Manual / Guide · 1992
TI-85 Guidebook
The guidebook for the TI-85 of 1992, TI's graphing calculator for calculus and engineering (scanned).
Manual / Guide · 1992
The guidebook for the TI-85 of 1992, TI's graphing calculator for calculus and engineering (scanned).
| | TI-85 NX Guidebook ~T 8 Texas INSTRUMENTS TI-85 &% M1 M2 M3 M4 M5 CF | f F27 | FS), Fa) ( FS | | Quit MODE [ A | 2nd MORE ees [ n EXIT) [ 4 > ; alpha LINK x INS nie _ _| [ALPHA] [x-VAR| [DEL ) [vj SOLVER SIMULT — POLY CATALOG TOLER [GRAPH [ STAT | [PRGM | (cusTOM) [CLEAR] 10* A SIN ' B COS-' C TAN"! D 7 E LOG | | SIN | | cos | TAN | nw : eo oF x! Git HI 1 CACY [ LN | [ EE | (| f ) | [ = | : Vv K MATRX L VECTR M CPLX N MATH O aa oe 4 __P CONS QO CONV R STANG S LIST T | ee RCL = BASE U TEST V VARS W MEM X rm) j OFF CHAR Y Z ANS . ENTRY rr) 1 i °! 2) Lo Oo Poll. fe) al Wy TEXAS INSTRUMENTS TI-85 GRAPHING CALCULATOR Guidebook The staff of Texas Instruments developed by: Instructional Communications With Brad Christensen Don LaTorre contributions = Franklin Demana Pat Milheron by: Doug Feltz John Powers Linda Ferrio Dave Stone Pat Hatcher Bert K. Waits Dave Hertling C. B. Wilson Texas Instruments gratefully acknowledges the contributions of Bert K. Waits and Franklin Demana, who provided ideas for some of the applications and examples in this manual. 6 7 8 9 10 Copyright © 1993 by Texas Instruments Incorporated. TI-GRAPH LINK, Calculator-Based Laboratory, CBL, Calculator-Based Ranger, and CBR are trademarks of Texas Instruments Incoporated. IBM is a registered trademark of International Business Machines Corporation Macintosh is a registered trademark of Apple Computer, Inc. Important US FCC Information Concerning Radio Frequency Interference 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. Inno event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this equipment. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference with radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, you can try to correct the interference by one or more of the following measures: e — Reorient or relocate the receiving antenna. e Increase the separation between the equipment and receiver. ¢ Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. ¢ — Consult the dealer or an experienced radio/television technician for help. Caution: Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment. Table of Contents This guidebook describes how to use the TI-85 Graphing Calculator. Getting Started gives a quick overview of its features. The first chapter gives general instructions on operating the TI-85. Chapters 3 through 16 describe its interactive features. Chapter 17 provides applications that show how to use these features together. Getting Started Chapter 1: Operating the TI-85 Using this Guidebook Effectively .............. x Glossary .. 2.2.6... cece cee eee eee eee xii The Menu Keys . 2 The First Steps 2.0.0.0... ccc cece eee eee eee 3 Entering Expressions: Savings Account Example. . 4 Recalling and EditingaCalculation............. 6 Graphing on the TI-85 ...................2-5. 7 Entering an Equation: Illumination Example ..... 9 Entering an Equationin the SOLVER ............ 10 Solving fora Variable ...............0..00000- ll Additional Solutions with the SOLVER ...... -. 12 Changing the Viewing Rectangle.......... 13 Finding a Solution from a SOLVERGraph ... . 14 Defining FunctionstoGraph ............. ~ 165 Displaying the Graph ..... 16 Tracing along a Function 17 Finding a Maximum Graphically ............... 18 Graphing the Derivative. ...............-0-006: 19 Zooming InontheGraph ...................0. 20 Finding a Root Graphically.................04. 21 Other Features .......... 0. e eee e eee eee eee 22 Turning the TI-85 On and Off...............00. 1-2 Setting the Display Contrast ..............-.6. 1-3 The 2ndand ALPHA Keys ...........0000e secu 1-4 The Display ....... 0.0... ccc cece eee eee 1-6 The Equation Operating System ............... 1-8 Entering and Editing ......................0. 1-10 Expressions and Instructions................25 1-12 Last Answer ............. 0222s 1-13 Last Entry 2... ccc cece cece eee eee 1-14 Example: Convergence of aSeries.............. 1-15 The TI-85 Menus ..............----0---0---2: Displaying Menus ........... 00... 