then =, and then the unevaluated expression. This is the opposite from the order for storing to most other variables on the TI-86. Enter the built-in equation variable y1. (:) - n ãYä 1 Enter the equals sign (=).

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10 Quick Start In the equation editor, you must express each equation in terms of the independent variable x (in Func graphing mode only; Chapter 5). Select y(x)= from the GRAPH menu to display the equation editor. 5(sin x) is the unevaluated expression stored to y1 in the previous activity. The equation editor menu is displayed as the lower menu. & Move the cursor down. The y2= prompt is displayed. # Enter the expression 5(cos x) at the y2= prompt.

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Quick Start 11 Plotting a Function on the Graph Screen Select GRAPH from the GRAPH menu to plot the graph on the graph screen. The xand y-axes and GRAPH menu are displayed. Then each selected graph is plotted in the order in which it is listed in the equation editor. -i When the graph is plotted, you can move the free-moving cursor ( + ) around the graph screen. The cursor coordinates are displayed at the bottom of the graph.

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12 Quick Start Trace the function y2. As you trace, the displayed y value is the solution for 5(cos x) at the current x value, which also is displayed on the screen. " and ! Evaluating y for a Specific x Value (During a Trace) Enter a real number (or an expression that resolves to a real number) that is within the dimensions of the current graph screen. When you enter the first character, the x= prompt is displayed. 6 Evaluate y2 at x=6. The trace cursor moves directly to the solution.

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Quick Start Change the value stored in the xMin window variable to 0. 0 Plot the graph on the redefined graph screen. Since xMin=0, only the first and fourth quadrants of the graph plane are displayed. * Deselecting a Function Select y(x)= from the GRAPH menu to display the equation editor and equation editor menu. The GRAPH menu shifts up and y(x)= is highlighted. & Select SELCT from the equation editor menu to deselect the function y1=. The equals sign is no longer highlighted.

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14 Quick Start Zooming In on a Portion of the Graph Screen Select ZOOM to display the GRAPH ZOOM menu. The GRAPH menu shifts up and ZOOM is highlighted. ( Select BOX from the GRAPH ZOOM menu to activate the zoom-box cursor. & Move the zoom-box cursor to a point that is to be a corner of the redefined graph screen, and then mark the point with a small square. "#!$ b Move the cursor away from the small square to a point that is to be the opposite corner of the redefined graph screen.

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1 Operating the TI-86 TI-86 Installing or Replacing Batteries ........................................ 16 Turning On and Turning Off the TI-86 ............................... 17 Adjusting the Display Contrast .......................................... 17 The Home Screen ............................................................... 18 Entering Numbers .............................................................. 19 Entering Other Characters .................................................

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16 Chapter 1: Operating the TI-86 Installing or Replacing Batteries Your new TI-86 includes four AAA alkaline batteries. You must install them before you can turn on the calculator. A lithium backup battery is installed in the calculator already. To express - and 1 keystroke combinations, this guidebook places brackets ( ã and ä ) around the word above the key to press. If the calculator is on, turn it off (press - ) to avoid loss of information stored in memory.

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17 Chapter 1: Operating the TI-86 Properly dispose of the old battery. To replace the lithium backup battery, remove the battery cover and unscrew the tiny screw holding the BACK UP BATTERY cover in place. Install a new CR1616 or CR1620 battery according to the polarity (+ and N) diagram on the cover. Replace the cover and screw. Turning On and Turning Off the TI-86 To turn on the TI-86, press ^.

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18 Chapter 1: Operating the TI-86 The TI-86 has 40 contrast settings, so each number 0 through 9 represents four settings. You can adjust the display contrast anytime to suit your viewing angle and lighting conditions. As you adjust, a number from 0 (lightest) to 9 (darkest) in the top-right corner indicates the current contrast setting. The number is not visible when the contrast is extremely light or dark. As the batteries weaken over time, the actual contrast level of each number shifts.

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Chapter 1: Operating the TI-86 The mode settings control the way the TI-86 interprets expressions and displays answers (page 34). When an entry is executed on the home screen, the answer is displayed on the right side of the next line. When you execute an instruction, Done is typically displayed on the right side of the next line. Entry Answer If an answer is too long to display on the screen, an ellipsis (...) is displayed, initially to the right. To view more of the answer, press ".

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20 Chapter 1: Operating the TI-86 Using Scientific or Engineering Notation Enter the mantissa (part of the number that precedes the exponent). This value can be an expression. D19 F2E Paste E to the cursor location. C In scientific notation only, one digit precedes the decimal. If the exponent is negative, paste L to the cursor location. Then enter a one-, two-, or three-digit exponent.

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Chapter 1: Operating the TI-86 The 2nd Key The - key is yellow. When you press -, the cursor becomes Æ (the 2nd cursor). When you press the next key, the yellow character, abbreviation, or word printed above that key is activated, instead of the key’s primary function. To enter a space within text, press 1 ¤. Spaces are not valid within variable names. The ALPHA Key The 1 key is blue. When you press 1, the cursor becomes ³ (the uppercase ALPHA cursor).

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22 Chapter 1: Operating the TI-86 ♦ To switch from alpha-lock to ALPHA-lock, press 1. You can use - when ALPHA-lock or alpha-lock is on. Also, if you press a key that has no blue character above it, such as 6, 3, or !, the key’s primary function still applies. Common Cursors In most cases, the appearance of the cursor indicates what will happen when you press the next key. Graphs and editors sometimes use additional cursors, which are described in other chapters.

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Chapter 1: Operating the TI-86 23 Cursor Direction Keys - $ scrolls/moves cursor up - $ darkens screen contrast ! moves cursor left " moves cursor right - ! moves cursor to beginning of entry - " moves cursor to end of entry - # scrolls/moves cursor down - # lightens screen contrast If you hold down ", #, !, or $, the cursor continues to move. Inserting, Deleting, and Clearing Characters The entry cursor ( Å ) overwrites characters.

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24 Chapter 1: Operating the TI-86 Entering Expressions and Instructions Entering an Expression An expression is any combination of numbers and variables that serve as arguments for one or more functions. On the TI-86, you typically enter an expression in the same order as you would write it on paper. For example, pr 2, 5 tan xStat, and 40((L5+3)N(2+3)) are expressions. You can use an expression on the home screen to calculate an answer.

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Chapter 1: Operating the TI-86 25 Using Functions in Expressions A function returns a value. Some examples of functions are ÷ , L , + , ‡ , and log. To use functions, you usually must enter one or more valid arguments. In this guidebook, optional arguments are shown in brackets ( ã and ä ). Do not include these brackets when you enter the arguments. When this guidebook describes the syntax of a function or instruction, each argument is in italics. For example: sin angle.

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26 Chapter 1: Operating the TI-86 When you select a function, instruction, or operator, a symbol comprising one or more characters is pasted to the cursor location. Once the symbol is pasted to the cursor location, you can edit individual characters. For example, assume that you pressed - w / / * & & b to paste yMin to the cursor location as part of an expression. Then you realized you wanted xMin. Instead of pressing nine keys to select xMin, you can simply press ! ! ! ! 2.

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Chapter 1: Operating the TI-86 Chapter 5: Function Graphing introduces graphing. 27 When you interrupt a graph, a partial graph and the GRAPH menu are displayed. ♦ To return to the home screen, press : : or any non-graphing key. ♦ To restart graphing, select an instruction that displays the graph. Diagnosing an Error If a syntax error occurs within a stored equation during program execution, select GOTO to return to the equation editor, not to the program (Chapter 5).

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28 Chapter 1: Operating the TI-86 Reusing Previous Entries and the Last Answer Retrieving the Last Entry When you press b on the home screen to evaluate an expression or to execute an instruction, the entire expression or instruction is placed in a storage area called ENTRY (last entry). When you turn off the TI-86, ENTRY is retained in memory. To retrieve the last entry, press - ¢. The current line is cleared and the entry is pasted to the line.

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Chapter 1: Operating the TI-86 29 Consecutively entered entries separated by colons (page 26) are stored as one entry. Retrieving Multiple Entries To store two or more expressions or instructions together to ENTRY, enter them on one line, separating each from the other with a colon, and then press b. Upon execution, the entire group is stored in ENTRY. The example below shows one of many ways you can manipulate this feature to avoid tedious manual re-entry.

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30 Chapter 1: Operating the TI-86 To copy the variable name Ans to the cursor location, press - ¡. You can use the variable Ans anywhere that the value stored to it is valid. When the expression is evaluated, the TI-86 calculates the result using the value stored in Ans. 1`7M4`2 Calculate the area of a garden plot 1.7 meters by 4.2 meters. Calculate the yield per square meter if the plot 147 F - ¡ b produces a total of 147 tomatoes.

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Chapter 1: Operating the TI-86 31 Using TI-86 Menus The symbols for many TI-86 features are found in menus instead of on the TI-86 keyboard. Displaying a Menu The way to display a particular menu depends on the menu’s location on the TI-86. Some TI-86 menus have as many as 25 items.

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32 Chapter 1: Operating the TI-86 The Menu Keys The Appendix Menu Map shows every TI-86 menu. Typically, a TI-86 menu item is five characters long or less. - upper menu keys M1 M2 M3 M4 M5 lower menu keys & ' ( ) * - l clears all menus - e through i selects upper menu items - ./ QUIT / scrolls lower menu groups . removes the lower menu Selecting a Menu Item When you display a menu, one to five items are displayed.

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Chapter 1: Operating the TI-86 33 To select an item from the upper menu, press - and the appropriate key e through i. To select PROB from the upper menu, press - f. To select iPart from the lower menu, press '. When an editor menu is displayed as the upper menu, and you select an item from the lower menu that displays yet another menu, the editor menu remains as the upper menu. When you select NUM from the lower menu... The MATH menu disappears. ...

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34 Chapter 1: Operating the TI-86 Viewing and Changing Modes In the screen to the right, the default mode settings are highlighted along the left side of the screen. To display the mode settings, press - m. The current settings are highlighted. Mode settings control how the TI-86 displays and interprets numbers and graphs. The Constant Memory feature retains current mode settings when the TI-86 is turned off.

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Chapter 1: Operating the TI-86 35 Decimal Modes Float (floating) Displays results up to 12 digits, plus any sign and the floating decimal point (fixed) (012345678901; each number is a setting) Displays results with the specified number of digits to the right of the decimal point (rounds answers to the specified decimal place); the second 0 sets 10; the second 1 sets 11 Angle Modes Radian Interprets angle values as radians; displays answers in radians Degree Interprets angle values as degrees; displ

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36 Chapter 1: Operating the TI-86 Vector Coordinate Modes Vector modes do not affect how you enter vectors.

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2 The CATALOG, Variables, and Characters TI-86 The CATALOG .................................................................... 38 Storing Data to Variables................................................... 39 Classifying Variables as Data Types................................... 42 The CUSTOM Menu ........................................................... 44 The CHAR (Character) Menu.............................................. 45 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 02CATVAR.

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38 Chapter 2: The CATALOG, Variables, and Characters The CATALOG The CATALOG is the first item on the CATLG-VARS menu. -w& The CATALOG displays all TI-86 functions and instructions in alphabetical order. Items that do not begin with a letter (such as + or 4Bin) are at the end of the CATALOG. The selection cursor ( 4 ) indicates the current item. To select an item from the CATALOG, move the selection cursor to the item and press b.

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Chapter 2: The CATALOG, Variables, and Characters 39 Storing Data to Variables This chapter describes the first two data storage methods listed here. The other methods are described in the appropriate chapters. On the TI-86, data can be stored to variables in several ways. You can: ♦ Use X to store a value to a variable. ♦ Use = to store an unevaluated expression to an equation variable. ♦ Use an editor’s Name= prompt to store several types of data to a variable.

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40 Chapter 2: The CATALOG, Variables, and Characters Storing a Value to a Variable Name Enter a value, which can be an expression. -~5I Enter ¶ (the store symbol) next to the value. X Create a variable name one to eight characters long, starting with a letter. ALPHA-lock is on. ãAä ãRä ãEä ãAä Store the value to the variable. The value stored to the variable is displayed as a result.

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Chapter 2: The CATALOG, Variables, and Characters 41 Storing an Answer To store an answer to a variable before you evaluate another expression, use X and Ans. In the example, the TI-86 multiplies the value stored to AREA times 3.3. Enter and evaluate an expression. 11 ãAä ãRä ãEä ãAä 1 M3`3b To paste AREA to the cursor location, you can press w (, move the selection cursor (4) to AREA, and press b. Store the answer to a user-created variable or to a valid built-in variable.

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42 Chapter 2: The CATALOG, Variables, and Characters Recalling a Variable Value To cancel RCL, press :. Editing a recalled value does not change the value stored to the variable. Move the cursor to where you want to insert the recalled variable value. 100 M Display the Rcl prompt at the bottom of the screen. ALPHA-lock is on. -– Enter the variable name you want to recall. [V] [O] [L] Recall the variable contents to the cursor location.

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Chapter 2: The CATALOG, Variables, and Characters -w The CATLG-VARS (CATALOG-Variables) Menu To display additional menu groups, press /. The list names fStat, xStat, and yStat are statistical result variables on the VARS STAT screen.

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44 Chapter 2: The CATALOG, Variables, and Characters Selecting a Variable Name The example assumes that the real-number variables AREA and VOL from the example on page 41 have not been deleted from memory. Select the appropriate data-type selection screen from the CATLG-VARS menu. -w( Move the cursor to the variable you want to select. # Select the variable you want.

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Chapter 2: The CATALOG, Variables, and Characters 45 Clearing CUSTOM Menu Items To clear an item from the second or third menu group, press / until the item is displayed, and then select it. You cannot delete a TI-86 built-in variable. You cannot delete a program variable using DelVar( . Select BLANK from the CATALOG menu. The CUSTOM BLANK menu is displayed. -w &) Clear the menu item. ( To clear more items, repeat steps 2 and 3.

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46 Chapter 2: The CATALOG, Variables, and Characters -Ÿ& The CHAR MISC (Miscellaneous) Menu Ñ, ñ, Ç, and ç are valid as any character of a variable name, including the first letter. MISC ? GREEK # INTL & % ' 4 ! @ $ ~ | 4 ¿ Ñ ñ Ç ç 4 H q l m r 4 G s τ f J %, ' , and ! can be functions. The CHAR GREEK Menu All CHAR GREEK menu items are valid variable-name characters, including the first letter. p ( - ~ ) is not valid as a character; p is a constant on the TI-86.

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3 Math, Calculus, and Test Operations TI-86 Keyboard Mathematical Functions .................................... 48 The MATH Menu................................................................ 49 The CALC (Calculus) Menu ................................................ 54 The TEST (Relational) Menu............................................... 55 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 03MATH.

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48 Chapter 3: Math, Calculus, and Test Operations Keyboard Mathematical Functions The A to Z Reference details which data types are valid arguments for each function. You can use these mathematical functions in expressions with real or complex values. You can use some of them with lists, vectors, matrices, or strings. When you use lists, vectors, or matrices, the valid functions return a list of results calculated on an element-by-element basis.

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Chapter 3: Math, Calculus, and Test Operations The MATH Menu NUM PROB number menu ANGLE angle menu probability menu -Œ HYP value can sometimes be an expression, list, vector, or matrix. For details about specific syntax options and examples, refer to the A to Z Reference.

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50 Chapter 3: Math, Calculus, and Test Operations The MATH PROB (Probability) Menu NUM ! ! (factorial) is valid for nonintegers. randInt, randNorm, and randBin are abbreviated in the MATH PROB menu.

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Chapter 3: Math, Calculus, and Test Operations The MATH ANGLE Menu NUM o angle can be a list for ¡ , r , and 4DMS. In a calculation, the result of a degrees'minutes'seconds' entry is treated as degrees in Degree angle mode only. It is treated as radians in Radian angle mode.

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52 Chapter 3: Math, Calculus, and Test Operations The MATH MISC (Miscellaneous) Menu NUM sum value can sometimes be an expression, list, vector, or matrix. For details about specific syntax options, refer to the A to Z Reference.

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Chapter 3: Math, Calculus, and Test Operations 53 The InterpolateàExtrapolate Editor - Œ / & Using the interpolateàextrapolate editor, you can interpolate or extrapolate a value linearly, given two known pairs and the x-value or y-value of the unknown pair. To interpolate y from the home screen, select inter( from the CATALOG, and then enter inter(x1,y1,x2,y2,x). Display the interpolateàextrapolate editor. -Œ/& Enter real values for the first known pair (x1,y1). The values can be expressions.

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54 Chapter 3: Math, Calculus, and Test Operations The CALC (Calculus) Menu You must set Dec mode to use the calculus functions. evalF nDer der1 der2 fnInt -† 4 fMin fMax arc The calculus functions return values with respect to any user-created variable, to built-in variables eqn and exp, and to graphing variables such as x, t, and q.

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Chapter 3: Math, Calculus, and Test Operations 55 The built-in variable d defines the step size in calculating nDer( (in dxNDer differentiation mode only) and arc(. The built-in variable tol defines the tolerance in calculating fnInt(, fMin(, fMax(, and arc(. The value of each must be >0. These factors affect the accuracy of the calculations. As d becomes smaller, the approximation typically is more accurate. For example, nDer(A^3,A,5) returns 75.0001 if d=.01, but returns 75 if d=.0001 (Appendix).

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56 Chapter 3: Math, Calculus, and Test Operations You can use relational functions to control program flow (Chapter 16).

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4 Constants, Conversions, Bases, and Complex Numbers TI-86 Using Built-In and User-Created Constants ....................... 58 Converting Units of Measure ............................................. 61 Number Bases.................................................................... 65 Using Complex Numbers ................................................... 70 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 04CCCB.

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58 Chapter 4: Constants, Conversions, Bases, and Complex Numbers Using Built-In and User-Created Constants A constant is a variable with a specific value stored to it. The CONS BLTIN menu items are common constants built into the TI-86. You cannot edit the value of a built-in constant. You can create your own constants and add them to the user-created constant menu for easy access.

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers To use p, press - ~ or select it from the CATALOG. To use e^, press - ‚. To use e, press - n ãEä. Built-In Constant Constant Name Constant Value Na Avogadro's number 6.0221367E23 mole L1 k Boltzman's constant 1.380658EL23 JàK Cc Coulomb constant 8.9875517873682E9 N m 2àC 2 ec Electron charge 1.60217733EL19 C Rc Gas constant 8.31451 Jàmole K Gc Gravitational constant 6.

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60 Chapter 4: Constants, Conversions, Bases, and Complex Numbers Creating or Redefining a User-Created Constant CONS USER menu items are Display the CONS menu. -‘ Display the constant editor. The Name= prompt, Value= prompt, and CONS USER menu are displayed. ALPHA-lock is on. ' 196.9665 is the atomic weight of gold (Au). Enter a constant name. Either enter a new name one to eight characters long, starting with a letter, or select a name from the CONS USER menu.

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers 61 Entering a Constant Name in an Expression You can enter a constant in an expression in any of three ways. ♦ Select the constant name from the CONS BLTIN menu or the CONS USER menu. ♦ Select a user-created constant name from the VARS CONS screen. ♦ Use the ALPHA keys, alpha keys, and other character keys to enter a constant name. Converting Units of Measure You can enter a conversion expression anywhere that an expression is valid.

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62 Chapter 4: Constants, Conversions, Bases, and Complex Numbers Select the current unit of measure (¡C) from the conversion group menu. The unit abbreviation and conversion symbol ( 4 ) are pasted to the cursor location. & Select the new unit of measure (¡F) from the conversion group menu. The unit abbreviation is pasted to the cursor location. ' b Convert the measurement.

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers -’& The CONV LNGTH (Length) Menu mm cm m in ft millimeters centimeters meters inches feet yd km mile nmile lt-yr The CONV AREA Menu ft 2 m2 mi 2 The CONV VOL (Volume) Menu liter gal qt pt oz square kilometers acres square inches seconds minutes hours cubic centimeters cubic inches cubic feet cubic meters cups day yr week days years weeks The CONV TEMP (Temperature) Menu ¡C degrees Celsius cm 2 yd 2 ha square centimeters square yards

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64 Chapter 4: Constants, Conversions, Bases, and Complex Numbers The CONV MASS Menu gm kg lb grams kilograms pounds The CONV FORCE Menu N dyne Newtons dynes -’/& atomic mass units slugs amu slug ton force kilogram force tonf kgf atm lbàin pounds per square inch atmospheres bar mmHg millimeters of mercury bars Nàm2 Newtons per square meter mmH2 millimeters of water The CONV ENRGY (Energy) Menu The CONV POWER Menu hp W horsepower Watts The CONV SPEED Menu ftàs màs feet per second meters per sec

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers To enter a forward slash ( à ), you can use the F key or paste it from the CATALOG. 65 Converting a Value Expressed as a Rate To convert a value expressed as a rate on the home screen, you can use parentheses and the division operator ( à ). For example, if a car travels 325 miles in 4 hours, and you want to know the rate of speed in kilometers per hour, enter this expression: (325à4)miàhr4kmàhr This expression returns 131 kmàhr (rounded up).

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66 Chapter 4: Constants, Conversions, Bases, and Complex Numbers Number Base Ranges Binary, octal, and hexadecimal numbers on the TI-86 are defined in these ranges.

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67 Chapter 4: Constants, Conversions, Bases, and Complex Numbers BASE Õ-Ú menu items and BASE TYPE menu items are not the same as regular alphabetical characters. In the example, the upper menu is the list editor menu ( - ” in Dec number base mode). If Hex number base mode is not set, you must enter the ß designator, even if the number contains a special hexadecimal character. The BASE Õ-Ú (Hexadecimal Characters) Menu -—& This is the BASE Õ-Ú menu displayed on the home screen. To use Õ, press - e.

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68 Chapter 4: Constants, Conversions, Bases, and Complex Numbers The BASE CONV (Conversion) Menu Õ-Ú 4Bin value can be an expression, list, vector, or matrix. For detailed syntax descriptions, refer to the A to Z Reference. value4Bin value4Hex TYPE 4Hex CONV 4Oct BOOL 4Dec -—( BIT Displays value as binary Displays value as hexadecimal value4Oct value4Dec Displays value as octal Displays value as decimal Converting Number Bases In Dec mode, solve 10Ü + Úß + 10Ý + 10.

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69 Chapter 4: Constants, Conversions, Bases, and Complex Numbers Both the argument and the result must be within defined number ranges (page 66). Results of Boolean Operations When a Boolean expression is evaluated, the arguments are converted to hexadecimal integers and the corresponding bits of the arguments are compared, as this table shows. Results If valueA is... ...and valueB is...

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70 Chapter 4: Constants, Conversions, Bases, and Complex Numbers Using Complex Numbers Variable names with complex numbers stored to them are listed on the VARS CPLX screen (Chapter 2). Lists, matrices, and vectors can have complex elements. A complex number has two components: real (a) and imaginary (+bi).

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Chapter 4: Constants, Conversions, Bases, and Complex Numbers 71 For example, when PolarC and Degree modes are set, (2,1)N(1±45) returns (1.32565429614±12.7643896828). Using a Complex Number in an Expression ♦ Enter the complex number directly. ♦ Use the ALPHA keys, alpha keys, and other character keys to enter a complex variable. ♦ Select a complex variable from the VARS CPLX screen.

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72 Chapter 4: Constants, Conversions, Bases, and Complex Numbers Select { and } from the LIST menu. You must enter commas to separate list elements.

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5 Function Graphing TI-86 Defining a Graph................................................................ 74 Setting the Graph Mode .................................................... 74 The GRAPH Menu .............................................................. 75 Using the Equation Editor .................................................. 76 Setting the Window Variables ........................................... 81 Setting the Graph Format ..................................................

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74 Chapter 5: Function Graphing Defining a Graph This chapter describes the process for graphing functions in Func graphing mode, but the process is similar for each TI-86 graphing mode. Chapters 8, 9, and 10 describe the unique aspects of polar, parametric, and differential equation graphing modes. Chapter 6 describes various graphing tools, many of which you can use in all graphing modes. Some of these steps are not necessary every time you define a graph. Set the graphing mode (page 74).

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Chapter 5: Function Graphing 75 Each graphing mode has a unique equation editor. You must select the graphing mode and Dec number base mode before you enter the functions. The TI-86 retains in memory all equations stored to the Func, Pol, Param, and DifEq equation editors. Each mode also has unique graph format settings and window variables. Stat plot onàoff status, zoom factors, mode settings, and tolerance apply to all graphing modes; changing the graphing mode does not affect them.

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76 Chapter 5: Function Graphing FORMT Displays the graph format screen; use this screen to select graph format settings STGDB Displays the Name= prompt and STGDB menu; use this prompt to enter a GDB variable RCGDB Displays the Name= prompt and RCGDB menu; use this menu to recall a graph database EVAL Displays the Eval x= prompt; enter an x for which you want to solve the current function STPIC Displays the Name= prompt and STPIC menu; use this prompt to enter a PIC variable RCPIC Displays the Na

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Chapter 5: Function Graphing x Pastes the variable x to the current cursor location (same as 2 or - n ãXä ) y Pastes the variable y to the current cursor location (same as - n ãYä ) INSf Inserts a deleted equation variable (function) name above the current cursor location (only the variable name is inserted) DELf Deletes the function that the cursor is on SELCT Changes the selection status of the function that the cursor is on (selects or deselects) ALL+ Selects all defined functions in the equat

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78 Chapter 5: Function Graphing You can edit expressions you inserted using Rcl. Notes about Defining Function Equations ♦ You can include functions, variables, constants, matrices, matrix elements, vectors, vector elements, lists, list elements, complex values, or other equations in the equation. ♦ If you include matrices, vectors, or complex values, the equation must evaluate to a real number at each point. ♦ You can include another defined function in an equation.

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Chapter 5: Function Graphing The TI-86 graphs all selected functions on the same graph screen. 79 Selecting Graph Styles Depending on which graphing mode is set, the TI-86 offers up to seven distinct graph styles. You can assign these styles to specific functions to visually differentiate each from the others. For example, you can show y1 as a connected line (»y1= in the equation editor) and y2 as a dotted line (Ây2=), and shade the area above y3 (¾y3=).

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80 Chapter 5: Function Graphing Setting the Graph Style in the Equation Editor In the example, ¾ (shade above) is selected for y2. All window variables are set to the default values (page 82). If you assign ¾ or ¿ to a function that graphs a family of curves (page 86), the same pattern rotation applies to the members of the family of curves. Display the equation editor. 6& Move the cursor to the function or functions for which you want to set the graph style.

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Chapter 5: Function Graphing 81 Viewing and Changing OnàOff Status of Stat Plots Plot1 Plot2 Plot3 on the top line of the equation editor displays the onàoff status of each stat plot (Chapter 14). When a plot name is highlighted on this line, the plot is on. To change the onàoff status of a stat plot from the equation editor, press $, ", and ! to place the cursor on Plot1, Plot2, or Plot3, and then press b.

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82 Chapter 5: Function Graphing Displaying the Window Editor To display the window editor, select WIND from the GRAPH menu (6 '). Each graphing mode has a unique window editor. The window editor to the right shows the default values in Func graphing mode. $ indicates that xRes=1 (x resolution) is below yScl on the window editor. Changing a Window Variable Value Display the window editor. 6' both must be true to graph successfully. Move the cursor to the window variable you want to change.

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Chapter 5: Function Graphing 83 Setting Graphing Accuracy with @x and @y The window variables @x and @y define the distance from the center of one pixel to the center of any adjacent pixel. When you display a graph, the values of @x and @y are calculated from xMin, xMax, yMin, and yMax using these formulas: @x=(xMin+xMax)à126 @y=(yMin+yMax)à62 @x and @y are not on the window editor.

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84 Chapter 5: Function Graphing DifEq graphing mode has a unique set of graph format settings (Chapter 10). Grid points cover the graph screen in rows that correspond to the tick marks on each axis.

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Chapter 5: Function Graphing 85 Displaying a Graph In the example graph to the right, all default settings related to graphing are set. To view the graph without the GRAPH menu on the bottom line, press : after plotting the graph. To display a graph, select GRAPH from the GRAPH menu. The graph screen is displayed. If the graph is newly defined, the busy indicator is displayed at the top-right corner as the TI-86 draws the graph.

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86 Chapter 5: Function Graphing Graphing a Family of Curves If you enter a list as an element in an equation, the TI-86 plots the function for each value in the list, graphing a family of curves. In SimulG graphing order mode, the TI-86 graphs all functions sequentially for the first element in each list, then for the second element, and so on. When you use more than one list in an expression, all lists must have the same dimension.

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6 Graph Tools TI-86 Graph Tools on the TI-86................................................... 88 Tracing a Graph ................................................................. 90 Resizing the Graph Screen with ZOOM Operations ........... 91 Using Interactive Math Functions ...................................... 95 Evaluating a Function for a Specified x............................ 101 Drawing on a Graph ........................................................

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88 Chapter 6: Graph Tools Graph Tools on the TI-86 Chapter 5 describes how to use the GRAPH menu items y(x)=, WIND, GRAPH, and FORMT to define and display the graph of a function in Func graphing mode. This chapter describes how to use the other GRAPH menu items to apply preset graph screen dimensions, explore the graph and trace specific functions, perform mathematical analyses, draw on graphs, and store and recall graphs and drawings. You can use most graph tools in all four graphing modes.

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Chapter 6: Graph Tools In the example, the function y(x)=x^3+.3x 2-4x is graphed. The numeric display mode settings do not affect coordinate display. 89 Using the Free-Moving Cursor When you select GRAPH from the GRAPH menu, the graph screen is displayed with the free-moving cursor at the center of the screen. The cursor appears as a plus sign with a flashing center pixel. To move the cursor, press ", #, !, or $; it moves in the direction of the cursor key you press.

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90 Chapter 6: Graph Tools Tracing a Graph To display the graph and begin a trace, select TRACE from the GRAPH menu. In the example, the function y(x)=x^3+.3x 2-4x is graphed. The trace cursor appears as a small square with a flashing diagonal line at each corner. Initially, the trace cursor appears on the first selected function, at the x value closest to the middle of the screen. If CoordOn format is selected, the cursor coordinates are displayed at the bottom of the screen.

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Chapter 6: Graph Tools 91 Quick Zoom: While tracing, you can press b to adjust the graph screen so that the trace cursor location becomes the center of a new graph screen, even if you have moved the cursor beyond the top or bottom of the display. In effect, this is vertical panning. Stopping and Resuming a Trace To stop tracing and restore the free-moving cursor, press : or 6. To resume tracing, select TRACE from the GRAPH menu.

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92 Chapter 6: Graph Tools To cancel the effect of any ZOOM menu item and return to the default window variable values, select ZSTD. If you graph a circle but it appears elliptical, you can use ZSQR to reset the window variable values so that the circle graph appears circular.

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Chapter 6: Graph Tools 93 Defining a Custom Zoom In Using BOX, you can zoom in on any rectangular area within the current graph screen. Before you begin these steps, enter a function in the equation editor. In the example, the function y(x)=x^3+.3x 2N4x is graphed. Select BOX from the GRAPH ZOOM menu. The zoom cursor is displayed at center screen. 6( & Move the cursor to any spot you want to define as a corner of the zoom box; mark the corner with a small square.

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94 Chapter 6: Graph Tools In the example, the function y(x)=x^3+.3x 2N4x is graphed. Check xFact and yFact; change as needed. 6( // ' When you select a ZOOM feature, Smart Graph displays the current graph. Select ZIN from the GRAPH ZOOM menu to display the zoom cursor. (' Move the zoom cursor to the intended new center point of the graph screen. Zoom in.

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95 Chapter 6: Graph Tools You can select all zoomwindow variables from the VARS WIND screen in any graph mode. You also can enter the variable characters individually. The zoom-window variables resume their standard default values when you reset defaults. Storing and Recalling Zoom-Window Variable Values ♦ To store all current zoom-window variable values simultaneously as a user-defined custom zoom feature, select ZSTO from the GRAPH ZOOM menu.

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96 Chapter 6: Graph Tools The GRAPH MATH menu differs slightly for Pol and Param graphing modes (Chapters 8 and 9). DifEq graphing mode has no GRAPH MATH menu.

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Chapter 6: Graph Tools 97 Using ROOT, FMIN, FMAX, or INFLC The steps for ROOT, FMIN, FMAX, and INFLC are the same, except for the menu selection in step 1. In the example, the function y(x)=x^3+.3x 2N4x is selected. Step 2 is not necessary here because only one function is selected. Select ROOT from the GRAPH MATH menu. A Left Bound? prompt is displayed. 6/ && Move the cursor onto the function for which you want to find a root.

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98 Chapter 6: Graph Tools Using ‰f(x), DIST, or ARC The steps for using ‰f(x), DIST, and ARC are the same, except for the menu selection in step 1. In the example, the function y(x)=x^3+.3x 2N4x is selected. Steps 2 and 4 are not necessary here because only one function is selected. For DIST, when you are specifying the right bound, a line is drawn from the left bound to the right bound. Select DIST from the GRAPH MATH menu. The current graph is displayed with a Left Bound? prompt.

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Chapter 6: Graph Tools 99 Using dyàdx or TANLN The steps for using dyàdx and TANLN are the same, except for the menu selection in step 1. In the example, the function y(x)=x^3+.3x 2N4x is selected. Select dyàdx from the GRAPH MATH menu. The current graph is displayed. 6/ &' Move the cursor to the function with the point for which you want to find the derivative, or slope.

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100 Chapter 6: Graph Tools Using ISECT In the example, the functions y(x)=x^3+.3x 2N4x and y(x)=x 2+3xN3 are selected. Select ISECT from the GRAPH MATH menu. The current graph is displayed with First Curve? at the bottom of the graph screen. 6/ &/( Select the first function (curve). The cursor moves to the next function and Second Curve? is displayed. #$b Select the second function (curve). Guess? is displayed. #$b Guess the intersection.

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Chapter 6: Graph Tools 101 Evaluating a Function for a Specified x To clear entered numbers from the Eval x= prompt, press :. Select EVAL from the GRAPH menu. The graph is displayed with the Eval x= prompt in the bottom-left corner. 6/ /& To cancel EVAL, press : after clearing the Eval x= prompt. Enter a real x value between window variables xMin and xMax. `5-~ Evaluate. The result cursor is on the first selected function at the entered x value. The coordinate values are displayed.

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102 Chapter 6: Graph Tools Before Drawing on a Graph All drawings are temporary; they are not stored in a graph database. Any action that causes Smart Graph to replot the graph erases all drawings. Therefore, before you use any drawing tool, consider whether you want to perform any of these graphing activities first.

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Chapter 6: Graph Tools 103 Clearing Drawn Pictures To clear drawn pictures while the graph is displayed, select CLDRW from the GRAPH DRAW menu. The graph is replotted and displayed with no drawn elements. To clear drawn pictures from the home screen, select ClDrw from the CATALOG. ClDrw is pasted to the cursor location. Press b. Done is displayed; when you display the graph again, no drawings are displayed.

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104 Chapter 6: Graph Tools Shading Areas of a Graph To shade an area of a graph, the syntax is: Shade(lowerFunc,upperFuncã,xLeft,xRight,pattern,patternResä) To replicate the example without additional graphs, turn off all equations and stat plots before entering the instructions as shown. pattern specifies one of four shading patterns. 1 2 3 4 vertical (default) horizontal negative slope( 45¡) positive slope (45¡) patternRes specifies one of eight shading resolutions.

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Chapter 6: Graph Tools HORIZ Draws a horizontal line, which you can move to any displayed y value CIRCL Draws a circle with a center point and radius you specify with the cursor PEN Draws the path of the cursor as you move it on the graph screen PTON Turns on the point at the cursor location PTOFF Turns off the point at the cursor location PTCHG Changes the onàoff status of a point at the cursor location CLDRW Clears all drawings from the graph screen; replots the graph TEXT Draws characters on the

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106 Chapter 6: Graph Tools Drawing a Vertical or Horizontal Line In the example, the function y(x)=x^3+.3x 2N4x is selected. Also, ZIN was executed once with the zoom cursor at (0,0), xFact=2, and yFact=2. Select VERT (or HORIZ) from the GRAPH DRAW menu. The graph is displayed and a vertical or horizontal line is drawn at the cursor. 6/ '( (or )) Move the line to the x value (or to the y value, if horizontal) through which you want the line to pass. !" (or $ #) Draw the line on the graph.

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Chapter 6: Graph Tools For DrawF, TanLn, and DrInv, you can use as expression any variable to which a valid expression is stored (including deselected equation variables). 107 Drawing a Function, Tangent Line, or Inverse Function For DrawF, TanLn, and DrInv, expression is in terms of x. When you select DrawF, TanLn, or DrInv from the GRAPH DRAW menu, it is pasted to the home screen or program editor. Upon execution, the drawing is returned.

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108 Chapter 6: Graph Tools Placing Text on a Graph This example adds to the PEN example drawing. Before you start, you may want to store the arrows to a picture variable (page 102). To erase a character when using TEXT, move the TEXT cursor above it and then press 1 ¤ or - n ¤ to overwrite it. Select TEXT from the GRAPH DRAW menu. The text cursor is displayed. 6/ ' /// & Move the cursor to where you want to enter text. Text is entered below the text cursor.

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7 Tables TI-86 Displaying the Table ........................................................ 110 Setting Up the Table ........................................................ 113 Clearing the Table............................................................ 114 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 07TABLES.

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110 Chapter 7: Tables Displaying the Table To display the equation editor, press 6 & (Chapter 5). The table displays the independent values and corresponding dependent values for up to 99 selected functions in the equation editor. Each dependent variable in the table represents a selected function stored in the equation editor for the current graphing mode. TABLE Menu 7 TABLE TBLST table screen table setup editor The Table In the example, y1=x 2+3x-4 and y2=sin (3x) are selected and all defaults set.

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Chapter 7: Tables 111 Independent and Dependent Variables in the Table Graphing Mode In DifEq mode, if an equation has an initial conditions list, the table uses the first list element to evaluate the equation (Chapter 10). Independent Variable Dependent (Equation) Variables Func (function) x y1 through y99 Pol (polar) q r1 through r99 Param (parametric) t xt1àyt1 through xt99àyt99 DifEq (differential equation) t Q1 through Q9 Navigating the Table To...

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112 Chapter 7: Tables The Table Menus 7 & The table has a unique menu for each graphing mode, as shown below.

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Chapter 7: Tables 113 Setting Up the Table To display the table using the current table setup settings, select TABLE from the TABLE menu. To display the table setup editor, select TBLST from the TABLE menu. The screen to the right shows the default table setup settings. TblStart specifies the first independent variable value (x, q, or t) in the table (only when Indpnt: Auto is selected).

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114 Chapter 7: Tables Viewing and Editing Dependent Variable Equations 2 In the example, y1=x +3x-4 and y2=sin (3x) are selected and all defaults set. When you display the equation in the edit line, the column equation name is highlighted. Display the table. 7& Move the cursor into the column of the dependent variable you want to edit, and then move up the column until the name is highlighted. "$ Display the equation in the edit line. b Edit the equation.

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8 Polar Graphing TI-86 Preview: Polar Graphing .................................................. 116 Defining a Polar Graph .................................................... 117 Using Graph Tools in Pol Graphing Mode........................ 119 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 08POL.

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116 Chapter 8: Polar Graphing Preview: Polar Graphing The graph of the polar equation A sin (Bq) forms the shape of a flower. Graph the flower for A=8 and B=2.5. Then explore the appearance of the flower for other values of A and B. Select Pol mode from the mode screen. -m### #"b Display the equation editor and polar equation editor menu. 6& (Deselect or delete all equations if any.) Store r1(q)=8sin(2.5q). Select ZSTD from the GRAPH ZOOM menu. r1 is plotted on the graph screen.

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Chapter 8: Polar Graphing 117 Defining a Polar Graph The steps for defining a polar graph are similar to the steps for defining a function graph. This chapter assumes that you are familiar with Chapter 5: Function Graphing and Chapter 6: Graph Tools. Chapter 8 details aspects of polar graphing that differ from function graphing. Setting Polar Graphing Mode To display the mode screen, press - m.

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118 Chapter 8: Polar Graphing Displaying the Polar Equation Editor To display the polar equation editor, select r(q)= from the GRAPH menu in Pol graphing mode (6 &). The polar equation editor menu displayed on the bottom line is the same as the Func mode equation editor menu, except that q and r replace x and y. In this editor, you can enter and display up to 99 polar equations, r1 through r99, if sufficient memory is available. Equations are defined in terms of the independent variable q.