00 cee eee eee Selecting from Menus....... Moving around the TI-85 ... . The CATALOG .............. The CUSTOM Menu.......... Setting Modes ....... 00... cece cece eee eee eee Error Conditions. ............ 00. e cece cece Introduction iii Table of Contents (Continued) Chapter 2: Entering and Using Data Chapter 3: Math, Calculus, and Test Operations DataTypes ........ 0... c cece cee eee eens 2-2 Entering and Using Numbers. . see «. 2-3 Variables ...............04. 2-4 Storing Values to Variables... . 2-5 Using Variable Values ........ 2-6 The VARS (Variables) Menu ... . 2-7 Accessing Variable Names . . 2-8 Equation Variables ........ 2-9 Recalling Variable Contents . . . see .. 2-10 Variable Examples .............0000000- .. 2-11 Constants, Programs, Graphs, and Pictures... .... 2-12 Keyboard Math Functions ................2065 3-2 The MATH Menu... ...... cece cece eee nee e eae 3-3 The NUM(Number) Menu .............0..--0-5 3-4 The PROB (Probability) Menu...............:.. 3-6 The ANGLE Menu............ 00-0 cece eee eens 3-7 The HYP(Hyperbolic)Menu .................4. 3-8 The MISC (Miscellaneous) Menu ..............65 3-9 The INTER (Interpolation) Feature .............. 3-11 The CALC(Calculus)Menu .................55- 3-12 The TOLER (Tolerance) Settings ................ 3-17 The TEST (Relational) Menu ..............-.6.- 8-18 iv Introduction Chapter 4: Function Graphing DefiningaGraph......... 00.0. c cece cece eens 4-2 Graphing Modes .............. The GRAPH Menu and Display ... Setting the Graph Format...............-2000 4-6 Defining Functions in the y(x) List .............. 4-8 Selecting Functions ..............2-0:eee eee Defining the Viewing Rectangle DisplayingaGraph ...............2--.0-0000- Exploring a Graph with the Free-Moving Cursor .. 4-16 Exploring a Graph with the TRACE Feature ....... Exploring a Graph with the ZOOM Features....... Using ZOOM Box .. 2.22... ccc e eee eee eee Zooming In or Out ......6 0.6 c cece ee eee eee Setting ZOOM Factors ........... 000 cece eeee Other ZOOM Features ...........2-20 0 cece eee The User-Defined ZOOM .......-...00e eee eeeee The GRAPH MATH Menu..........-.----+---20- Setting an Interval for MATH Operations ......... Using the MATH Operations... .......-50.cseeeee Using EVALto AnalyzeaGraph...............-. The DRAWMenu ..........0 ccc cece eee eee DrawingonaGraph ........... 0.0. eee eeee Shading AreasonaGraph .............-..---- Drawing Lines. ... 1.0.0.0... cece Drawing Vertical Lines and Tangent Lines. . . Drawing Circles .............222..--20- Drawing Functions and Inverses ............-.- Using PEN to Draw onaGraph ..........-.2.--- Drawing Points ..............222 222 ena Storing and Recalling Graph Databases.......... Storing and Recalling Graph Pictures ...... 7 GRAPH Menu Items in the Program Editor . GRAPH MenuChart .......-.......000 . Example: Using Listsin Graphing .............- Introduction v Table of Contents (Continued) Chapter 5: Polar Graphing Chapter 6: Parametric Graphing Chapter 7: Differential Equation Graphing Chapter 8: Constants and Conversions Chapter 9: Strings and Characters Chapter 10: Number Bases Defining and Displaying a PolarGraph .......... 5-2 Exploring and Analyzing a PolarGraph.......... 5-4 Example: Graphing aLimagon................. 5-6 Defining and Displaying a Parametric Graph... ... 6-2 Exploring and Analyzing a Parametric Graph... .. 6-4 Example: Simulating Motion .................. 6-6 Defining a DifeqGraph .............-..0 0000 ee 7-2 Displaying and Exploring a DifEqGraph.......... 7-5 Example: Transforming a Differential Equation... 7-7 Example: Solving a Differential Equation........ 7-8 Example: Linear Harmonic Oscillator ........... 7-9 The CONS (Constants)Menu................... 8-2 Using Constants ............2...0.0.2..00000. 8-3 Creating and Editing User-Defined Constants .... 8-4 The CONV (Conversions) Menu................. 8-6 Using Conversions ..............20..0..0.000- 8-8 Entering and Using Strings.................065 9-2 The STRNG (String) Menu ...............2...05 9-4 The CHAR(Character)Menu.........-...----2- 9-6 Accessing Miscellaneous and Greek Characters ... 9-7 Accessing International Characters............. 9-8 Using Number Bases..............00 000s secu The BASE (Number Base) Menu Designating Number Bases ... . Accessing Hex Digits........... 