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Chapter 8: Polar Graphing DrawLine graph format typically displays a more meaningful polar graph than DrawDot graph format. 119 Setting the Graph Format To display the format screen in Pol graphing mode, select FORMT from the GRAPH menu (6 / (). Chapter 5 describes the format settings. Although the same settings are available for Func, Pol, and Param graphing modes, the TI-86 retains in memory separate format settings for each mode.

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120 Chapter 8: Polar Graphing Tracing a Polar Equation To begin a trace, select TRACE from the GRAPH menu (press 6 )). The trace cursor appears on the first selected equation at qMin. ♦ In RectGC format, moving the trace cursor updates the values of q, x, and y; if CoordOn format is selected, q, x, and y are displayed. ♦ In PolarGC format, moving the trace cursor updates x, y, r, and q; if CoordOn format is selected, r and q are displayed.

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Chapter 8: Polar Graphing 121 Moving the Trace Cursor to a q Value To move the trace cursor to any valid q value on the current equation, enter the number. When you enter the first digit, a q= prompt is displayed in the bottom-left corner. The value you enter must be valid for the current graph screen. When you have completed the entry, press b to reactivate the trace cursor. In the example, r1=8sin(2.5q) is graphed.

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122 Chapter 8: Polar Graphing The GRAPH MATH Menu MATH DIST The other GRAPH MATH menu items are the same as described in Chapter 6. dràdq 6/& DRAW FORMT STGDB RCGDB dyàdx dràdq ARC TANLN Finds the numerical derivative (slope) of a function at a point The distances calculated by DIST and ARC are distances in the rectangular coordinate plane. dyàdx and dràdq are independent of the RectGC or PolarGC format.

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9 Parametric Graphing TI-86 Preview: Parametric Graphing ......................................... 124 Defining a Parametric Graph ........................................... 125 Using Graph Tools in Param Graphing Mode .................. 128 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 09PARA.

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124 Chapter 9: Parametric Graphing Preview: Parametric Graphing Graph the parametric equation that describes the path of a ball kicked 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? In the example, ignore all forces except gravity. For initial velocity v0 and angle q, the position of the ball as a function of time has horizontal and vertical components.

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Chapter 9: Parametric Graphing Enter these window variable values. tMin=0 tMax=5 tStep=.1 To simulate the ball in flight, change the graph style of xt1àyt1 to Á (animate). xMin=L20 xMax=100 xScl=50 yMin=L5 yMax=15 yScl=10 125 -f0#5# ` 1 # a 20 # 100 # 50 # a 5 # 15 # 10 Set SimulG and AxesOff graphing formats, so the path of the ball and the vectors will be plotted simultaneously on a clear graph screen. /(### "b##" b Plot the graph.

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126 Chapter 9: Parametric Graphing Setting Parametric Graphing Mode To display the mode screen, press - m. To graph parametric equations, you must select Param graphing mode before you enter equations, set the format, or edit window variable values. The TI-86 retains in memory separate equation, format, and window data for each graphing mode. The GRAPH Menu Chapter 5 describes these GRAPH menu items: GRAPH and FORMT.

#### Page 139

Chapter 9: Parametric Graphing 127 Selecting and Deselecting a Parametric Equation When a parametric equation is selected, the equals signs (=) of both xt and yt are highlighted. To change the selection status of a parametric equation, move the cursor onto either xt or yt, and then select SELCT from the equation editor menu. The status is changed for xt and yt.

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128 Chapter 9: Parametric Graphing DrawLine graph format typically displays a more meaningful parametric graph than DrawDot graphing format. Setting the Graph Format To display the format screen in Param graphing mode, select FORMT from the GRAPH menu (6 / (). Chapter 5 describes the format settings. The TI-86 retains in memory separate format settings for Func, Pol, Param , and DifEq graphing modes.

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Chapter 9: Parametric Graphing ♦ QuickZoom is available in Param graphing; panning is not (Chapter 6). You can enter an expression at the t= prompt. 129 In PolarGC format, moving the trace cursor updates x, y, r, q, and t; 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 the trace cursor...

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130 Chapter 9: Parametric Graphing The GRAPH ZOOM menu items affect only the x window variables (xMin, xMax, and xScl) and the y window variables (yMin, yMax, and yScl), except ZSTO and ZRCL, which also affect the t window variables (tMin, tMax, and tStep). The GRAPH MATH Menu MATH DIST The other GRAPH MATH menu items are the same as described in Chapter 5.

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10 Differential Equation Graphing TI-86 Defining a Differential Equation Graph............................ 132 Entering and Solving Differential Equations .................... 139 Using Graph Tools in DifEq Graphing Mode .................... 144 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 10DIFFEQ.

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132 Chapter 10: Differential Equation Graphing Defining a Differential Equation Graph Chapters 8 and 9 each begin with an example; Chapter 10 has several differential equation examples throughout the chapter. Most steps for defining a differential equation graph are similar to the steps for defining a function graph. This chapter assumes that you are familiar with Chapter 5: Function Graphing and Chapter 6: Graph Tools.

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133 Chapter 10: Differential Equation Graphing The GRAPH Menu Chapter 5 describes the GRAPH menu item GRAPH. Chapter 6 describes these GRAPH menu items: DRAW, ZOOM, TRACE, EVAL, STGDB, RCGDB, STPIC, and RCPIC. The TI-86 retains independent format settings for each graphing mode.

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134 Chapter 10: Differential Equation Graphing Field Format SlpFld (slope field) Adds the slope field to the graph of only one first-order equation with t on the x-axis and a specified Qn equation on the y-axis DirFld (direction field) Adds the direction field to the graph of only one second-order equation with Qx# on the x-axis and Qy# on the y-axis FldOff (field off) Graphs all selected differential equations with t or Q1 on the x-axis, Q1 or Q2 on the y-axis, and no field; initial conditions must

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Chapter 10: Differential Equation Graphing 135 In this editor, you can enter and display a system of up to nine first-order differential equations, Q'1 through Q'9, if sufficient memory is available. Equations are defined in terms of the independent variable t andàor Q'. You can refer to another differential equation variable in a DifEq equation, as in Q'2=Q1. However, you cannot enter a list in a DifEq equation.

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136 Chapter 10: Differential Equation Graphing The values shown in the picture on page 135 are defaults in Radian mode. x and y settings correspond to the axes variables (page 137). $ indicates that xScl=1, yMin=L10, yMax=10, yScl=1, and difTol=.001 (in RK format) or EStep=1 (in Euler format) are beyond the screen. tMin=0 Specifies the t value at which to begin evaluating within a graph screen tMax default is 2p. tMax=6.

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Chapter 10: Differential Equation Graphing 137 Setting the Axes To display the axes editor, select AXES from the GRAPH menu in DifEq mode (6 )). x= assigns a variable to the x-axis dTime= specifies a point in time (real number) y= assigns a variable to the y-axis fldRes= (resolution) sets number of rows (1 through 25) At the x= and y= prompts, you can enter the independent variable t, as well as Q, Q' , Qn, or Q'n, where n is an integer ‚ 1 and 9.

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138 Chapter 10: Differential Equation Graphing Stat plot and screen drawings are not stored to fldPic. The Built-In Variable fldPic As the TI-86 plots a field, it stores the field and any displayed label, axes, or cursor coordinate information to the built-in variable fldPic. These actions do not update fldPic.

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Chapter 10: Differential Equation Graphing 139 Entering and Solving Differential Equations In Func graphing mode, x is the independent variable and y is the equation variable. To avoid conflict between Func equations and DifEq equations on the TI-86, t is the independent variable and Q'n is the equation variable in DifEq graphing mode. Therefore, when you enter an equation in the differential equation editor, you must express it in terms of t and Q'n.

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140 Chapter 10: Differential Equation Graphing In SlpFld field format, x=t is always true; y=Q1 and fldRes=15 are the default axes settings. Display the axes editor and enter the equation variable for which you want to solve. (Do not set y=Q.) Accept or change fldRes (resolution). Display the graph. With the default window variable values set, the slope fields for this graph are not very illustrative. -i Change the window variables xMin, xMax, yMin, and yMax.

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Chapter 10: Differential Equation Graphing Graphing in DirFld Format In DifEq graphing mode, t is the independent variable and Q'n is the dependent variable, where n ‚ 1 and 9. Display the mode screen and set DifEq graphing mode. -m### #"""b Display the format screen and set DirFld graphing format. 6/&# ####"b Display the equation editor and store the transformed system of differential equations for y''=Ly to the equation editor, substituting Q1 for y and Q2 for y'.

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142 Chapter 10: Differential Equation Graphing Graphing a System of Equations in FldOff Format For this example, you must transform the fourth-order differential equation y (4)Ny=e Lx into an equivalent system of first-order differential equations, as shown in the chart below. Differentiate... Define the variables as...

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Chapter 10: Differential Equation Graphing When FldOff field format is selected, x=t and y=Q are the default axes settings. Display the window editor and set the window variable values. - f # 10 # ` 01 # # 0 # ##a4#4 Display the initial conditions editor and enter the initial conditions. A small square indicates that an initial condition is required. ( 3 # a 5 ` 25 #7`5# a 5 ` 75 Display the axes editor. Enter the equation variables for which you want to solve. ) Display the graph.

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144 Chapter 10: Differential Equation Graphing To paste ' to the home screen, you can select it from the CHAR MISC menu or from the CATALOG. Due to TI-86 system requirements, you must express Q1(3) as Q'1(3) on the calculator. Solving a Differential Equation for a Specified Value On the home screen in DifEq graphing mode, you can solve a differential equation stored to a specified independent variable value or expression. The syntax is: Q'n(value).

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Chapter 10: Differential Equation Graphing 145 Moving the Trace Cursor to a t Value To move the trace cursor to any valid t value on the current equation, enter the number. When you enter the first digit, a t= prompt is displayed in the bottom-left corner. The value you enter must be valid for the current graph screen. When you have completed the entry, press b to reactivate the trace cursor. Values for t and Q are displayed on the graph to the right because x=t and y=Q graph axes are selected.

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146 Chapter 10: Differential Equation Graphing DrEqu( does not store values to x, y, or t. xList, yList, and tList are optional list names to which you can store the solutions x, y, and t. You then can display the lists on the home screen or in the list editor (Chapter 11). Use the free-moving cursor to select initial conditions. You cannot trace the drawing. However, you can plot xList, yList, or tList as a stat plot after you draw the equation, and then trace them (Chapter 14).

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Chapter 10: Differential Equation Graphing In the example, since no initial conditions were set, the equation in Q'1 is not plotted. Display the graph screen and plot the direction field. b Move the free-moving cursor to the initial condition coordinates you want. "#!$ 147 Draw the solution. The solution lists for b x, y, and t are stored to LX, LY, and LT. The Again? prompt is displayed and ALPHA-lock is on for ãYä and ãNä only.

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148 Chapter 10: Differential Equation Graphing Drawing Solutions Interactively with EXPLR Display the mode screen and set DifEq graphing mode. -m### #"""b Display the format screen and set FldOff field format. 6/&# ####"" b Display the equation editor and store the equation Q'1=.001Q1(100NQ1). (Delete all other equations.) & ` 001 ' 1 D 100 T ' 1 E Set the axes to x=t and y=Q1. -h#"1 Display the window editor and set the window variable values.

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Chapter 10: Differential Equation Graphing Select EXPLR from the GRAPH menu. /* Move the free-moving cursor to the initial condition for which you want to solve. "#!$ Draw the solution to Q1, using the cursor coordinates (x,y) as initial condition ( t,Q'1(t) ). 149 b To continue drawing more solutions, move the free-moving cursor and then press b. To stop using EXPLR, press .. If SlpFld or DirFld is set, the axes are set to specific solutions automatically.

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150 Chapter 10: Differential Equation Graphing Evaluating Differential Equations for a Specified t When the trace cursor is not active, the GRAPH menu item EVAL evaluates currently selected differential equations Qn for a specified value of t, tMinttMax. You can use it directly on the graph. In a program or from the home screen, eval returns a list of Q values. When DirFld or SlpFld field format is set, you must specify initial conditions before using EVAL. 10DIFFEQ.

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11 Lists TI-86 Lists on the TI-86............................................................. 152 Creating, Storing, and Displaying Lists ............................ 153 The List Editor .................................................................. 156 Using List Operations....................................................... 159 Using Mathematical Functions with Lists ........................ 161 Attaching a Formula to a List Name ................................

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152 Chapter 11: Lists Lists on the TI-86 The length and number of lists you can store in the TI-86 is limited only by memory capacity. A list is a set of real or complex elements, as in {5,L20,13,9}.

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Chapter 11: Lists The LIST NAMES Menu The LIST NAMES menu shown here has no usercreated list names. Chapter 14 describes fStat, xStat, and yStat. { fStat } xStat NAMES yStat -”( EDIT OPS Each user-created list name is added to the LIST NAMES menu and VARS LIST screen. List names, including fStat, xStat, and yStat, are sorted in alphanumeric order in both places.

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154 Chapter 11: Lists Creating a List Name by Storing a List To store a list, the syntax is: {element1,element2, ... ,element n}¶listName You need not enter the close brace ( } ) when you use X to store a list name. To delete a list name from memory, use the MEM DELETE:LIST screen (Chapter 17). Enter a list directly. (To store a result expressed as a list and currently stored in Ans, as shown in the example, begin these steps at step 2.) (steps 2 through 5 above) Paste ¶ to the cursor location.

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Chapter 11: Lists 155 Displaying or Using a Single List Element To display or use a single list element, the syntax is: listName(element#) listName(element#) is valid as part of an expression. Enter the list name; either select it from the LIST NAMES menu or enter the characters. -”( & element# is ‚ 1 and the dimension of the list. In parentheses, enter the element’s place number in the list. D4E Display the list element. b value can be an expression.

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156 Chapter 11: Lists Complex List Elements A complex number can be a list element. If at least one list element is a complex number, all elements in the list are displayed as complex. (‡L4 results in a complex number.) -”) The List Editor The list editor is a table where you can store, edit, and view up to 20 lists that are in memory. Also, you can create list names and attach formulas to lists in the list editor. You also can press - š ' to display the list editor.

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Chapter 11: Lists Creating a List Name in the Unnamed Column After memory is reset, xStat, yStat, and fStat are stored to columns 1, 2, and 3. Resetting defaults does not affect the list editor. Display the list editor. -”) Move the cursor to the unnamed column (column 4). The Name= prompt is displayed in the entry line. ALPHA-lock is on. $""" To move from the list name in column 1 to the unnamed column, press ! ". Enter the list name.

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158 Chapter 11: Lists Displaying and Editing a List Element To cancel any editing and restore the original element at the cursor, press : b. Move the cursor onto the fifth element of ABC123. In the entry line, the list name, the element number in parentheses, and the element’s full value are displayed. ##### You can enter an expression as an element. Switch to edit-element context and edit the element in the entry line. 5MD6-~E F4 Enter the edited element.

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159 Chapter 11: Lists You can remove all user-created lists from the list editor and restore list names xStat, yStat, and fStat to columns 1, 2, and 3 in either of two ways. ♦ Use SetLEdit with no arguments (page 161). ♦ Reset all memory (Chapter 17). Resetting defaults does not affect the list editor.

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160 Chapter 11: Lists For a complex list, min or max returns the smallest or largest magnitude (modulus). Selecting Deltal from the menu pastes Deltalst( to the cursor location.

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Chapter 11: Lists Selecting SetLE from the menu pastes SetLEdit to the cursor location. You can create new list names as SetLEdit arguments. 161 Select(xListName, yListName) Selects one or more specific data points from a scatter plot or xyLine plot (only), then stores the selected data points to xListName and yListName (Chapter 14) SetLEdit ãcolumn1ListName, column2ListName,...

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162 Chapter 11: Lists Attaching a Formula to a List Name You cannot edit an element of a list created from an attached formula unless you first detach the formula from the list name. When you include more than one list name in an attached formula, each list must have the same dimension. You can attach a formula to a list name so that the formula generates a list that is stored and dynamically updated in the list name.

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Chapter 11: Lists 163 Comparing an Attached List with a Regular List To see the differences between an attached list and a regular list, follow these steps. The example below builds on the example above for attaching a formula to a list. Notice that the formula in step 1 below is not attached to LX because it is not set off by quotation marks. If other list names are stored on the LIST NAMES menu, pressing & and ( may not paste ADD10 and LX to the home screen as shown.

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164 Chapter 11: Lists The list editor displays a formula-lock symbol next to each list name that has a formula attached to it. Attach the formula and generate the list. The TI-86 calculates each list element. A lock symbol is displayed next to the list name to which the formula is attached. b ♦ ♦ To edit an attached formula, press b in step 3, and then edit the formula.

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Chapter 11: Lists 165 You can successfully attach to a list a formula that does not yet resolve to a list. For example, you can attach "5¹xStat" to the list name BY5 with no elements stored to xStat. However, if you attempt to display BY5 when xStat has no elements, an error occurs. When you attach such a formula to a list name in the list editor, the formula is successfully attached, but an error occurs.

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166 Chapter 11: Lists Detaching a Formula from a List Name You can detach a formula in any of five ways. ♦ Use dimL to change the dimension of the list (page 159). ♦ Use value¶listName(element#) to store value to an attached-formula list element. ♦ Use ""¶listName, where listName is the attached-formula list. ♦ In the list editor, move the cursor onto the name of the attached-formula list, and then press b : b. All list elements remain, but the formula is detached and the lock symbol disappears.

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12 Vectors TI-86 Vectors on the TI-86 ........................................................ 168 Creating, Storing, and Displaying Vectors........................ 169 Using Mathematical Functions with Vectors.................... 176 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 12VECTR.

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168 Chapter 12: Vectors Vectors on the TI-86 A vector is a one-dimensional array, arranged in either one row or one column. The vector elements can be real or complex. You can create, display, and edit vectors on the home screen or in the vector editor. When you create a vector, the elements are stored to the vector name. The TI-86 vector editor displays a vector vertically. On the home screen, a vector is entered and displayed horizontally.

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Chapter 12: Vectors 169 Creating, Storing, and Displaying Vectors The VECTR (Vector) Menu NAMES EDIT vector names menu MATH vector math menu vector editor -Š OPS CPLX complex vector menu vector operations menu The VECTR NAMES Menu - Š & The VECTR NAMES menu contains all currently stored vector names in alphanumeric order. To paste a vector name to the current cursor location, select it from the menu.

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170 Chapter 12: Vectors You can enter an expression at a vector element prompt. Enter each vector element value at each vector element prompt. You can enter expressions. To move to the next prompt, press b or #. The vector elements are stored to VECT1, which becomes a VECTR NAMES menu item.

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Chapter 12: Vectors 171 Creating a Complex Vector If any element of a vector is complex, all elements of the vector are displayed as complex. For example, when you enter the vector ã1,2,(3,1)ä , the TI-86 displays ã(1,0) (2,0) (3,1)ä. To create a complex vector from two real vectors, the syntax is: realVector+(0,1)imaginaryVector¶complexVectorName realVector contains the real part of each element and imaginaryVector contains the imaginary part.

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172 Chapter 12: Vectors When you execute the expression, the answer is displayed as a vector. Using a Vector in an Expression ♦ You can enter the vector directly (for example, 35Nã5,10,15ä). ♦ You can use 1 and - n to enter a vector name’s individual characters. ♦ You can select the vector name from the VECTR NAMES menu (- Š &). ♦ You can select the vector name from the VARS VECTR screen (- w / &). Editing Vector Dimension and Elements Display the vector Name= prompt screen.

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Chapter 12: Vectors The VECTR MATH Menu NAMES cross EDIT unitV 173 -Š( MATH norm OPS dot CPLX cross(vectorA,vectorB) Returns the cross product of vectorA and vectorB, both of which are real or complex two-element or three-element vectors; expressed with variables, cross(ãa,b,cä,ãd,e,fä) returns ãbfNce cdNaf aeNbdä unitV vector Returns a unit vector where each element of a real or complex vector is divided by the vector norm norm vector Returns the Frobenius norm ( G(real 2+imaginary 2)) where th

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174 Chapter 12: Vectors For the conversion functions below, the three-element vector conversion equations for cylindrical form ãr q zä are: x = r cosq y = r sinq z=z The three-element vector conversion equations for spherical form ãr q fä are: x = r cosq sinf y = r sinq sinf z = r cosf Complex elements are valid only for li4vc and vc4li.

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Chapter 12: Vectors The VECTR CPLX (Complex) Menu NAMES conj EDIT real MATH imag OPS abs 175 -Š* CPLX angle conj complexVector Returns a vector in which each element is the complex conjugate of the corresponding element of a complexVector real complexVector Returns a real vector in which each element is the real portion of the corresponding element of a complexVector imag complexVector Returns a real vector in which each element is the imaginary portion of the corresponding element of a complexV

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176 Chapter 12: Vectors Using Mathematical Functions with Vectors To add or subtract two vectors, the dimension of vectorA must equal the dimension of vectorB. vectorA+vectorB Adds each vectorA element to the corresponding vectorB element; returns a vector of the sums vectorANvectorB Subtracts each vectorB element from the corresponding vectorA element; returns a vector of the differences You cannot multiply two vectors or divide one vector by another vector.

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13 Matrices TI-86 Matrices on the TI-86 ...................................................... 178 Creating, Storing, and Displaying Matrices...................... 178 Using Mathematical Functions with Matrices.................. 185 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 13MATRX.

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178 Chapter 13: Matrices Matrices on the TI-86 A matrix is a two-dimensional array, arranged in rows and columns. The matrix elements can be real or complex. You can create, display, and edit matrices on the home screen or in the matrix editor. When you create a matrix, the elements are stored to the matrix name.

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Chapter 13: Matrices An ellipsis (…) at either end of matrix rows indicates additional columns. Display the matrix editor and the matrix editor menu. b Accept or change the matrix dimensions (row × column) in the top-right corner of the screen, (1row255 and 1column255); maximum combination is subject to memory availability. The matrix is displayed; all elements are 0. 10 b 4 b Enter each matrix element value at the element prompt (1,1= for row 1, column 1). You can enter expressions.

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180 Chapter 13: Matrices Creating a Matrix on the Home Screen Define the start of the matrix with ã, and then define the start of the first row with another ã. Enter each element for the row, separating them with commas. Define the end of the first row with ä. The close bracket is not necessary when it precedes X. Define the start of each subsequent row with ã . Enter the row elements, separating each from the next with a comma. Define the end of each row with ä.

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Chapter 13: Matrices To view elements beyond the current screen, use ", #, !, and $. 181 Displaying Matrix Elements, Rows, and Submatrices To display an existing matrix on the home screen, enter the matrix name’s individual characters or select it from the MATRX NAMES menu, and then press b. The full value of each element is displayed. Elements with very large values may be expressed exponentially.

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182 Chapter 13: Matrices Editing Matrices in the Matrix Editor You can use :, 3, and - p to edit matrix elements. You also can overwrite existing characters. Display the matrix Name= prompt screen. -‰' Enter the matrix name. Either select it from the MATRX NAMES menu or enter the characters. ãMäãAäãTä 11 Display the matrix editor. b Edit or accept the row dimension, and then edit or accept the column dimension. 53b 3b Move the cursor to any element and edit it.

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Chapter 13: Matrices The MATRX MATH Menu NAMES det EDIT T det squareMatrix matrix T MATH norm 183 -‰( OPS eigVl CPLX eigVc 4 rnorm cnorm LU cond Returns the determinant of squareMatrix Returns a transposed matrix; each element’s (row,column) coordinates switch norm matrix Returns the Frobenius norm ( G(real 2+imaginary 2)) where the sum is over all elements of a real or complex matrix eigVl squareMatrix Returns a list of the normalized eigenvalues of a real or complex squareMatrix eigVc

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184 Chapter 13: Matrices The MATRX OPS (Operations) Menu NAMES dim Press X to enter the ¶ symbol after the close brace.

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Chapter 13: Matrices The MATRX CPLX (Complex ) Menu NAMES conj EDIT real MATH imag OPS abs 185 -‰* CPLX angle conj complexMatrix Returns a matrix in which each element is the complex conjugate of the corresponding element of a complexMatrix real complexMatrix Returns a real matrix in which each element is the real portion of the corresponding element of a complexMatrix imag complexMatrix Returns a real matrix in which each element is the imaginary portion of the corresponding element of a comple

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186 Chapter 13: Matrices To multiply two matrices, the column dimension of matrixA must equal the row dimension of matrixB. To enter M1, press - ƒ. Do not use 2 @ a 1. e^, sin, and cos do not return the exponential, sine, or cosine of each matrix element. To make relational comparisons, matrixA and matrixB must have equal dimensions.

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14 Statistics TI-86 Statistical Analysis on the TI-86 ...................................... 188 Setting Up a Statistical Analysis....................................... 188 Results of a Statistical Analysis........................................ 192 Plotting Statistical Data ................................................... 194 The STAT DRAW Menu .................................................... 199 Forecasting a Statistical Data Value ................................

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188 Chapter 14: Statistics Statistical Analysis on the TI-86 With the TI-86, you can analyze one-variable and two-variable statistical data, which are stored in lists. One-variable data has one measured variable. Two-variable data has pairs comprising an independent variable and a dependent variable. When analyzing either kind of data, you can specify a frequency of occurrence for the independent variable values. These specified frequencies must be real numbers ‚ 0.

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Chapter 14: Statistics 189 Entering Statistical Data Data for statistical analysis is stored in lists, which you can create and edit in the list editor (Chapter 11), on the home screen (Chapter 11), or in a program (Chapter 16). The TI-86 has three built-in list names for statistics, xStat (x-variable list), yStat (y-variable list), and fStat (frequency list). TI-86 statistical functions use these lists as defaults. The LIST NAMES Menu The LIST NAMES menu shown here has no usercreated list names.

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190 Chapter 14: Statistics For regression analysis, the statistical results are calculated using a leastsquares fit.

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Chapter 14: Statistics When you select OneVa or TwoVa, the abbreviation OneVar or TwoVar is displayed. For OneVa, the syntax is: For PwrR and ExpR, the elements of xList and yList must be integers ‚ 1.

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192 Chapter 14: Statistics PRegC is the only statistical result variable calculated for a polynomial regression. The result for a polynomial regression, sinusoidal regression, or logistic regression is stored in PRegC (polynomialàregression coefficients). PRegC is a list containing the coefficients for an equation. For example, for P3Reg, the result PRegC={3 5 L2 7} would represent y=3x3+5x2N2x+7. Results of a Statistical Analysis One- and two-variable statistical functions share the result variables.

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193 Chapter 14: Statistics These words are abbreviated in the table: pop = population std dev = standard deviation coeff = coefficient int = intercept reg eq = regression equation pts = points min = minimum max = maximum Result Variables 1-Var Stats 2-Var Stats mean of x values v v correlation coeff corr sx sx y-intercept of reg eq a sample std dev of x Sx mean of y values Sx slope of reg eq b w regressionàfit coeff a, b pop std dev of y sy number of data pts n n sample std dev of

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194 Chapter 14: Statistics Plotting Statistical Data You can plot one, two, or three sets of statistical list data. The five available plot types are scatter plot, xyLine, histogram, modified box plot, and regular box plot. Store the statistical data in one or more lists (Chapter 11). Select or deselect functions in the current equation editor as appropriate (Chapter 5). Define the statistical plot. Turn on the plots you want to display.

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Chapter 14: Statistics When you display a stat plot editor, the STAT PLOT menu remains so that you can easily switch to another stat plot. In this guidebook, brackets ( ã and ä ) with syntax specify arguments as optional. Do not enter brackets, except with vectors and matrices. You need not turn on a stat plot to change the settings. You also can use STAT PLOT menu items PlOn or PlOff to turn on or turn off stat plots.

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196 Chapter 14: Statistics The PLOT TYPE Menu (Selecting a Plot Type) To display the PLOT TYPE menu, move the cursor onto the plot type icon at the Type= prompt. When you select a plot type, the appearance of the stat plot editor may change. PLOT1 PLOT2 PLOT3 SCAT xyLINE MBOX In these stat plot examples, all functions are deselected. Also, menus are cleared from the screen with :. PlOff BOX At this prompt...

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Chapter 14: Statistics 197 − xyLINE is a scatter plot in which the data points are plotted and connected in order of appearance in Xlist Name and Ylist Name. You may want to use SortA or SortD from the LIST OPS menu (Chapter 11) to sort the lists before you plot them. For the example: xStat={1 2 3 4 5 6 7 8 9 10} yStat=5 sin(xStat) Window variable values: xMin=0 xMax=10 yMin=L10 yMax=10 ¯ MBOX (modified box plot) plots one-variable data, like the regular box plot, except that the points are 1.

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198 Chapter 14: Statistics second plots in the middle. When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom. ¬ HIST (histogram) plots one-variable data. The xScl window variable value determines the width of each bar, beginning at xMin. ZDATA (GRAPH ZOOM menu) adjusts xMin, xMax, yMin, and yMax to include all values, and also adjusts xScl. (xMax N xMin) à xScl 47 must be true.

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Chapter 14: Statistics 199 middle. When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom. The STAT DRAW Menu CALC HIST When you select any of the first five STAT DRAW menu items, the TI-86 plots the data stored in the lists xStat and yStat.

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200 Chapter 14: Statistics Enter stat data in the list editor. The screen to the right shows all fStat elements as 1, but you need not enter them. 1 is the default for all fStat elements. However, if other elements are stored to fStat, you must clear them. -š' Display the home screen. . Execute a linear regression for xStat and yStat. The statistical results are displayed. -š& (b Remove the STAT CALC menu to display all results, including n. . Display the forecast editor.

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15 Equation Solving TI-86 Preview: The Equation Solver .......................................... 202 Entering an Equation in the Equation-Entry Editor .......... 203 Setting Up the Interactive-Solver Editor........................... 204 Solving for the Unknown Variable ................................... 206 Graphing the Solution...................................................... 207 Solver Graph Tools........................................................... 207 The Simultaneous Equation Solver ...

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202 Chapter 15: Equation Solving Preview: The Equation Solver -t With the equation solver, you can enter an expression or equation, store values to all but one variable in the expression or equation, and then solve for the unknown variable. These steps introduce the solver. For details, read this chapter. The VARS EQU menu is a menu version of the VARS EQU screen (Chapter 2). Display the equation-entry editor. The VARS EQU menu is displayed on the bottom of the screen.

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Chapter 15: Equation Solving 203 Entering an Equation in the Equation-Entry Editor The equation solver uses two editors: the equation-entry editor, where you enter and edit the equation you want to solve, and the interactive-solver editor, where you enter known variable values, select the variable for which you want to solve, and display the solution. The equation can have more than one variable to the left of the equal sign, as in A+B=C+sin D. To display the equation-entry editor, press - t.

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204 Chapter 15: Equation Solving Setting Up the Interactive-Solver Editor In the example, the equation V1=V(R1à(R1+R2)) was entered in the equation-entry editor. If you entered an expression for eqn, then exp= is the first variable prompt on the interactive-solver editor. After you have stored an equation to eqn in the equation-entry editor, press b to display the interactive-solver editor. The equation is displayed across the top of the editor. Each variable in the equation is displayed as a prompt.

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Chapter 15: Equation Solving 205 The TI-86 solves equations through an iterative process. To control that process, you can enter lower bounds and upper bounds that are close to the solution, and enter a guess within those bounds in the prompt for the unknown variable. Controlling the process with specific bounds and a guess helps the TI-86 in two ways. ♦ It finds a solution more quickly. ♦ It is more likely to find the solution you want when an equation has multiple solutions.

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206 Chapter 15: Equation Solving The Solver Menu You can display other menus in the interactive-solver editor GRAPH WIND - t equation b ZOOM TRACE SOLVE graphs the solver zoom solves for the unknown variable or menu displays the interactive-solver editor equation in eqn window graphs eqn and editor activates the trace cursor To display the window editor, select WIND from the solver menu. When you select GRAPH or WIND from the solver menu, EDIT replaces the item you selected on the menu.

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Chapter 15: Equation Solving 207 Graphing the Solution The graph to the right plots the solution from the example on page 202. The window variable values are: xMin=L10 yMin=L50 xMax=50 yMax=50 When you select GRAPH from the solver menu (&), the solver graph is displayed with the free-moving cursor. ♦ The vertical axis represents the result of the left side of the equation minus the right side of the equation (leftNright) at each independent variable value.

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208 Chapter 15: Equation Solving The Solver ZOOM Menu GRAPH BOX Chapter 6 and the A to Z Reference describe these features in detail.

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Chapter 15: Equation Solving To move from the coefficients-entry editor for one equation to the editor for another equation, select PREV or NEXT. Enter a real or complex value (or an expression that resolves to one) for each coefficient in the equation and for b 1 , which is the solution to that equation. 9#8#7#2 To move among coefficients, press #, $, or b. From the last or first coefficient, these keys move to the next or previous coefficients-entry screen, if possible.

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210 Chapter 15: Equation Solving Storing Equation Coefficients and Results to Variables ♦ To store coefficients a 1,1; a 1,2;...;a n,n to an n×n matrix, select STOa. ♦ To store solutions b 1,b 2,...,bn to a vector of dimension n, select STOb. ♦ To store the results x 1, x 2,..., x n to a vector of dimension n, select STOx. To store a single value on the coefficients-entry screen or result screen, follow these steps. To switch to the coefficientsentry screen, select COEFS from the SIMULT RESULT menu.

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Chapter 15: Equation Solving The Polynomial Root-Finder -v The root finder solves up to 30th-order real or complex polynomials. Entering and Solving a Polynomial The POLY coefficients are not variables. You can display other menus in the coefficients-entry editor. Display the POLY order screen. -v Enter an integer between 2 and 30. The coefficients-entry editor is displayed with the equation across the top, the coefficient prompts along the left side, and the POLY ENTRY menu on the bottom.

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212 Chapter 15: Equation Solving Storing a Polynomial Coefficient or Root to a Variable To switch to the coefficientsentry screen, select COEFS from the POLY RESULT menu. To find roots on the home screen or in a program, select poly from the CATALOG. Move the cursor to the = sign next to the coefficient or root value you want to store. ### Display the Sto prompt. ALPHA-lock is on. X Enter the variable to which you want to store the value. ãRä ãOä ãOä ãTä 11 Store the value.

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16 Programming TI-86 Writing a Program on the TI-86 ....................................... 214 Running a Program.......................................................... 221 Working with Programs ................................................... 223 Running an Assembly Language Program ....................... 225 Entering and Storing a String........................................... 226 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 16PROG.

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214 Chapter 16: Programming Writing a Program on the TI-86 A program is a set of expressions, instructions, or both, which you enter or download. Expressions and instructions in the program are executed when you run the program. You can use most TI-86 features in a program. Programs can retrieve and update all variables stored to memory. Also, the program editor menu has inputàoutput commands, such as Input and Disp, and program control commands, such as If, Then, For, and While.

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Chapter 16: Programming 215 After you enter a program name, press b. The program editor and program editor menu are displayed. The program name is displayed at the top of the screen. The cursor is on the first command line, which begins with a colon. The TI-86 automatically places a colon at the beginning of each command line. As you write the program, the commands are stored to the program name.

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216 Chapter 16: Programming Input Displays the current graph and lets you use the free-moving cursor Input variable Pauses a program, displays ? as a prompt, and then stores your response to variable If you enter an expression for variable at an Input or Prompt prompt, it is evaluated and stored.

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Chapter 16: Programming 217 "string" Specifies the beginning and end of a string Outpt(row,column,"string") Outpt(row,column,stringName) Outpt(row,column,value) Outpt(row,column,variable) Displays string, stringName, value, or a value stored to variable beginning at the specified row and column on the display Outpt("CBLSEND",listName) Although using Send( is preferred on the TI-86, you can use Outpt( to send listName to a CBL 2/CBL or CBR (for TI-85 compatibility) InpSt promptString,variable InpSt v

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218 Chapter 16: Programming The PRGM CTL Menu PAGE$ PAGE# If Then 8 ' programName b ) IàO Else CTL For INSc End 4 While Repea Menu Lbl Goto 4 IS> DS< Pause Retur Stop 4 DelVa GrStl LCust To see examples that show how to use PRGM CTL menu items in programs, refer to the A to Z Reference. If, While, and Repeat instructions can be nested. For( loops can be nested.

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Chapter 16: Programming 219 tested when the End instruction is encountered Menu(item#,"title1", label1ã,item#, "title2",label2,...

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220 Chapter 16: Programming A command line that is longer than the screen is wide automatically continues at the beginning of the next line.

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Chapter 16: Programming 221 Variables to which you typically store values from an editor, such as the window variables, become items on program-only menus, such as the GRAPH WIND menu. When you select them, they are pasted to the cursor location on the command line. Running a Program To resume the program after a pause, press b. Paste the program name to the home screen. Either select it from the PRGM NAMES menu (8 &) or enter individual characters. Press b. The program begins to run.

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222 Chapter 16: Programming PROGRAM:FUNCTABL :Func:Fix 2:FnOff:PlO ff :y1=.

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Chapter 16: Programming 223 Working with Programs Managing Memory and Deleting a Program To check whether adequate memory is available for a program you want to enter or download, display the Check RAM screen (- ™ &; Chapter 17). To increase available memory, consider deleting selected items or data types from memory (Chapter 17). Editing a Program After you write a program, you can display it in the program editor and edit any command line.

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224 Chapter 16: Programming Calling a Program from Another Program On the TI-86, any stored program can be called from another program as a subroutine. In the program editor, enter the subroutine program name on a command line by itself. ♦ Press 8 to display the PRGM NAMES menu, and then select the program name. ♦ Use ALPHA keys and alpha keys to enter the program name’s individual characters.

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Chapter 16: Programming 225 Copying a Program to Another Program Name Display a new or existing program in the program editor. Move the cursor to the command line on which you want to copy a program. Display the Rcl prompt (- –). Enter the name of the program you want to copy. Either select the name from the PRGM NAMES menu or enter individual characters. Press b. The contents of the recalled program name are inserted into the other program at the cursor location.

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226 Chapter 16: Programming TI assembly language programs and other programs are available on TI’s World Wide Web site: http:ààwww.ti.comàcalc When you download an assembly language program, it is stored among the other programs as a PRGM NAMES menu item. You can: ♦ Transmit it using the TI-86 communication link (Chapter 18). ♦ Delete it using the MEM DELETE:PRGM screen (Chapter 17). ♦ Call it from another program as a subroutine (page 224).

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Chapter 16: Programming The STRNG (String) Menu " sub lngth 227 -“ Eq4St St4Eq " also marks the start and "string" Marks the start and end of string end of a formula to be attached to a list; it is also an item on the list editor menu (Chapter 11).

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228 Chapter 16: Programming 16PROG.

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17 Memory Management TI-86 Checking Available Memory ............................................ 230 Deleting Items from Memory ........................................... 231 Resetting the TI-86 .......................................................... 232 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 17MEMORY.

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230 Chapter 17: Memory Management Checking Available Memory The MEM (Memory) Menu For information on TOL (the tolerance editor), refer to the Appendix. RAM DELET RESET -™ TOL ClrEnt check-RAM memory/default clears ENTRY screen reset menu storage area memory delete tolerance menu editor Checking Memory Usage - ™ & When all memory is cleared and all defaults are set, the standard TI-86 has 98,224 bytes of available random-access memory (RAM).

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Chapter 17: Memory Management 231 Deleting Items from Memory The MEM DELET (Delete) Menu ALL REAL CPLX LIST -™' VECTR 4 4 MATRX STRNG GDB EQU CONS PRGM PIC To delete a parametric equation, delete the xt component. Each MEM DELET menu item displays the deletion screen for that data type. For example, when you select LIST, the MEM DELETE:LIST screen is displayed. Use the DELETE screens to delete any user-created variable and the information stored to it.

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232 Chapter 17: Memory Management Resetting the TI-86 The MEM RESET (Reset) Menu Before resetting all memory, consider deleting selected information to increase memory capacity (page 231). When you select and confirm ALL or DFLTS, the default contrast is reset; to adjust it, use - $ or - # (Chapter 1).

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18 The TI-86 Communication Link TI-86 TI-86 Linking Options ...................................................... 234 Connecting the TI-86 to Another Device ......................... 235 Selecting Data to Send..................................................... 236 Preparing the Receiving Device ....................................... 240 Transmitting Data ............................................................ 240 Receiving Transmitted Data.............................................

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234 Chapter 18: The TI-86 Communication Link TI-86 Linking Options Using the unit-to-unit cable included with the TI-86, you can transmit data between the TI-86 and several other devices. Linking Two TI-86s You can link two TI-86 units and select the data types to be transmitted, including programs. You can back up the entire memory of a TI-86 onto another TI-86. Linking a TI-86 and a TI-85 You can select the data types, including programs, to transfer from a TI-85 to a TI-86.