00.02. ee cee eae Displaying Results in Another Number Base... .. . 10-6 Using Boolean Operators ..........2---.0---5. 10-7 Manipulating Number Base Digits .............. 10-8 vi Introduction Chapter 11: Complex Numbers Chapter 12: Lists Chapter 13: Matrices and Vectors Chapter 14: Equation Solving Entering and Using Complex Numbers ....... - 2 The CPLX (Complex Number) Menu............ 11-3 Entering and Using Lists 12-2 The LIST Menu 12-4 Selecting a List .... 12-5 Defining and Editing Lists with the Editor . . 12-6 Using Math Functions with Lists ......... sees. 12-7 List Functions............. 0... cece reece eee 12-8 Defining and Recalling List Dimensions ........ 12-10 Entering and Using Matrices 13-2 The MATRX(Matrix)Menu ........... -. 18-5 Defining and Editing Matrices withthe Editor... 13-6 Using Math Functions with Matrices........... 13-10 The MATRX MATH Menu........... The MATRX OPS (Operations) Menu Defining and Recalling Matrix Dimensions ...... 13-15 The Row Functions ............eceeceeeeees 13-16 The MATRXCPLX(Complex)Menu ............. 13-18 Storing and Using Portions of a Matrix 13-19 Entering and Using Vectors ....... 13-20 The VECTR(Vector)Menu............2200000 13-23 Defining and Editing Vectors with the Editor.... 13-24 Using Math Functions with Vectors............ 13-26 The VECTRMATH Menu .............00006 +++ 13-27 The VECTROPS (Operations) Menu......... «-+. 13-28 Conversions The VECTRCPLX (Complex) Menu............. 13-30 Entering an Equationin the SOLVER .. 14-2 Defining the Variables ............. 14-3 Solving the Equation .............. sees 14-4 Exploring the Solution Graphically . . . - 146 Controlling the Solution. ................0005 14-7 Entering the POLY (Polynomial) Equation....... 14-8 Solving the Polynomial .................000- 14-9 Entering SIMULT (Simultaneous) Equations ..... 14-10 Solving Simultaneous Equations. .... vee. 14-11 Example: Simultaneous Equations 14-12 Introduction vii Table of Contents (Continued) Chapter 15: Statistical Calculations Chapter 16: Programming Chapter 17: Applications Statistical Analysis ......... cee cece cee eee The STAT (Statistical) Menu ..........00.5005 Selecting and Loading Lists ...............0-4 Loading Lists in the Editor .............00005 Entering and Editing Data ...............04. Calculating Statistical Results ............04- Statistical Results Display ............020086 Statistical Results 0.0... 0... cece eee eee The DRAW Menu ..... 20... cece cece eee eee Drawing Statistical Data... 1... cece eee eee Forecasting a Statistical Data Value ........... Using STAT Operations on a Command Line . Example: Analyzing Two-Variable Statistics Using ProgramS 2.1.0.2... eee e eee eee Sample Program . 2.0... cece eee eee The PRGM (Program) Menu ...... eee see eeee Entering and Editing a Program ............4. The W/O (Input/Output) Menu ............2608 The Input/Output Instructions ............... The CTL (Control) Menu The Control Instructions Calling Other Programs Using Application Operations in Programs Characteristic Polynomial and Eigenvalues The Fundamental Theorem of Calculus ......... Symmetry of the Roots of aComplex Number .... 17-6 Fractions and Matrices ........ 6.6 eee eee ee 17-7 Finding the Area between Curves ..........045 17-8 Minimizing the Solid of Revolution .... . 17-9 Electrical Circuits . 17-10 Unusual Equation .... . . 17-12 Program: Taylor Series ....... 0.00 ce eee eeee 17-14 Convergence of the Power Series .........5045 17-16 Linear Circuits 22.0... ccc eee eee eee Reservoir Problem Predator-Prey Model Program: Sierpinski Triangle ..... cece ee eeee 17-24 viii Introduction Chapter 18: The MEM (Memory) Menu .... Memory Managing Memory .......... Management Deleting Items from Memory Resetting the TI-85 ................ Leaving a Memory Management Screen .......... 18-6 Chapter 19: The TI-85 LINK ....... 0... eee 19-2 Communications Selecting Items to Send .....................0. 19-3 Link Transmitting Items ........... 0... eee eee eee 19-5 Receiving Items ........... 0.000. c eee eee eee 19-6 Backing Up Memory . See e tee cence eens 19-7 Example ........ 