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Chapter 18: The TI-86 Communication Link 235 Linking a TI-86 and a PC or Macintosh TI-86 TI-GRAPH LINKè is an optional system that links a TI-86 with an IBMê-compatible or Macintoshê computer. Downloading Programs from the Internet If you have TI-GRAPH LINK and internet services, you can download programs from TI’s World Wide Web site at: http:ààwww.ti.

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236 Chapter 18: The TI-86 Communication Link The LINK Menu SEND The link menus are not available in the program editor. RECV -o SND85 menu of data menu of data types types to send to send to a TI-85 receive mode (waiting) Selecting Data to Send The CBL 2/CBL, CBR, and TI-86 TI-GRAPH LINK have built-in Silent Link, which eliminates the need for you to set up the devices to send or receive.

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Chapter 18: The TI-86 Communication Link 237 Initiating a Memory Backup To initiate a memory backup, select BCKUP from the LINK SEND menu (- o & &). The screen to the right is displayed. To complete memory backup, prepare the other unit to receive data transmission (page 239), and then select XMIT from the memory backup menu (&). Warning: When you transmit BCKUP, the transmitted memory overwrites all memory in the receiving unit; all information in the memory of the receiving unit is lost.

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238 Chapter 18: The TI-86 Communication Link When you select any LINK SEND menu item, except BCKUP or WIND, each variable of the selected data type is listed in alphanumeric order on a selection screen. The screen to the right is the SEND ALL screen (- o & *). ♦ The data type of each variable is specified. ♦ Small squares indicate that xStat, yStat, and Q2 are selected to be sent. ♦ The selection cursor is next to Q4.

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Chapter 18: The TI-86 Communication Link 239 Pol Select to send Pol graphing mode window variable values and format settings Param Select to send Param graphing mode window variable values and format settings DifEq Select to send DifEq graphing mode window variable values, difTol, axes settings, and format settings ZRCL Select to send user-created zoom window variables, and format settings in any mode To complete transmission of the selected variables, prepare the other unit to receive data transm

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240 Chapter 18: The TI-86 Communication Link Preparing the Receiving Device To prepare a PC to receive data, consult the TI-GRAPH LINK guidebook. To prepare a TI-86 or TI-85 to receive data transmission, select RECV from the LINK menu (- o '). The message Waiting and the busy indicator are displayed. The calculator is ready to receive transmitted items. To cancel receive mode without receiving items, press ^. When the LINK TRANSMISSION ERROR message is displayed, select EXIT from the menu (&).

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Chapter 18: The TI-86 Communication Link 241 During transmission, if a transmitted variable name is stored already in the memory of the receiving calculator, transmission is interrupted. The duplicated variable name, its data type, and the DUPLICATE NAME menu are displayed, as shown in the screen to the right. To resume or cancel transmission, you must select an item from the DUPLICATE NAME menu.

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242 Chapter 18: The TI-86 Communication Link Repeating Transmission to Several Devices After transmission is complete, the LINK menu is displayed and all selections remain. You can transmit the same selections to a different TI-86 without having to re-select data. To repeat a transmission with another device, disconnect the unit-to-unit cable from the receiving unit; connect it to another device; prepare the device to receive data; and then select SEND, then ALL, and then XMIT.

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19 Applications TI-86 Using Math Operations with Matrices ............................. 244 Finding the Area between Curves.................................... 245 The Fundamental Theorem of Calculus............................ 246 Electrical Circuits.............................................................. 248 Program: Taylor Series ..................................................... 250 Characteristic Polynomial and Eigenvalues...................... 252 Convergence of the Power Series ...........

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244 Chapter 19: Applications Using Math Operations with Matrices Displaying the result matrix elements to 11 decimal places illustrates accuracy. In the matrix editor, enter matrix A as shown. On the home screen, select rref from the MATRX OPS menu. To append a 3×3 identity matrix to matrix A, select aug from the MATRX OPS menu, enter A, select ident from the MATRX OPS menu, and then enter 3. Execute the expression. Enter Ans (to which the matrix from step 3 is stored).

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Chapter 19: Applications 245 Finding the Area between Curves Find the area of the region bounded by: If necessary, select ALLfrom the equation editor menu to deselect all functions. Also, turn off all stat plots. In Func graphing mode, select y(x)= from the GRAPH menu to display the equation editor and enter the equations as shown. y1=300 xà(x 2+625) f(x)=300 xà(x 2+625) g(x)=3 cos (.1 x) x=75 y2=3 cos (.1 x) Select WIND from the GRAPH menu and set the window variables as shown.

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246 Chapter 19: Applications The Fundamental Theorem of Calculus If necessary, select ALLfrom the equation editor menu to deselect all functions. Also, turn off all stat plots. Consider these three functions: F(x)1 = (sin x)àx In the example, nDer(y2,x) only approximates y3; you cannot define y3 as der1(y2,x). F(x) 3 = d dx x ‰0 (sin t)àt dt In Func graphing mode, select y(x)= from the GRAPH menu, and then enter the functions and set graph styles in the equation editor as shown.

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Chapter 19: Applications Deselect y2 in the equation editor. Select TBLST from the TABLE menu. Set TblStart=1, @Tbl=1, and Indpnt: Auto. Select TABLE from the TABLE menu to display the table. Compare the solution of y1 with the solution of y3 to numerically support the formula above. 19APPS.

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248 Chapter 19: Applications Electrical Circuits A measurement device has measured the DC current (C) in milliamperes and voltage (V) in volts on an unknown circuit. From these measurements, you can calculate power (P) in milliwatts using the equation CV=P. What is the average of the measured power? With the TI-86, you can estimate the power in milliwatts at a current of 125 milliamperes using the trace cursor, the interpolateàextrapolate editor, and a regression forecast.

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Chapter 19: Applications The 7s and 8s in parentheses specify the 7th and 8th elements of POWER and CURR. To enter each regression after LinR, press - ¢ and edit as needed. Select TRACE from the GRAPH menu to display the stat plot and trace cursor on the graph screen. Trace the stat plot to approximate the value of POWER at CURR=125. With this statistical data, the closest to CURR=125 that you can trace to is CURR=120 (on the y-axis).

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250 Chapter 19: Applications Program: Taylor Series When you run this program, you can enter a function and specify the order and center point. Then the program calculates the Taylor Series approximation for the function and plots the function you entered. This example shows how to call a program from another program as a subroutine. Before you enter the program TAYLOR, select EDIT from the PRGM menu, enter MOBIUS at the Name= prompt, and then enter this brief program to store the Mobius Series.

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Chapter 19: Applications Begins Then group Calls subroutine Begins For group Begins While group Creates nested While group Creates nested For group Ends While group Ends For group Ends Then group :If order‚1 :der1(y13,x,center)¶TPOLY(order) :If order‚2 :der2(y13,x,center)à2¶TPOLY(orderN1) :If order‚3 :Then :MOBIUS :For(N,3,order,1) :abs f0¶gmax:gmax¶bmi :1¶m:0¶ssum :While abs bmi‚H¹gmax :While MSERIES(m)==0 :m+1¶m :End :0¶bsum :For(J,1,m¹N,1) :rr¹e^(2p(Jà(m¹N))¹(0,1))+(center,0)¶x :real y13¶gval :bsum+g

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252 Chapter 19: Applications On the home screen, select TAYLOR from the PRGM NAMES menu, and then press b to run the program. When prompted, enter: FUNCTION: sin x ORDER: 5 CENTER: 0 Characteristic Polynomial and Eigenvalues In the matrix editor or on the home screen, enter matrix A as shown. [[L1,2,5][3,L6,9][2,L5,7]]¶A The first eigenvalue is real, since the imaginary part is 0. If necessary, select ALLfrom the equation editor menu to deselect all functions. Also, turn off all stat plots.

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Chapter 19: Applications 253 Next, use the list editor and a degree-three polynomial regression to find an analytic formula in terms of x for the characteristic polynomial y1=det(ANx¹ident 3). Create two lists that you can use to find the analytic formula. To clear the menus from the graph screen, press :. In the list editor, create elements for xStat by entering the expression seq(N,N,L10,21) in the xStat entry line. seq is on the MATH MISC menu.

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254 Chapter 19: Applications 쐈 Support this conjecture by graphing y1, y2 (to which Cp(x) is stored), and Plot1 together. 쐉 In the equation editor, enter the apparent characteristic polynomial of matrix A and select ¼ (thick) graph style as shown. ¼y3=Lx^3+14xN24 씈 Graph y1, y2, y3, and Plot1. 씉 Deselect y2 in the equation editor. 씊 Select TABLE from the TABLE menu to display y1 and y3 in the table. Compare the values for the characteristic polynomial.

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Chapter 19: Applications If necessary, select ALLN from the equation editor menu to deselect all functions. Also, turn off all stat plots. Select TOL from the MEM menu and set tol=1. On the mode screen, set Radian angle mode and Param graphing mode. In the equation editor, enter the parametric equations for the power series approximation as shown. Select sum and seq from the LIST OPS menu. Select ! from the MATH PROB menu.

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256 Chapter 19: Applications Reservoir Problem On the TI-86, you can use parametric graphing animation to solve a problem. Consider a water reservoir with a height of 2 meters. You must install a small valve on the side of the reservoir such that water spraying from the open valve hits the ground as far away from the reservoir as possible.

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Chapter 19: Applications If necessary, select ALLN from the equation editor menu to deselect all functions. Also, turn off all stat plots. To clear the menus from the graph screen, press :. 257 In Param graphing mode, select E(t)= from the GRAPH menu and enter the equations in the equation editor as shown. This pair of equations plots the path of the water stream when the valve is installed at a height of 0.5 meters. »xt1=t‡(2g(2N0.5)) yt1=0.5N(g¹t 2)à2 Move the cursor to xt2=.

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258 Chapter 19: Applications Predator-Prey Model The growth rates of predator and prey populations, such as foxes and rabbits, depend upon the populations of both species. This initial-value problem is a form of the predator-prey model. F'=LF+0.1F¹R R'=3RNF¹R Q1 = population of foxes (F) Q2 = population of rabbits (R) Q[1= initial population of foxes (2) Q[2 = initial population of rabbits (5) Find the population of foxes and rabbits after 3 months (t=3).

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Chapter 19: Applications Select GRAPH from the GRAPH menu to plot the graph of the two populations over time. To see the direction field of the phase-plane solution, select FORMT from the GRAPH screen, and then set DirFld field format. Select INITC from the GRAPH menu and delete the values for Q[1 and Q[2. Select GRAPH from the GRAPH menu to display the direction field of the phase-plane solution.

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260 Chapter 19: Applications Program: Sierpinski Triangle This program creates a drawing of a widely known fractal, the Sierpinski Triangle, and stores the drawing to the picture variable TRI. Select EDIT from the PRGM menu, enter SIERP at the Name= prompt, and then enter this program. Sets viewing window Begins For group IfàThen group PROGRAM:SIERP :FnOff :ClDrw :PlOff :AxesOff :0¶xMin:1¶xMax :0¶yMin:1¶yMax :rand¶X:rand¶Y :For(K,1,3000) :rand¶N :If N(1 à 3 ) :Then :.5X¶X :.

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20 A to Z Function and Instruction Reference TI-86 Quick-Find Locator........................................................... 262 Alphabetical Listing of Operations................................... 266 M1 M2 M3 M4 M5 F1 F2 F3 F4 F5 20ATOZ.

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262 Chapter 20: A to Z Function and Instruction Reference Quick-Find Locator This section lists the TI-86 functions and instructions in functional groups along with the page numbers where they are described in this chapter. Graphing Axes( ................... 271 AxesOff ............... 271 AxesOn................ 271 Circl( .................... 273 ClDrw ................... 273 CoordOff ............. 275 CoordOn.............. 275 DifEq .................... 281 DirFld ................... 282 DrawDot .......

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Chapter 20: A to Z Function and Instruction Reference 263 Mathematics, Algebra, and Calculus abs ....................... 267 Addition: + ............ 267 and ....................... 268 angle .................... 269 Ans ...................... 269 arc(....................... 269 Assignment: = ...... 270 Ü ........................... 271 Bin ....................... 272 4Bin ...................... 272 ClrEnt .................. 273 ClTbl .................... 273 conj ...................... 275 cos ..........

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264 Chapter 20: A to Z Function and Instruction Reference Matrices aug( ..................... 270 cnorm .................. 273 cond .................... 274 det........................ 281 dim....................... 281 ¶dim .................... 281 eigVc ................... 289 eigVl .................... 289 Fill( ...................... 295 ident .................... 304 LU(....................... 318 Matrix entry: [ ] .... 319 mRAdd(............... 321 multR( ................. 322 norm................

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Chapter 20: A to Z Function and Instruction Reference 265 Strings Concatenation: + .. 274 Eq4St( .................. 290 lngth .................... 316 St4Eq( .................. 361 String entry: " .......363 sub( ......................363 4Sph .....................360 SphereV ...............360 unitV ....................368 vc4li ......................369 Vector entry: [ ] ....369 Vectors cnorm .................. 273 cross( .................. 277 4Cyl ...................... 278 CylV ...............

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266 Chapter 20: A to Z Function and Instruction Reference Alphabetical Listing of Operations All the operations in this section are included in the CATALOG. Non-alphabetic operations (such as +, !, and >) are listed at the end of the CATALOG. In this A to Z Reference, however, these operations are listed under their alphabetic equivalent (such as addition, factorial, and greater than).

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Chapter 20: A to Z Function and Instruction Reference abs MATH NUM menu CPLX menu MATRX CPLX menu VECTR CPLX menu abs realNumber or abs (realExpression) Returns the absolute value of realNumber or realExpression. abs (complexNumber) Returns the magnitude (modulus) of complexNumber. abs L256.4 b 267 256.4 abs L4…3+13 b abs (L4…3+13) b 25 1 abs (3,4) b abs (3±4) b 5 3 abs (real,imaginary) returns (real 2+imaginary2). abs (magnitude±angle) returns magnitude. abs list abs matrix abs vector abs {1.

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268 Chapter 20: A to Z Function and Instruction Reference listA + listB matrixA + matrixB vectorA + vectorB Returns a list, matrix, or vector that is the sum of the corresponding real or complex elements in the arguments. The two arguments must have the same dimension. {1,2,3}+{4,5,6} b {5 7 9} [[1,2,3][4,5,6]]+[[4,5,6][7,8,9]] [[5 7 9 ] b [11 13 15]] [1,2,3]+[4,5,6] b [5 7 9] For information about adding two strings, refer to Concatenation on page 274.

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Chapter 20: A to Z Function and Instruction Reference angle angle (complexNumber) Returns the polar angle of complexNumber, adjusted by +p in the 2nd quadrant or Lp in the 3rd quadrant. The polar angle of a real number is always 0. CPLX menu MATRX CPLX menu VECTR CPLX menu L1 angle (real,imaginary) returns tan (imaginary/real). angle (magnitude±angle) returns angle, Lp < angle p.

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270 Chapter 20: A to Z Function and Instruction Reference AsmComp( CATALOG AsmComp(AsciiAssemblyPrgmName,HexAssemblyPrgmName) Compiles an assembly language program written in ASCII and stores the hex version. The compiled hex version, which uses about half the storage space of the ASCII version, cannot be edited. When you execute the ASCII version, the TI-86 compiles it each time.

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Chapter 20: A to Z Function and Instruction Reference aug(matrixA,matrixB) Returns a matrix consisting of matrixB appended as new columns to the end of matrixA. The matrices can be real or complex. Both must have the same number of rows. aug(matrix,vector) Returns a matrix consisting of vector appended as a new column to the end of matrix. The arguments can be real or complex. The number of rows in matrix must equal the number of elements in vector.

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272 Chapter 20: A to Z Function and Instruction Reference Bin Bin 4Bin BASE CONV menu In Bin number base mode: Sets binary number base mode. Results are displayed with the Ü suffix. In any number base mode, you can designate an appropriate value as binary, decimal, hexadecimal, or octal by using the Ü, Þ, ß, or Ý designator, respectively, from the BASE TYPE menu. † mode screen number 4Bin list 4Bin matrix 4Bin vector 4Bin Returns the binary equivalent of the real or complex argument.

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Chapter 20: A to Z Function and Instruction Reference Circl( Circl(x,y,radius) Draws a circle with center (x,y) and radius on the current graph. † GRAPH DRAW menu ClDrw 273 Starting with a ZStd graph screen: ZSqr:Circl(1,2,7) b ClDrw Clears all drawn elements from the current graph. † GRAPH DRAW menu † STAT DRAW menu CILCD ClLCD Clears the home screen (LCD). ‡ program editor I/O menu ClrEnt ClrEnt Clears the contents of the Last Entry storage area.

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274 Chapter 20: A to Z Function and Instruction Reference cnorm vector Returns the sum of the absolute values of the real or complex elements in vector. Concatenation: + \ cond MATRX MATH menu stringA + stringB Returns a string consisting of stringB appended (concatenated) to the end of stringA.

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Chapter 20: A to Z Function and Instruction Reference conj conj (complexNumber) CPLX menu Returns the complex conjugate of complexNumber. MATRX CPLX menu In RectC mode, conj (real,imaginary) returns (real,Limaginary). VECTR CPLX menu In PolarC mode, conj (magnitude±angle) returns (magnitude±Langle), Lp < angle p. conj complexList conj complexMatrix conj complexVector In RectC complex number mode: conj (3,4) b (3,L4) conj (3±2) b (L1.24844050964,L2.

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276 Chapter 20: A to Z Function and Instruction Reference cos cos angle or cos (expression) > cos p/2 b cos (p/2) b cos 45¡ b An angle is interpreted as degrees or radians according to the current angle mode. In any angle mode, you can designate an angle as degrees or radians by using the ¡ or r designator, respectively, from the MATH ANGLE menu. cos 45 b cos (p/2) r b cos list Returns a list in which each element is the cosine of the corresponding element in list.

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Chapter 20: A to Z Function and Instruction Reference cosh MATH HYP menu cosh number or cosh (expression) Returns a list in which each element is the hyperbolic cosine of the corresponding element in list. MATH HYP menu cosh L1 number or cosL1 (expression) Returns a list in which each element is the inverse hyperbolic cosine of the corresponding element in list. VECTR MATH menu cosh {0,1.2} b {1 1.

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278 Chapter 20: A to Z Function and Instruction Reference cSum( cSum(list) Returns a list of the cumulative sums of the real or complex elements in list, starting with the first element. LIST OPS menu 4Cyl vector 4Cyl Displays a 2- or 3-element real vector result in cylindrical form, [rq z], even if the display mode is not set for cylindrical (CylV). VECTR OPS menu CylV CylV Sets cylindrical vector coordinate mode ( [rq z] ).

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Chapter 20: A to Z Function and Instruction Reference 4Dec BASE CONV menu number 4Dec list 4Dec matrix 4Dec vector 4Dec Returns the decimal equivalent of the real or complex argument. Degree Degree Sets degree angle mode. † mode screen Degree entry: ¡ number ¡ or (expression) ¡ Designates a real number or expression as degrees, regardless of the angle mode setting. MATH ANGLE menu list ¡ Designates each element in list as degrees.

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280 Chapter 20: A to Z Function and Instruction Reference DelVar( ‡ program editor CTL menu (DelVa shows on menu) der1( CALC menu DelVar(variable) Deletes the specified user-created variable from memory. 2¶A b 2 16 (A+2) 2 b DelVar(A) b Done ERROR 14 UNDEFINED (A+2) 2 b You cannot use DelVar( to delete a program variable or built-in variable.

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Chapter 20: A to Z Function and Instruction Reference det det squareMatrix Returns the determinant of squareMatrix. The result is real for a real matrix, complex for a complex matrix. MATRX MATH menu DifEq † mode screen dim MATRX OPS menu VECTR OPS menu [[1,2][3,4]]¶MAT b det MAT b 281 [[1 2] [3 4]] L2 DifEq Sets differential equation graphing mode. dim matrix Returns a list containing the dimensions (number of rows and columns) of a real or complex matrix.

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282 Chapter 20: A to Z Function and Instruction Reference #ofElements¶dim vectorName If vectorName does not exist, creates a new vector with the specified #ofElements and fills it with zeros. If vectorName exists, redimensions that vector to the specified #ofElements. Existing elements within the new dimension are not changed; elements outside the new dimension are deleted. If additional elements are created, they are filled with zeros.

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Chapter 20: A to Z Function and Instruction Reference Disp Disp valueA,valueB,valueC, ... Displays each value. The values can include strings and variable names. ‡ program editor I/O menu Displays the home screen. † GRAPH menu ‡ program editor I/O menu 10 1024 Done "Hello"¶STR b Hello Disp STR+", Jan" b Hello, Jan Done Disp DispG 10¶x b Disp x^3+3 xN6 b 283 DispG Program segment in Func graphing mode: Displays the current graph. Function names are case-sensitive. Use y1, not Y1.

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284 Chapter 20: A to Z Function and Instruction Reference DispT ‡ program editor I/O menu Division: / F DispT Program segment in Func graphing mode: Displays the table. Function names are case-sensitive. Use y1, not Y1. numberA / numberB or (expressionA) / (expressionB) Returns one argument divided by another. The arguments can be real or complex. number / list or (expression) / list © :y1=4cos x :DispT © L98/4 b L98/(4¹3) b L24.5 L8.

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Chapter 20: A to Z Function and Instruction Reference DMS entry: ' MATH ANGLE menu In a trig calculation, the result of a DMS entry is treated as degrees in the Degree angle mode only. It is treated as radians in Radian angle mode. 4DMS MATH ANGLE menu dot( VECTR MATH menu degrees'minutes'seconds' Designates the entered angle is in DMS format. degrees ( 999,999), minutes (< 60), and seconds (< 60, may have decimal places) must be entered as real numbers, not as variable names or expressions.

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286 Chapter 20: A to Z Function and Instruction Reference DrawF GRAPH DRAW menu DrawLine † graph format screen DrawF expression Draws expression (in terms of x) on the current graph. In Func graphing mode: ZStd:DrawF 1.25 x cos x b DrawLine Sets connected line graphing format. 20ATOZ.

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Chapter 20: A to Z Function and Instruction Reference DrEqu( † GRAPH menu To enter the ' character for the Q' variables, use the CHAR MISC menu. DrEqu(xAxisVariable,yAxisVariable,xList,yList,tList) In DifEq graphing mode, draws the solution to a set of differential equations stored in the Q' variables specified by xAxisVariable and yAxisVariable. If direction fields are off (FldOff is selected), the initial values must be stored also.

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288 Chapter 20: A to Z Function and Instruction Reference DS<( ‡ program editor CTL menu :DS<(variable,value) :command-if-variable‚value :commands Decrements variable by 1. If the result is < value, skips command-if-variable‚value. If the result is ‚ value, then command-if-variable‚value is executed. Program segment: © :9¶A :Lbl Start :Disp A :DS<(A,5) :Goto Start :Disp "A is now <5" © variable cannot be a built-in variable.

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Chapter 20: A to Z Function and Instruction Reference e^list Returns a list in which each element is e raised to the power specified by the corresponding element in list. 289 e^{1,0,.5} b {2.71828182846 1 1.6… e^squareMatrix The squareMatrix cannot have repeated eigenvalues. eigVc MATRX MATH menu The squareMatrix cannot have repeated eigenvalues. eigVl MATRX MATH menu Returns a square matrix that is the matrix exponential of squareMatrix.

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290 Chapter 20: A to Z Function and Instruction Reference Else ‡ program editor CTL menu End Refer to syntax information for If, beginning on page 305. See the If:Then:Else:End syntax. End Identifies the end of a While, For, Repeat, or If-Then- ‡ program editor CTL menu Eng † mode screen Else loop. Eng In Eng notation mode: Sets engineering notation mode, in which the power-of10 exponent is a multiple of 3.

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Chapter 20: A to Z Function and Instruction Reference Equal to: == TEST menu The == operator is used to compare arguments, while = is used to assign a value or expression to a variable. numberA == numberB matrixA == matrixB vectorA == vectorB stringA == stringB Tests whether the condition argumentA == argumentB is true or false. Numbers, matrices, and vectors can be real or complex. If complex, the magnitude (modulus) of each element is compared. Strings are case-sensitive.

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292 Chapter 20: A to Z Function and Instruction Reference evalF( CALC menu evalF(expression,variable,value) evalF(expression,variable,list) Returns a list containing the values of expression evaluated with respect to variable at each element in list. Exponent: E C evalF(x^3+x+5,x,5) b 135 Returns the value of expression evaluated with respect to variable at a real or complex value.

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Chapter 20: A to Z Function and Instruction Reference ExpR STAT CALC menu Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1. ExpR xList,yList,frequencyList,equationVariable Fits an exponential regression model (y=ab x) to real data pairs in xList and yList (y values must be > 0) and frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1.

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294 Chapter 20: A to Z Function and Instruction Reference ExpR Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only. Factorial: ! number ! or (expression) ! Returns the factorial of a real integer or non-integer, where 0 integer 449 and 0 non-integer 449.9. For a non-integer, the Gamma function is used to find the factorial. An expression must evaluate to an appropriate value. MATH PROB menu 6! b 12.

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Chapter 20: A to Z Function and Instruction Reference Fill( LIST OPS menu MATRX OPS menu Fill(number,listName) Fill(number,matrixName) Fill(number,vectorName) Replaces each element in an existing listName, matrixName, or vectorName with a real or complex number. VECTR OPS menu Fix Fix integer or Fix (expression) Sets fixed decimal mode for integer number of decimal places, where 0 integer 11. An expression must evaluate to an appropriate integer.

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296 Chapter 20: A to Z Function and Instruction Reference fMax( CALC menu fMax(expression,variable,lower,upper) Returns the value at which a local maximum of expression with respect to variable occurs, between real lower and upper values for variable. fMax(sin x,x,Lp,p) b 1.57079632598 The tolerance is controlled by the built-in variable tol, whose default is 1EL5. To view or set tol, press - ™ ) to display the tolerance editor.

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Chapter 20: A to Z Function and Instruction Reference FnOff 297 FnOff b Done FnOn 1,3 b Done FnOn b Done Deselects all equation function numbers. FnOn FnOn function#,function#, ... Selects the specified equation function numbers, in addition to any others already selected. † GRAPH VARS menu FnOn Selects all equation function numbers.

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298 Chapter 20: A to Z Function and Instruction Reference Form( LIST OPS menu Form("formula",listName) Generates the contents of listName automatically, based on the attached formula. If you express formula in terms of a list, you can generate one list based on the contents of another. The contents of listName are updated automatically if you edit formula or edit a list referenced in formula.

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Chapter 20: A to Z Function and Instruction Reference list 4Frac matrix 4Frac vector 4Frac 299 {1/2+1/3,1/6N3/8}¶L1 b {.833333333333 L.208… Ans4Frac b {5/6 L5/24} Returns a list, matrix, or vector in which each element is the rational equivalent of the corresponding element in the argument. Func † mode screen gcd( MATH MISC menu Func Sets function graphing mode.

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300 Chapter 20: A to Z Function and Instruction Reference getKy ‡ program editor I/O menu getKy Returns the key code for the last key pressed. If no key has been pressed, getKy returns 0. Refer to the TI-86 key code diagram in Chapter 16. Program: PROGRAM:CODES :Lbl TOP :getKy¶KEY :While KEY==0 : getKy¶KEY :End :Disp KEY :Goto TOP To break the program, press ^ and then *.

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Chapter 20: A to Z Function and Instruction Reference number > list 301 1>{1,L6,10} b {0 1 0} {1,5,9}>{1,L6,10} b {0 1 0} Returns a list of 1s and/or 0s to indicate if number is > the corresponding element in list. listA > listB Returns a list of 1s and/or 0s to indicate if each element in listA is > the corresponding element in listB. Greater than or equal to: ‚ TEST menu numberA ‚ numberB or (expressionA) ‚ (expressionB) Tests whether the condition is true or false.

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302 Chapter 20: A to Z Function and Instruction Reference GridOn GridOn Turns on grid format so that grid points are displayed in rows and columns corresponding to the tick marks on each axis. † graph format screen GrStl( GrStl(function#,graphStyle#) In Func graphing mode: Sets the graph style for function#.

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Chapter 20: A to Z Function and Instruction Reference 4Hex BASE CONV menu number 4Hex list 4Hex matrix 4Hex vector 4Hex In Bin number base mode: 1010¹1110 b Ans4Hex b Hist xList,frequencyList Draws a histogram on the current graph, using the real data in xList and the frequencies in frequencyList. † STAT DRAW menu Hist xList Uses frequencies of 1. 10001100Ü 8×ß {100,101,110}4Hex b Returns the hexadecimal equivalent of the real or complex argument.

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304 Chapter 20: A to Z Function and Instruction Reference Horiz Horiz yValue Draws a horizontal line on the current graph at yValue. † GRAPH DRAW menu IAsk CATALOG ident MATRX OPS menu Horiz 4.5 b IAsk Sets the table so that the user can enter individual values for the independent variable. CATALOG IAuto In a ZStd graph screen: IAuto Sets the table so that the TIN86 generates the independent-variable values automatically, based on values entered for TblStart and @Tbl.

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Chapter 20: A to Z Function and Instruction Reference If ‡ program editor CTL menu :If condition :command-if-true :commands If condition is true, executes command-if-true. Otherwise, skips command-if-true. The condition is true if it evaluates to any nonzero number, or false if it evaluates to zero. Program segment: © :If x<0 :Disp "x is negative" © To execute multiple commands if condition is true, use If:Then:End instead.

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306 Chapter 20: A to Z Function and Instruction Reference :If condition :Then :commands-if-true :Else :commands-if-false :End :commands If condition is true (nonzero), executes commands-iftrue from Then to Else and then continues with the next command following End. Program segment: © :If x<0 :Then : Disp "x is negative" :Else : Disp "x is positive or zero" :End © If condition is false (zero), executes commands-if-false from Else to End and then continues with the next command following End.

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Chapter 20: A to Z Function and Instruction Reference InpSt ‡ program editor I/O menu InpSt promptString,variable Pauses a program, displays promptString, and waits for the user to enter a response. The response is stored to variable always as a string. When entering the response, the user should not enter quotation marks. 307 Program segment: © :InpSt "Enter your name:",STR © To prompt for a number or expression instead of a string, use Input. InpSt variable Displays ? as the prompt.

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308 Chapter 20: A to Z Function and Instruction Reference Input Program segment in RectGC graph format: Pauses a program, displays the graph screen, and lets the user update x and y (or r and q in PolarGC graph format) by moving the free-moving cursor. To resume the program, press b. Input "CBLGET",variable © :Input :Disp x,y © Input "CBLGET",L1 b Done Receives list data sent from a CBL or CBR System and stores it to variable on the TIN86. Use this "CBLGET" syntax for both CBL and CBR.

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Chapter 20: A to Z Function and Instruction Reference inter( inter(x1,y1,x2,y2,xValue) Calculates the line through points (x1,y1) and (x2,y2) and then interpolates or extrapolates a y value for the specified xValue. † MATH menu inter(y1,x1,y2,x2,yValue) Interpolates or extrapolates an x value for the specified yValue. Notice that points (x1,y1) and (x2,y2) must be entered as (y1,x1) and (y2,x2).

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310 Chapter 20: A to Z Function and Instruction Reference iPart list iPart matrix iPart vector Returns a list, matrix, or vector in which each element is the integer part of the corresponding element in the specified argument. IS>( ‡ program editor CTL menu :IS>(variable,value) :command-if-variablevalue :commands Increments variable by 1. If the result is > value, skips command-if-variablevalue. If the result is value, then command-if-variablevalue is executed. [[1.25,L23.45][L99.5,47.

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Chapter 20: A to Z Function and Instruction Reference Lbl ‡ program editor CTL menu Lbl label Creates a label of up to eight characters. A program can use a Goto instruction to transfer control (branch) to a specified label. InpSt stores input as a string, so be sure to store a string to the password variable. lcm( MATH MISC menu LCust( ‡ program editor CTL menu lcm(integerA,integerB) Returns the least common multiple of two nonnegative integers. LCust(item#,"title" [,item#,"title", ...

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312 Chapter 20: A to Z Function and Instruction Reference Less than: < TEST menu numberA < numberB or (expressionA) < (expressionB) Tests whether the condition is true or false. The arguments must be real numbers. • If true (numberA < numberB), returns 1. • If false (numberA ‚ numberB), returns 0.

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Chapter 20: A to Z Function and Instruction Reference LgstR STAT CALC menu Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1. LgstR returns a tolMet value that indicates if the result meets the TI-86’s internal tolerance. • If tolMet=1, the result is within the internal tolerance. • If tolmet=0, the result is outside the internal tolerance, although it may be useful for general purposes.

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314 Chapter 20: A to Z Function and Instruction Reference LgstR [iterations,]equationVariable Uses xStat, yStat, and fStat for xList, yList, and frequencyList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq. LgstR [iterations] Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only.

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Chapter 20: A to Z Function and Instruction Reference LinR STAT CALC menu Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1. LinR xList,yList,frequencyList,equationVariable Fits a linear regression model (y=a+bx) to real data pairs in xList and yList and frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1.

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316 Chapter 20: A to Z Function and Instruction Reference LinR Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only. List entry: { } LIST menu li4vc LIST OPS menu {element1,element2, ...} Defines a list in which each element is a real or complex number or variable. li4vc list {1,2,3}¶L1 b {1 2 3} In RectC complex number mode: {3,(2,4),8¹2}¶L2 b {(3,0) (2,4) (16,0)} li4vc {2,7,L8,0} b [2 7 L8 0] Returns a vector converted from a real or complex list.

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Chapter 20: A to Z Function and Instruction Reference LnR STAT CALC menu Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1. LnR xList,yList,frequencyList,equationVariable Fits a logarithmic regression model (y=a+b ln x) to the real data pairs in xList and yList (x values must be > 0) and frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1.

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318 Chapter 20: A to Z Function and Instruction Reference LnR Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only. log < log number or log (expression) Returns the logarithm of a real or complex number or expression, where: 10 logarithm = number log list Returns a list in which each element is the logarithm of the corresponding element in list.

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Chapter 20: A to Z Function and Instruction Reference Matrix entry: [ ] - „ and - … [ [row1] [row2] ... ] Defines a matrix entered row-by-row in which each element is a real or complex number or variable. 319 [[1,2,3][4,5,6]]¶MAT b [[1 2 3] [4 5 6]] Enter each [row] as [element,element, ... ]. max( MATH NUM menu max(numberA,numberB) max(2.3,1.4) b 2.3 Returns the larger of two real or complex numbers. max(list) max({1,9,p/2,e^2}) b 9 Returns the largest element in list.

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320 Chapter 20: A to Z Function and Instruction Reference Menu( ‡ program editor CTL menu Menu(item#,"title1",label1[, ... ,item#,"title15",label15]) Generates a menu of up to 15 items during program execution. Menus are displayed as three groups of five items. For each item: • item# — integer from 1 through 15 that identifies this item’s position in the menu. • "title" — text string that will be displayed for this item on the menu.

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Chapter 20: A to Z Function and Instruction Reference mRAdd( MATRX OPS menu mRAdd(number,matrix,rowA,rowB) Returns the result of a “multiply and add row” matrix operation, where: a. rowA of a real or complex matrix is multiplied by a real or complex number. [[5,3,1][2,0,4][3,L1,2]]¶MAT [[5 3 1] b [2 0 4] [3 L1 2]] mRAdd(5,MAT,2,3) b [[5 3 1 ] [2 0 4 ] [13 L1 22]] b. The results are added to (and then stored in) rowB.

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322 Chapter 20: A to Z Function and Instruction Reference matrixA ¹ matrixB Returns a matrix in which matrixA is multiplied by matrixB. The number of columns in matrixA must equal the number of rows in matrixB. [[2,2][3,4]]¶MATA b [[1,2,3][4,5,6]]¶MATB b [[1 2 3] [4 5 6]] MATA¹MATB b multR( MATRX OPS menu multR(number,matrix,row) Returns the result of a “row multiplication” matrix operation, where: a. The specified row of a real or complex matrix is multiplied by a real or complex number.

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Chapter 20: A to Z Function and Instruction Reference nDer( CALC menu To view or set the value for d, press - ™ ) to display the tolerance screen. nDer(expression,variable,value) Returns an approximate numerical derivative of expression with respect to variable evaluated at a real or complex value. The approximate numerical derivative is the slope of the secant line through the points: nDer(x^3,x,5) b 75.

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324 Chapter 20: A to Z Function and Instruction Reference norm [3,4,5] b norm vector 7.07106781187 Returns the length of a real or complex vector, where: norm [a,b,c] returns a 2+b 2+c 2. norm number or norm (expression) norm list Returns the absolute value of a real or complex number or expression, or of each element in list. Normal † mode screen Normal Sets normal notation mode. norm L25 b 25 In Radian angle mode: norm {L25,cos L(p/3)} b {25 .5} In Eng notation mode: 123456789 b 123.

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Chapter 20: A to Z Function and Instruction Reference not BASE BOOL menu not integer 325 In Dec number base mode: Returns the one’s complement of a real integer. Internally, integer is represented as a 16-bit binary number. The value of each bit is flipped (0 becomes 1, and vice versa) for the one’s complement.

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326 Chapter 20: A to Z Function and Instruction Reference Not equal to: ƒ TEST menu numberA ƒ numberB matrixA ƒ matrixB vectorA ƒ vectorB stringA ƒ stringB Tests whether the condition argumentA ƒ argumentB is true or false. Numbers, matrices, and vectors can be real or complex. If complex, the magnitude (modulus) of each element is compared. Strings are case-sensitive. 2+2ƒ3+2 b 1 2+(2ƒ3)+2 b 5 [1,2]ƒ[3N2,L1+3] b 0 "A"ƒ"a" b 1 • If true (argumentA ƒ argumentB), returns 1.

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Chapter 20: A to Z Function and Instruction Reference Oct † mode screen 4Oct BASE CONV menu Oct In Oct number base mode: Sets octal number base mode. Results are displayed with the Ý suffix. In any number base mode, you can designate an appropriate value as binary, decimal, hexadecimal, or octal by using the Ü, Þ, ß, or Ý designator, respectively, from the BASE TYPE menu. number 4Oct list 4Oct matrix 4Oct vector 4Oct Returns the octal equivalent of the real or complex argument.

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328 Chapter 20: A to Z Function and Instruction Reference OneVar Uses xStat and fStat for xList and frequencyList. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. or BASE BOOL menu integerA or integerB Compares two real integers bit by bit. Internally, both integers are converted to binary. When corresponding bits are compared, the result is 1 if either bit is 1; the result is 0 only if both bits are 0. The returned value is the sum of the bit results.

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Chapter 20: A to Z Function and Instruction Reference Outpt( ‡ program editor I/O menu Outpt(row,column,string) Displays string beginning at row and column, where 1 row 8 and 1 column 21. Outpt(row,column,value) Displays value beginning at the specified row and column. Program segment: © :ClLCD :For(i,1,8) : Outpt(i,randInt(1,21),"A") :End © Example result after execution: Outpt("CBLSEND",listName) Sends the contents of listName to the CBL or CBR System.

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330 Chapter 20: A to Z Function and Instruction Reference P2Reg STAT CALC menu Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1. P2Reg xList,yList,frequencyList,equationVariable Performs a second order polynomial regression using real data pairs in xList and yList and frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1.

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Chapter 20: A to Z Function and Instruction Reference 331 P2Reg Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only. P3Reg STAT CALC menu Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1. P3Reg xList,yList,frequencyList,equationVariable Performs a third order polynomial regression using real data pairs in xList and yList and frequencies in frequencyList.

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332 Chapter 20: A to Z Function and Instruction Reference P3Reg equationVariable Uses xStat, yStat, and fStat for xList, yList, and frequencyList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq. P3Reg Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only. P4Reg STAT CALC menu Built-in equation variables such as y1, r1, and xt1 are case-sensitive.

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Chapter 20: A to Z Function and Instruction Reference 333 P4Reg xList,yList Uses frequencies of 1, and stores the regression equation to RegEq only. P4Reg equationVariable Uses xStat, yStat, and fStat for xList, yList, and frequencyList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq. P4Reg Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only.

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334 Chapter 20: A to Z Function and Instruction Reference Pause Suspends program execution until the user presses b. Percent: % number% or (expression)% Returns a real number or expression divided by 100. MATH MISC menu pEval( pEval(coefficientList,xValue) Returns the value of a polynomial (whose coefficients are given in coefficientList) at xValue. MATH MISC menu PlOff PlOff [1,2,3] 5% b 5%¹200 b (10+5)%¹200 b .