0.000. c cece eee eee eee eee 19-8 Appendix A: Table of Functions and Instructions ............. A-2 Tables Table of System Variables ..................00. A-22 Appendix B: Battery Information ................00..000005 B-2 Reference Accuracy Information ....... B-3 Information Error Conditions ............0....0000 0c eee B-4 In Case of Difficulty ................00.0000005 B-9 Support and Service Information .... tee B-10 Warranty Information ..................0005 B-11 Index Introduction ix 8500TOC.DOC TI-85 International English changes Texas Instruments Inc Revised: 02/08/98 3:22 PM _ Printed: 11/20/98 9:42 AM Page ix of 12 Using this Guidebook Effectively The structure of the TI-85 guidebook and the design of its pages can help you find the information you need quickly. Consistent presentation techniques are used throughout to make the guidebook easy to use. Structure of the Guidebook Page-Design Conventions x Introduction The guidebook contains sections that teach you how to use the calculator. © Getting Started is a fast-paced introduction to several important features of the TI-85. © Chapters | and 2 describe general operation and lay the foundation for Chapters 3 through 16, which describe specific functional areas of the TI-85 and include short examples. e Chapter 17 contains application examples that incorporate features from different functional areas of the calculator. These examples can help you see how commands, functions, and instructions work together to accomplish meaningful tasks. © Chapter 18 describes memory management and. Chapter 19 describes the communications link. When possible, units of information are presented on a single page or on two facing pages. Several page-design elements help you find information quickly. © Page headings—The descriptive heading at the top of the page or two-page unit identifies the subject of the unit. © General text—Just below the page heading, a short section of bold text provides general information about the subject covered in the unit. © Left-column subheadings—Each subheading identifies a specific topic or task related to the page or unit subject. ¢ Specific text—The text to the right of asubheading presents detailed information about that specific topic or task. The information may be presented as paragraphs, numbered procedures, bulleted lists, or illustrations. * Page “footers” —The bottom of each page shows the chapter name, chapter number, and page number. Information- Mapping Conventions Reference Aids Several conventions are used to present information concisely and in an easily referenced format. ¢ Numbered procedures—A procedure is a sequence of steps that performs a task. In this guidebook, each step is numbered in the order in which it is performed. No other text in the guidebook is numbered; therefore, when you see numbered text, you know you must perform the steps sequentially. ¢ “Bulleted” lists—If several items have equal importance, or if you may choose one of several alternative actions, this guidebook precedes each item with a “bullet” (¢) to highlight it—like this list you are reading now. © Tables and charts—Sets of related information are presented in tables or charts for quick reference. Several techniques have been used to help you look up specific information when you need it. These include: e Achapter table of contents on the first page of each chapter, as well as the full table of contents at the front of the guidebook. ¢ Aglossary at the end of this section, defining important terms used throughout the guidebook. ¢ Analphabetical table of commands in Appendix A, showing their correct formats, the keys and menus that access them, and page references for more information. © Tables of system variables and built-in constants in Appendix A. e A table of error codes in Appendix B, showing the codes and their meanings, with problem-handling information. ¢ Analphabetical index at the back of the guidebook, listing tasks and topics you may need to look up. Introduction xi Glossary This glossary provides definitions for important terms that are used throughout this guidebook. Command Equation Variable Expression Function Home Screen Instruction List Matrix Menu Items Menu Keys Variable Vector Acommand is either an instruction or an expression used tocalculate a result. An equation variable may contain an equation or an expression. An equation is two expressions that are equal or a variable