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Chapter 20: A to Z Function and Instruction Reference Plot1( Plot2( Plot3( † STAT PLOT menu The syntax and descriptions to the right refer to Plot1(, but they apply as well to Plot2( and Plot3(. Scatter plot ® Plot1(1,xListName,yListName,mark) Plot1(1,xListName,yListName) Defines and selects the plot using real data pairs in xListName and yListName.

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336 Chapter 20: A to Z Function and Instruction Reference Pol † mode screen 4Pol CPLX menu Pol Sets polar graphing mode. complexNumber 4Pol Displays complexNumber in polar form (magnitudeangle), regardless of the complex number mode. list 4Pol matrix 4Pol vector 4Pol Returns a list, matrix, or vector in which each element of the argument is displayed in polar form. PolarC † mode screen Polar complex: - PolarGC † graph format screen PolarC Sets polar complex number mode (magnitudeangle).

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337 Chapter 20: A to Z Function and Instruction Reference poly †-v poly coefficientList Returns a list containing the real and complex roots of a polynomial whose coefficients are given in coefficientList. Find the roots of 2x 3N8x 2N14x+20=0: poly {2,L8,L14,20} b {5 L2 1} a nx n + ... + a 2x 2 + a 1x 1 + a 0x 0 = 0 Power: ^ @ number^power or (expression)^(expression) Returns number raised to power. The arguments can be real or complex.

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338 Chapter 20: A to Z Function and Instruction Reference 10^list 10^{1.5,L2} Returns a list in which each element is 10 raised to the power specified by the corresponding element in list. prod LIST OPS menu MATH MISC menu Prompt ‡ program editor I/O menu (Promp shows on menu) PtChg( † GRAPH DRAW menu PtOff( † GRAPH DRAW menu PtOn( † GRAPH DRAW menu prod list Returns the product of all real or complex elements in list. Prompt variableA[,variableB, ...

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Chapter 20: A to Z Function and Instruction Reference PwrR STAT CALC menu Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1. PwrR xList,yList,frequencyList,equationVariable Fits a power regression model (y=ax b) to positive real data pairs in xList and yList, using frequencies in frequencyList. The regression equation is stored to equationVariable, which must be a built-in equation variable such as y1, r1, and xt1.

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340 Chapter 20: A to Z Function and Instruction Reference PwrR Uses xStat, yStat, and fStat, and stores the regression equation to RegEq only. PxChg( GRAPH DRAW menu PxOff( GRAPH DRAW menu PxOn( GRAPH DRAW menu PxTest( GRAPH DRAW menu rAdd( MATRX OPS menu PxChg(row,column) PxChg(10,95) Reverses the pixel at (row, column), where 0 row 62 and 0 column 126. PxOff(row,column) PxOff(10,95) Erases the pixel at (row, column), where 0 row 62 and 0 column 126.

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Chapter 20: A to Z Function and Instruction Reference Radian Radian †-m Radian entry: Sets radian angle mode. r number r or (expression) r Designates a real number or expression as radians, regardless of the angle mode setting. MATH ANGLE menu list r 341 In Radian angle mode: sin (p/2) b sin 90 b 1 .893996663601 In Degree angle mode: cos (p/2) b cos (p/2) r b .999624216859 0 cos {p/2,p}r b {0 L1} Designates each element in a real list as radians.

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342 Chapter 20: A to Z Function and Instruction Reference randInt( MATH PROB menu (randIn shows on menu) randInt(lower,upper,#ofTrials) Returns a list of random integers bound by the specified integers, lower integer upper. The #ofTrials is an integer ‚ 1 that specifies the number of integers returned in the list. 1¶rand:randInt(1,10,3) b {8 9 3} A seed value stored to rand also affects randInt(. randInt(lower,upper) 0¶rand:randInt(1,10) b 10 Returns a single random integer.

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Chapter 20: A to Z Function and Instruction Reference RcGDB † GRAPH menu RcPic † GRAPH menu real CPLX menu 343 RcGDB graphDataBaseName Restores all settings stored in graphDataBaseName. For a list of settings, refer to StGDB on page 361. RcPic pictureName Displays the current graph and adds the picture stored in pictureName. real (complexNumber) Returns the real part of complexNumber. real (real,imaginary) returns real. real (magnitude±angle) returns magnitude ¹cos (angle).

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344 Chapter 20: A to Z Function and Instruction Reference complexList 4Rec complexMatrix 4Rec complexVector 4Rec Returns a list, matrix, or vector in which each element of the argument is displayed in rectangular form. RectC † mode screen RectGC † graph format screen RectV † mode screen ref MATRX OPS menu RectC Sets rectangular complex number mode (real,imaginary). In PolarC complex number mode: [(3±p/6),‡L2] b [(3±.523598775598) (… Ans4Rec b [(2.59807621135,1.

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Chapter 20: A to Z Function and Instruction Reference Repeat ‡ program editor CTL menu (Repea shows on menu) Return :Repeat condition :commands-to-repeat :End :commands Executes commands-to-repeat until condition is true. Return In a subroutine, exits the subroutine and returns to the calling program. In the main program, stops execution and returns to the home screen.

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346 Chapter 20: A to Z Function and Instruction Reference rnorm MATRX MATH menu rnorm matrix Returns the row norm of a real or complex matrix. For each row, rnorm sums the absolute values (magnitudes of complex elements) of all elements on that row. The returned value is the largest of the sums. [[L5,6,L7][3,3,9][9,L9,L7]] [[L5 6 L7] ¶MAT b [3 3 9 ] [9 L9 L7]] rnorm MAT b 25 rnorm [15,L18,7] b rnorm vector 18 Returns the largest absolute value (or magnitude) in a real or complex vector.

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Chapter 20: A to Z Function and Instruction Reference rotL BASE BIT menu rotL integer Returns a real integer with bits rotated one to the left. Internally, integer is represented as a 16-bit binary number. When the bits are rotated left, the leftmost bit rotates to the rightmost bit. 347 In Bin number base mode: rotL 0000111100001111 b 1111000011110Ü Leading zeros are not displayed. rotL 0000111100001111Ü = 0001111000011110Ü rotL is not valid in Dec number base mode.

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348 Chapter 20: A to Z Function and Instruction Reference round( MATH NUM menu round(number,#ofDecimals) round(number) Returns a real or complex number rounded to the specified #ofDecimals (0 to 11). If #ofDecimals is omitted, number is rounded to 12 decimal places. round(list,#ofDecimals) round(matrix,#ofDecimals) round(vector,#ofDecimals) Returns a list, matrix, or vector in which each element is the rounded value of the corresponding element in the argument. #ofDecimals is optional.

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Chapter 20: A to Z Function and Instruction Reference Scatter † STAT DRAW menu (Scatte shows on menu) Scatter xList,yList Draws a scatter plot on the current graph, using the real data pairs in xList and yList. Scatter 349 {L9,L6,L4,L1,2,5,7,10}¶XL b {L9 L6 L4 L1 2 5 7 1… {L7,L6,L2,1,3,6,7,9}¶YL b {L7 L6 L2 1 3 6 7 9} ZStd:Scatter XL,YL b Uses the data in built-in variables xStat and yStat. These variables must contain valid data of the same dimension; otherwise, an error occurs.

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350 Chapter 20: A to Z Function and Instruction Reference Select( LIST OPS menu Select(xListName,yListName) If a scatter plot or xyline plot is currently selected and plotted on the graph screen, you can select a subset (range) of those data points. The selected data points are stored to xListName and yListName.

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Chapter 20: A to Z Function and Instruction Reference seq( seq(expression,variable,begin,end,step) seq(expression,variable,begin,end) Uses a step of 1. SeqG † graph format screen SetLEdit LIST OPS menu (SetLE shows on menu) seq(x 2,x,1,8,2) b {1 9 25 49} Returns a list containing a sequence of numbers created by evaluating expression from variable = begin to variable = end in increments of step.

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352 Chapter 20: A to Z Function and Instruction Reference Shade( GRAPH DRAW menu Shade(lowerFunc,upperFunc,xLeft,xRight,pattern,patternRes) Draws lowerFunc and upperFunc in terms of x on the current graph and shades the area bounded by lowerFunc, upperFunc, xLeft, and xRight. The shading style is determined by pattern (1 through 4) and patternRes (1 through 8).

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Chapter 20: A to Z Function and Instruction Reference shftL BASE BIT menu shftL integer 353 In Bin number base mode: Returns a real integer with bits shifted one to the left. Internally, integer is represented as a 16-bit binary number. When the bits are shifted left, the leftmost bit is dropped and 0 is used as the rightmost bit. shftL 0000111100001111 b 1111000011110Ü Leading zeros are not displayed. shftL 0000111100001111Ü = 0001111000011110Ü 0 shftL is not valid in Dec number base mode.

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354 Chapter 20: A to Z Function and Instruction Reference ShwSt CATALOG sign MATH NUM menu ShwSt Displays the results of the most recent stat calculation. sign number or sign (expression) Returns L1 if the argument is < 0, 1 if it is > 0, or 0 if it is = 0. The argument must be real. sign list Returns a list in which each element is L1, 1, or 0 to indicate the sign of the corresponding element in list. SimulG † graph format screen simult( †-u sign L3.2 b sign (6+2N8) b L1 0 sign {L3.2,16.

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Chapter 20: A to Z Function and Instruction Reference sin = sin angle or sin (expression) sin p/2 b sin (p/2) b sin 45¡ b An angle is interpreted as degrees or radians according to the current angle mode. In any angle mode, you can designate an angle as degrees or radians by using the ¡ or r designator, respectively, from the MATH ANGLE menu. sin 45 b sin (p/2) r b Returns a list in which each element is the sine of the corresponding element in list.

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356 Chapter 20: A to Z Function and Instruction Reference sinh MATH HYP menu sinh number or sinh (expression) sinh list Returns a list in which each element is the hyperbolic sine of the corresponding element in list. sinhL1 MATH HYP menu sinh 1.2 b 1.50946135541 Returns the hyperbolic sine of number or expression, which can be real or complex. sinh L1 number or sinh L1(expression) sinh {0,1.2} b {0 1.50946135541} sinhL1 1 b .

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Chapter 20: A to Z Function and Instruction Reference SinR STAT CALC menu Built-in equation variables such as y1, r1, and xt1 are case-sensitive. Do not use Y1, R1, and XT1. If you specify a period, the TI-86 may find a solution more quickly or it may find a solution when one would not have been found otherwise.

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358 Chapter 20: A to Z Function and Instruction Reference SinR [iterations,] equationVariable Uses xStat and yStat for xList and yList, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. The regression equation is stored to equationVariable and RegEq. SinR [iterations] Uses xStat and yStat, and stores the regression equation to RegEq only.

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Chapter 20: A to Z Function and Instruction Reference sortA SortA list Returns a list in which the real or complex elements of list are sorted in ascending order. LIST OPS menu sortD SortD list Returns a list in which the real or complex elements of list are sorted in descending order.

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360 Chapter 20: A to Z Function and Instruction Reference Sorty Uses built-in variables xStat and yStat for xListName and yListName, respectively. These built-in variables must contain valid data of the same dimension; otherwise, an error occurs. 4Sph vector 4Sph VECTR OPS menu SphereV †-m Square: 2 I Displays a 2- or 3-element vector as spherical coordinates in [r q 0] or [r q f] form, respectively, even if the display mode is not set for spherical (SphereV).

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Chapter 20: A to Z Function and Instruction Reference ‡list In RectC complex number mode: Returns a list in which element is the square root of the corresponding element in list. St4Eq( STRNG menu St4Eq(stringVariable,equationVariable) Converts stringVariable to a number, expression, or equation, and stores it in equationVariable. To convert the string and retain the same variable name, you can set equationVariable equal to stringVariable.

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362 Chapter 20: A to Z Function and Instruction Reference Stop ‡ program editor CTL menu Stop Program segment: Ends program execution and returns to the home screen. Use N==999, not N=999. Store to variable: ¶ X number ¶ variable or (expression) ¶ variable string ¶ variable list ¶ variable vector ¶ variable matrix ¶ variable Stores the specified argument to variable.

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Chapter 20: A to Z Function and Instruction Reference String entry: " STRNG menu ‡ program editor I/O menu sub( STRNG menu Subtraction: N T "string" Defines a string. When you display a string, it is leftjustified on the screen. Strings are interpreted as text characters, not numbers. For example, you cannot perform a calculation with strings such as "4" or "A¹8". To convert between string variables and equation variables, use Eq4St( and St4Eq( as described on pages 290 and 361, respectively.

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364 Chapter 20: A to Z Function and Instruction Reference listA N listB matrixA N matrixB vectorA N vectorB Returns a list, matrix, or vector that is the result of each element in the second argument subtracted from the corresponding element in the first argument. The two real or complex arguments must have the same dimension. sum MATH MISC menu sum list Returns the sum of all real or complex elements in list.

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Chapter 20: A to Z Function and Instruction Reference tan L1 -} tanL1 number or tanL1 (expression) Returns the arctangent of number or expression, which can be real or complex. In Radian angle mode: tanL1 .5 b .463647609001 In Degree angle mode: tanL1 1 b tanL1 list Returns a list in which each element is the arctangent of the corresponding element in list.

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366 Chapter 20: A to Z Function and Instruction Reference TanLn( GRAPH DRAW menu Text( † GRAPH DRAW menu TanLn(expression,xValue) Draws expression on the current graph and then draws a tangent line at xValue. Text(row,column,string) Writes a text string on the current graph beginning at pixel (row,column), where 0 row 57 and 0 column 123. Text at the bottom of the graph may be covered by a displayed menu. To remove the menu, press :.

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Chapter 20: A to Z Function and Instruction Reference Trace Trace † GRAPH menu Transpose: 367 T MATRX MATH menu Displays the current graph and lets the user trace a function. From a program, press b to stop tracing and continue with the program. [[1,2][3,4]]¶MATA b matrixT Returns a transposed real or complex matrix in which element row,column is swapped with element column,row of matrix.

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368 Chapter 20: A to Z Function and Instruction Reference TwoVar STAT CALC menu (TwoVa shows on menu) TwoVar xList,yList,frequencyList Performs two-variable statistical analysis on the real data pairs in xList and yList, using the frequencies in frequencyList. {0,1,2,3,4,5,6}¶L1 b {0 1 2 3 4 5 6} {0,1,2,3,4,5,6}¶L2 b {0 1 2 3 4 5 6} TwoVar L1,L2 b Values used for xList, yList, and frequencyList are stored automatically to the built-in variables xStat, yStat, and fStat, respectively.

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Chapter 20: A to Z Function and Instruction Reference vc4li LIST OPS menu vc4li vector Returns a real or complex vector converted to a list. VECTR OPS menu Vector entry: [ ] - „ and - … Vert † GRAPH DRAW menu While ‡ program editor CTL menu [element1,element2, ... ] Defines a vector in which each element is a real or complex number or variable. Vert xValue Draws a vertical line on the current graph at xValue.

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370 Chapter 20: A to Z Function and Instruction Reference xor BASE BOOL menu integerA xor integerB Compares two real integers bit by bit. Internally, both integers are converted to binary. When corresponding bits are compared, the result is 1 if either bit (but not both) is 1; the result is 0 if both bits are 0 or both bits are 1. The returned value is the sum of the bit results. For example, 78 xor 23 = 89.

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Chapter 20: A to Z Function and Instruction Reference ZData † GRAPH ZOOM menu ZData Adjusts the window variable values based on the currently defined statistical plots so that all stat data points will be plotted, and then updates the graph screen. 371 In Func graphing mode: {1,2,3,4}¶XL b {2,3,4,5}¶YL b Plot1(1,XL,YL) b ZStd b ZData b 20ATOZ.

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372 Chapter 20: A to Z Function and Instruction Reference ZDecm † GRAPH ZOOM menu ZDecm In Func graphing mode: Sets the window variable values such that @x=@y=.1, and then updates the graph screen with the origin centered on the screen. xMin=L6.3 xMax=6.3 xScl=1 y1=x sin x b ZStd b Done yMin=L3.1 yMax=3.1 yScl=1 One of the benefits of ZDecm is that you can trace in .1 increments. If you trace the graph above, x values start at 0 and increment by .1587301587.

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Chapter 20: A to Z Function and Instruction Reference ZFit ZFit In Func graphing mode: Recalculates yMin and yMax to include the minimum and maximum y values of the selected functions between the current xMin and xMax, and then updates the graph screen. † GRAPH ZOOM menu 373 y1=x 2N20 b ZStd b Done This does not affect xMin and xMax. ZFit b ZIn † GRAPH ZOOM menu ZIn In Func graphing mode: Zooms in on the part of the graph centered around the current cursor location.

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374 Chapter 20: A to Z Function and Instruction Reference ZInt † GRAPH ZOOM menu ZInt In Func graphing mode: Sets the window variable values so that each pixel is an integer in all directions (@x=@y=1), sets xScl=yScl=10, and then updates the graph screen. y1=der1(x 2N20,x) b ZStd b Done The current cursor location becomes the center of the new graph. One of the benefits of ZInt is that you can trace in whole number increments. If you trace the graph above, x values start at 0 and increment by .

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Chapter 20: A to Z Function and Instruction Reference ZOut † GRAPH ZOOM menu ZOut In Func graphing mode: Zooms out to display more of the graph, centered around the current cursor location. y1=x sin x b ZStd b Zoom factors are set by the values of built-in variables xFact and yFact; the default is 4 for both factors. ZOut b ZPrev † GRAPH ZOOM menu 375 ZPrev Replots the graph using the window variable values of the graph that was displayed before you executed the previous ZOOM instruction.

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376 Chapter 20: A to Z Function and Instruction Reference ZRcl ZRcl Sets the window variables to values stored previously in the user-defined zoom-window variables, and then updates the graph screen. † GRAPH ZOOM menu To set user-defined zoom-window variables, either: • Press 6 ( / / / & (ZSTO) to store the current graph’s window variables. – or – • Store the applicable values to the zoom-window variables, whose names begin with z followed by the regular window variable name.

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Chapter 20: A to Z Function and Instruction Reference ZStd † GRAPH ZOOM menu ZStd 377 In Func graphing mode: Sets the window variables to the standard default values, and then updates the graph screen. y1=x sin x b ZStd b Func graphing mode: xMin=L10 xMax=10 xScl=1 yMin=L10 yMax=10 yScl=1 Pol graphing mode: qMin=0 xMin=L10 yMin=L10 qMax=6.28318530718 (2p) xMax=10 yMax=10 qStep=.130899693899… (p/24) xScl=1 yScl=1 Param graphing mode: tMin=0 xMin=L10 yMin=L10 tMax=6.

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378 Chapter 20: A to Z Function and Instruction Reference ZTrig † GRAPH ZOOM menu ZTrig In Func graphing mode: Sets the window variables to preset values appropriate for plotting trig functions in Radian angle mode (@x=p/24), and then updates the graph screen. xMin=L8.24668071567 xMax=8.24668071567 xScl=1.5707963267949 (p/2) y1=sin x b ZStd b yMin=L4 yMax=4 yScl=1 ZTrig b 20ATOZ.

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379 Appendix A Appendix TI-86 TI-86 Menu Map.............................................................. 380 Handling a Difficulty ........................................................ 392 Error Conditions............................................................... 393 Equation Operating System (EOSé) ................................ 397 TOL (The Tolerance Editor) - ™ )................... 398 Computational Accuracy..................................................

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380 Appendix TI-86 Menu Map This section presents the TI-86 menus as they appear on the TI-86 keyboard, starting at the top. If a menu has items that display other menus, the other menus follow directly below the main menu. In the program editor, the appearance of some menus changes slightly. The menu map omits user-created-name menus, such as the LIST NAMES and CONS USER menus. -o LINK Menu The link menus are not available in the program editor.

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Appendix GRAPH Menu r(q)= WIND GRAPH Menu E(t)= WIND GRAPH Menu Q'(t)= WIND 6 in Pol graphing mode ZOOM TRACE GRAPH 4 WIND y WIND r WIND xt MATH DRAW FORMT STGDB RCGDB 4 AXES GRAPH 4 FORMT DRAW ZOOM TRACE EXPLR 4 STPIC RCPIC EVAL STPIC RCPIC EVAL STGDB RCGDB STPIC RCPIC 6 & in Func graphing mode ZOOM TRACE GRAPH INSf DELf SELCT 4 ALL+ ALLN STYLE 6 & in Pol graphing mode ZOOM TRACE GRAPH INSf DELf SELCT 4 Equation Editor Menu E(t)= t EVAL 6 in DifEq graphing mode INITC Equation Edito

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382 Appendix GRAPH VARS (Graph Variables) Menu y(x)= y WIND x ZOOM TRACE GRAPH xt yt t 4 r GRAPH WIND (Window Variables) Menu y(x)= xMin WIND xMax ZOOM TRACE GRAPH xScl yMin yMax 4 GRAPH ZOOM Menu To display the GRAPH ZOOM menu in DifEq mode, press 6 / (.

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Appendix 383 6 / & in Param graphing mode GRAPH MATH Menu MATH DRAW FORMT STGDB RCGDB DIST dyàdx dyàdt dxàdt ARC 4 TANLN 6/' GRAPH DRAW Menu DrInv is available only in Func graphing mode. MATH DRAW FORMT STGDB RCGDB Shade LINE VERT HORIZ CIRCL 4 DrawF PEN PTON PTOFF PTCHG 4 CLDRW PxOn DrEqu is available only in DifEq graphing mode.

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384 Appendix 8 PRGM Menu NAMES EDIT 8 ' program name b Program Editor Menu PAGE$ PAGE# IàO CTL 4 INSc IàO Disp CTL DispG INSc DispT IàO Else CTL For POLY ENTRY Menu ClTbl Get Send getKy ClLCD INSc End 4 While Repea Menu Lbl - v (integer ‚ 2 & 30) b CLRq SOLVE CUSTOM Menu Use the CUSTOM menu to create your own menu (Chapter 2).

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Appendix CALC Menu evalF nDer MATRX Menu NAMES EDIT -† der1 der2 fnInt 4 MATH norm OPS MATH ident MATRX CPLX Menu NAMES EDIT conj real VECTR Menu NAMES EDIT MATH imag INSr VECTR MATH Menu NAMES EDIT cross unitV MATH norm arc DELr INSc - ‰ ' matrixName b DELc 4REAL -‰( OPS eigVl CPLX eigVc 4 OPS ref CPLX rref rnorm cnorm LU cond -‰) 4 aug rSwap rAdd multR mRAdd 4 randM -‰* OPS abs CPLX angle -Š MATH fMax Matrix Editor Menu CPLX MATRX OPS (Operations) Menu NAMES EDIT d

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386 Appendix VECTR OPS (Operations) Menu -Š) NAMES EDIT dim Fill 4 MATH 4Pol VECTR CPLX Menu NAMES EDIT conj real MATH imag OPS 4Cyl CPLX 4Sph real MATH Menu NUM imag abs -‹ angle 4 4Rec MISC 4 INTER PROB ANGLE iPart fPart PROB ANGLE nPr nCr MATH ANGLE Menu NUM ¡ 4Pol -Œ PROB ANGLE HYP HYP int -Œ& MISC abs 4 HYP rand MISC randln sign min max mod -Œ' MATH PROB (Probability) Menu NUM ! vc4li CPLX angle MATH NUM (Number) Menu NUM round li4vc -Š* OPS abs CPLX (Compl

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387 Appendix MATH HYP (Hyperbolic) Menu NUM sinh PROB ANGLE HYP cosh tanh sinh L1 MISC cosh L1 -Œ) 4 tanh L1 -Œ* MATH MISC (Miscellaneous) Menu NUM sum PROB ANGLE prod seq HYP lcm CONS (Constants) Menu BLTIN EDIT MISC gcd 4 4Frac EDIT k USER Cc ec Rc VOL TIME VOL m CONV AREA Menu LNGTH AREA ft 2 m2 eval VOL mi2 TIME in 4 Gc Mp Mn -‘& g Me 4 TEMP ft 4 H0 h c u Ang fermi rod fath MASS FORCE PRESS ENRGY POWER 4 SPEED -’& 4 yd km mile nmile in2 cm2 yd2 ha lt-

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388 Appendix -’( CONV VOL (Volume) Menu LNGTH AREA liter gal VOL qt TIME pt TEMP oz 4 CONV TIME Menu -’) LNGTH AREA sec mn TIME day VOL hr TEMP yr 4 CONV TEMP (Temperature) Menu LNGTH AREA ¡C ¡F VOL ¡K CONV MASS Menu TIME ¡R in 3 ft 3 m3 week ms µs ns cup 4 -’* TEMP -’/& MASS FORCE PRESS ENRGY POWER gm kg lb amu slug 4 CONV FORCE Menu cm 3 ton mton -’/' MASS FORCE PRESS ENRGY POWER N dyne tonf kgf lbf CONV PRESS (Pressure) Menu -’/( MASS FORCE PRESS ENRGY POWER atm bar

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Appendix -’/* CONV POWER Menu STRNG Menu " sub LIST Menu { } } -” NAMES EDIT NAMES " } NAMES EDIT sortA sortD min TYPE CONV BOOL BASE TYPE Menu Õ-Ú Ü TYPE ß knot -”( LIST NAMES Menu OPS { fStat } NAMES EDIT xStat yStat OPS -”) The (Number) BASE Menu Õ-Ú miàhr kmàhr Eq4St St4Eq 4 OPS OPS max 4 sum -— BIT -—' CONV BOOL Ý Þ 4REAL -”* LIST OPS (Operations) Menu { dimL SPEED ftàs màs -“ lngth List Editor Menu { -’//& CONV SPEED Menu MASS FORCE PRESS ENRGY POWER hp W ftlbà

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390 Appendix -—) BASE BOOL (Boolean) Menu Õ-Ú and TYPE or CONV BOOL xor not TEST (Relational) Menu == < MEM (Memory) Menu RAM DELET RESET TOL ‚ REAL CPLX MEM RESET Menu RAM ALL DELET RESET MEM DFLTS LIST STAT (Statistics) Menu When you press - š ', the list editor and list menu are displayed.

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391 Appendix STAT PLOT Menu PLOT1 PLOT2 PLOT3 Plot Mark Menu PLOT1 PLOT2 PLOT3 › + ¦ STAT DRAW Menu CALC HIST -š( PlOn PLOT1 PLOT2 PLOT3 SCAT xyLINE MBOX PlOn PlOff BOX PlOff -š) EDIT PLOT DRAW VARS SCAT xyLINE BOX MBOX EDIT sx PlOn HIST - š ( ( &, ', or ( ) # ( &, ', or ( ) # # # 4 DRREG CLDRW DrawF STPIC RCPIC STAT VARS (Statistical Result Variables) Menu CALC v - š ( ( &, ', or ( ) # Plot Type Menu PlOff PLOT DRAW VARS Sx w sy CHAR (Character) Menu -š* 4 Sy Gx Gx 2 Gy Gy 2 4

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392 Appendix CHAR GREEK Menu All CHAR GREEK menu items are valid variable-name characters, including the first letter. p (- ~) is not valid as a character; p is a constant on the TI-86. MISC GREEK INTL a b g -Ÿ' @ d 4 H q l m r 4 G s ι f J CHAR INTL (International Letter Symbols) Menu -Ÿ( MISC GREEK INTL ´ ` ^ ¨ Handling a Difficulty If you cannot see anything on the screen, you may need to adjust the contrast (Chapter 1).

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Appendix 393 Error Conditions When the TI-86 detects an error, it displays an error message ERROR # type and the error menu. Chapter 1 describes how to correct an error. This section describes possible causes for the errors and examples. To find the proper arguments for a function or instruction, as well as restrictions on those arguments, refer to Chapter 20: A to Z Function and Instruction Reference. Errors 1 through 5 do not occur during graphing. The TI-86 allows for undefined values on a graph.

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394 Appendix 08 NUMBER BASE ♦ ♦ 09 MODE You attempted to store to a window variable of a noncurrent graphing mode. or to use an instruction valid only in noncurrent graphing modes; for example, using DrInv in Pol, Param, or DifEq graphing mode. 10 DATA TYPE ♦ ♦ ♦ ♦ ♦ You entered an invalid digit in a number base, such as 7Ü. You attempted an operation that is not allowed in Bin, Oct , or Hex base mode. You entered a value or variable that is an inappropriate data type.

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Appendix 18 ILLEGAL NEST You attempted to use an invalid function in an argument for seq( or a CALC function; for example, der1(der1(x^3,x),x)). 19 BOUND You defined an upper bound that is less than the specified lower bound or a lower bound that is greater than the specified upper bound. 20 GRAPH WINDOW ♦ ♦ One or more window variable values is incompatible with the others for defining the graph screen; for example, you defined xMax < xMin.

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396 Appendix 30 DIF EQ SETUP In DifEq graphing mode, equations in the equation editor must be from Q'1 to Q'9 and each must have an associated initial condition from Q[1 to Q[9. 31 DIF EQ MATH The step size used by the fitting algorithm has become too small; check the equations and initial values; try a larger value for the window variable difTol; try changing tMin or tMax to examine a different region of the solution. 32 POLY All coefficients are 0.

#### Page 409

Appendix 397 Equation Operating System (EOS™) The Equation Operating System (EOS) governs the order of evaluation on the TI-86. Calculations within parentheses are evaluated first, and then EOS evaluates functions within an expression in this order: Within a priority level, EOS evaluates functions from left to right. Multi-argument functions, such as nDeriv(A2,A,6), are evaluated as they are encountered. TI-86 implied multiplication rules differ from those of the TI-85.

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398 Appendix You can omit the close parenthesis ( ) ) at the end of an expression. All open parenthetical elements are closed automatically at the end of an expression. This is also true for open parenthetical elements that precede the store or display-conversion instructions. Open parentheses after list names, matrix names, or equation function names are not interpreted as implied multiplication.

#### Page 411

Appendix 399 Computational Accuracy To maximize accuracy, the TI-86 carries more digits internally than it displays. Values are stored in memory using up to 14 digits with a 3-digit exponent. ♦ You can store values up to 12 digits long to most window variables. To xScl, yScl, tStep, and qStep, you can store values up to 14 digits long. ♦ When a value is displayed, the displayed value is rounded as specified by the mode setting (Chapter 1), with a maximum of 12 digits and a 3-digit exponent.

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400 Appendix Support and Service Information Product Support Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands For general questions, contact Texas Instruments Customer Support: phone: e-mail: 1.800.TI.CARES (1.800.842.2737) ti-cares@ti.com For technical questions, call the Programming Assistance Group of Customer Support: phone: 1.972.917.8324 Customers outside the U.S.

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Appendix 401 Product Service Customers in the U.S. and Canada Only Always contact Texas Instruments Customer Support before returning a product for service. Customers outside the U.S. and Canada Refer to the leaflet enclosed with this product or contact your local Texas Instruments retailer/distributor. Other TI Products and Services Visit the TI Calculator home page on the World Wide Web. education.ti.com 99APPX.

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402 Appendix Warranty Information Customers in the U.S. and Canada Only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage.

#### Page 415

Appendix 403 Australia & New Zealand Customers only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction.

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404 Appendix All Customers outside the U.S. and Canada For information about the length and terms of the warranty, refer to your package and/or to the warranty statement enclosed with this product, or contact your local Texas Instruments retailer/distributor. 99APPX.

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Index " (string), 216, 227 " (List Editor menu), 156 ! (factorial), 294 ¶, 362 ‚ (greater than or equal to), 56, 301 (less than or equal to), 55, 312 ƒ (not equal to), 56, 326 p (pi), 48 ‡ (square root), 360 ˆ (square root) key, 48 v (statistical result variable), 193 w (statistical result variable), 193 L1 (inverse), 48, 309 ¶dim, 184, 281 ¶dimL, 282 ‰f(x) (function numerical integral), 96, 98 @Tbl (table step), 113 sx (statistical result variable), 193 Gx 2 (statistical result variable), 193 sy (statis

#### Page 418

406 Index BASE Õ-Ú (Hexadecimal) menu, 67 BASE BIT menu, 69 BASE BOOL (Boolean) menu, 68 BASE CONV (Conversion) menu, 68 BASE menu, 66 BASE TYPE menu, 67 base type symbol, 67 batteries, 2, 16-18 battery compartment, 16 BCKUP (memory backup), 237 Bin (binary), 35, 272 4Bin (to binary), 68, 272 binary integer, 271 binary number base, 35, 66 Boolean operators, 68, 268, 325, 328, 370 bound={L1E99,1E99}, 204 bounds, 204 BOX (GRAPH ZOOM menu), 14, 92, 93 Box (stat plot), 272 BOX (ZOOM menu), 208 break (program)

#### Page 419

Index contrast adjusting, 2, 18 CONV (Conversions) menu, 62 CONV AREA menu, 63 CONV ENRGY (Energy) menu, 64 CONV FORCE menu, 64 CONV LNGTH (Length) menu, 63 CONV MASS menu, 64 CONV POWER menu, 64 CONV PRESS (Pressure) menu, 64 CONV SPEED menu, 64 CONV TEMP (Temperature) menu, 8, 63 CONV TIME menu, 63 CONV VOL (Volume) menu, 63 conversions 4Bin, 272 4Dec, 279 4DMS, 51, 285 4Frac, 52, 298 4Hex, 303 4Oct, 327 4Pol, 336 4REAL, 156 conversions (continued) 4Rec, 343 4Sph, 360 Eq4St, 227 li4vc, 160 St4Eq(, 227, 3

#### Page 420

408 Index DELf (delete function), 77 DELi (delete element), 170 DELr (delete row), 179 Deltalst( (delta list), 160, 279 DelVar( (delete variable), 219, 280 der1( (first derivative), 54, 280 der2( (second derivative), 54, 280 derivatives calculating, 7 det (determinant), 183, 281 DFLTS (defaults), 232 DifEq (differential equation mode), 35, 74, 239, 281 differential equation editor, 134 differential equation graphs, 74 displaying, 138 drawing, 145 mode, 35 differential equations changing to first order, 14

#### Page 421

Index element matrix, 181 ellipsis at end of line, 19 in matrix row, 179 Else, 218, 306 e-mail address (TI Customer Support), 392 End, 218, 290, 297, 306 Eng (engineering notation), 34, 20, 290 entry executing, 19 storing to, 29 entry cursor, 18, 22, 23 [ENTRY] key, 19 ENTRY Storage Area, 28, 29 EOS.

#### Page 422

410 Index FMAX (function maximum), 96, 97 fMax( (function maximum), 54, 296 FMIN (function minimum), 96, 97 fMin( (function minimum), 54, 296 fnInt( (function integral), 54, 296 FnOff (functions off), 296 FnOn (functions on), 297 For(, 218, 297 Form(, 161, 298 FORMT (graph format), 76 formulas attaching, 163 attaching to list name, 162 detaching, 166 fPart (fractional part), 49, 176, 186, 298 4Frac (to fractions), 52, 298 fraction, 3, 19 free-moving cursor, 84, 144 parametric graphs, 128 polar graphs, 119

#### Page 423

Index graph tools (continued) in parametric graphs, 128 in polar graphs, 119 graph zoom defining custom, 93 defining screen, 92 setting zoom factors, 93 Smart Graph, 94 zooming in, 92, 93 zooming out, 92, 93 GRAPH ZOOM menu, 75, 91, 147 graphing accuracy, 89 greater than (>), 300 greater than or equal to (‚), 301 grid points, 84 GridOff, 84, 301 GridOn, 84, 302 GrStl( (graph style), 220, 302 Guess, 204 in interactive solver editor, 205 H ß (hexadecimal), 302 Hex (hexadecimal), 35, 302 4Hex (to hexadecima

#### Page 424

412 Index last answer, 28, 29 storing to variable, 3 last entry, 26, 28 Lbl (label), 219, 224, 311 lcm( (least common multiple), 52, 311 LCust( (load custom menu), 220, 311 leftNrt, 202 length of segment of curve, 54 less than (<), 312 less than or equal to (), 312 LgstR (logistic regression), 190, 193, 313 li4vc (list to vector), 160, 174, 316 LINE, 104, 105 Line(, 314 Lines drawing, 107 LINK menu, 236 LINK SEND menu, 236 LINK SEND85 menu, 239 linking instructions, 235 linking options, 234 LinR (linear

#### Page 425

Index MATRX MATH menu, 183 MATRX NAMES menu, 178 MATRX OPS (Operations) menu, 184 max(, 49, 160, 319 maximum characters, 22 maxX, 193 maxY, 193 MBox, 319 Med (median), 193 MEM (clear memory), 232 MEM (Memory) menu, 29, 230 MEM RESET menu, 232 MEM DELET (Delete) menu, 231 MEM FREE (available memory), 230 memory, 16, 17, 22, 28, 29, 223 available, 230 deleting items, 231 resetting, 3, 232 memory backup initiating, 237 overwrite warning, 237 menus displaying, 31 exiting, 6 menus (continued) in editors, 33 key

#### Page 426

414 Index P P2Reg (quadratic regression), 190, 330 P3Reg (cubic regression), 190, 331 P4Reg (quartic regression), 190, 332 panning, 90 Par, 74 Param (parametric mode), 35, 239, 333 parametric equation deleting, 127 graphing, 126 selecting and deselecting, 127 parametric graphs, 74 default graph style, 126 defining, 125 displaying, 128 drawing, 130 equation editor, 126 free-moving cursor, 128 graph format, 128 graph tools, 128 mode, 35, 126 tracing, 128 window variables, 127 Zoom, 129 parentheses, 20, 25,

#### Page 427

Index reusing, 28 PRGM (program names), 43 PRGM CTL menu, 218 PRGM I/O (Input/Output) menu, 215 PRGM menu, 214 prod (product), 52, 160, 338 program editor, 214 menus and screens, 215, 220 program flow, 56 programming assembly language, 225 calling a program, 224 copying a program, 225 creating programs, 214 defined, 214 deleting a program, 223 downloading assembly programs, 225 editing a program, 223 entering a command line, 220 getting started, 214 interrupting program, 222 running program, 221 using varia

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416 Index RECV (LINK SND85 menu), 240 redefining user-created constants, 60 ref (row echelon form), 184, 344 regression models, 191 relational functions, 55, 56 RENAM (rename), 241 Repeat (PRGM CTL menu), 218, 345 replacing batteries, 16 resetting memory, 232 result, 20, 24 result of last expression, 26 Return (PRGM CTL menu), 219, 345 RK (Runge-Kutta) method, 133, 345 rnorm (row norm), 183, 346 ROOT, 96, 97 x‡, 346 root-finder, 211 RotL (rotate left), 69, 347 RotR (rotate right), 69, 347 round(, 49, 176,

#### Page 429

Index SphereV (spherical vector coordinate mode), 36, 360 square ( 2), 360 square root (‡), 7, 360 St4Eq( (string to equation), 227, 361 STAT (statistical result variables), 43 STAT CALC (Calculations) menu, 189 STAT menu, 188 Stat Plot changing on/off status, 81 setting up, 195 turning on and off, 195 STAT PLOT menu, 195 STAT PLOT status screen, 194 STAT VARS (Statistical Variables) menu, 192 statistical analysis, 188 results, 192 statistical data entering, 189 plotting, 194, 195 STGDB (store graph databas

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418 Index stopping and resuming, 91 tracing a function, 11 transmitting data, 234, 240 error conditions, 242 insufficient memory, 242 transmitting data (continued) repeating to several devices, 242 selecting variables, 238 window variables, 239 transpose ( T), 367 tStep, 127, 136, 138 turning off TI-86, 2, 17 turning on TI-86, 2, 17 TwoVa (TwoVar), 189, 368 U unevaluated expression storing, 9, 40 units of measure converting, 61 unit-to-unit cable, 234, 235 unitV (unit vector), 173, 368 unknown variable s

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Index xyline, 370 Y y variable, 77 y(x)=, 75 YICPT (y-intercept), 96, 100 yScl (scale), 81 yStat (y-variable list), 189 Z ZData, 371 ZDATA (GRAPH ZOOM menu), 92 ZDecm, 372 ZDECM (GRAPH ZOOM menu), 92 ZFACT (ZOOM FACTOR), 92, 208 ZFit, 129, 373 ZFIT (GRAPH ZOOM menu), 92 ZIn (zoom in), 373 ZIN (zoom in), 92, 208 ZInt, 374 ZINT (GRAPH ZOOM menu), 92 ZOOM, 14, 75, 88 custom, 93 parametric graphs, 129 polar graphs, 121 ZOOM operations, 147 zoom window variables storing and recalling, 95 ZOOMX (GRAPH ZOOM me