equal to an expression. Anexpression isa complete sequence of numbers, variables, functions, and their arguments that can be evaluated to a single result. An expression can include an = sign (a mathematical equation). A function, which may have arguments, returns a value and can be used in an expression. The Home Screen is the primary screen of the TI-85, where expressions can be entered and evaluated and instructions can be entered and executed. Aninstruction, which may have arguments, initiatesan action. Instructions are not valid in expressions. A list is aset of values that the TI-85 can use for activities such as graphing a family of curves or evaluating a function at multiple values. A matrix is a two-dimensional array on which the TI-85 can perform operations. Menu items are shown on the seventh and eighth lines of the display and are associated with the menu keys below them. Menu keys are the keys (Fi) through [Fs] below the display. They are used to select menu items. A variable is the name given to a location in memory in which a value, an expression, a list, a matrix, a vector, or astring is stored. A vector is a one-dimensional array on which the TI-85 can perform operations. xii Introduction Getting Started This section takes you through several examples to introduce you to some of the principal operating and graphing features of the TI-85. You can learn to use the TI-85 more quickly by completing these examples first. Operating details are provided in the remaining chapters of the guidebook. Contents The Menu KeyS .........0: sce eeeeeenceenees 2 The First Steps 0... 0... ec cece cece eee e eee 3 Entering Expressions: Savings Account Example. . 4 Recalling and Editing a Calculation............. 6 Graphing on the TI-85 «0.0... cece eee eee 7 Entering an Equation: Mumination Example ..... 9 Entering an Equationin the SOLVER ............ 10 Solving fora Variable ............ 00.00.00 ee ee ll Additional Solutions with the SOLVER ........... 12 Changing the Viewing Rectangle............... 13 Finding a Solution from aSOLVERGraph ......... 14 Defining FunctionstoGraph ...............005 15 DisplayingtheGraph ...................0000 16 Tracing alongaFunction ..............00000ee 17 Finding a Maximum Graphically ............... 18 Graphing the Derivative...................005 19 Zooming In onthe Graph .. 20 Finding a Root Graphically.................00. 21 Other Features ...........0.0 00. c eee eee eee 22 Getting Started 1 The Menu Keys The TI-85 uses display menus to give you access to more operations than you can access from the keyboard alone. The Menus and Menu Keys Selecting Menu Items ‘TEXAS INSTRUMENTS T/-85 & M1 M2 M3 M4 M5 (Fi) (Fe) (F377) (Fa) (5 9 On the TI-85 keyboard, the menu keys are [F4), (F2], [F3], , and (F5). The 2nd functions of the menu keys are [m1], [M2], [M3], (M4), and [M5]. Menu items are shown on the bottom line(s) of the display, above the five menu keys. © Toselect a menu item from the eighth (bottom) line of the display, press the menu key below the item. © Toselect amenu item from the seventh (next-to-the- bottom) line of the display, press and release and then press the menu key below the item. In this guidebook, the menu items are indicated by < > brackets. For example, press [F2] to select <ZIN> or press [M5] to select <GRAPH>. 2 Getting Started The First Steps Before beginning these sample problems, follow the steps on this page to ensure that the TI-85 is reset to its factory settings. (Resetting the TI-85 erases all previously entered data types.) 1. Press {ON) to turn the calculator on. 2. Press and release and then press [+]. (Pressing accesses the operation printed to the left above the next key that you press. MEM is the 2nd operation of (¢].) The bottom line of the display shows the MEM (memory) menu, Tn tar 7 ma am | 3. Press the [F3) menu key to select <RESET>, the third item in the MEM menu. The bottom line is relabeled with the RESET menu and the MEM menu Pabh Emem Vorprst =f I 4. Press [Fi] to select <ALL>. The display shows the message Are you sure? Press [F4] to select <YES>. The display shows the messages Mem cleared and Defaults set. Fire you sure? CTT es Ta The display contrast was reset to the default. To adjust the display contrast, press and release and then press [4] (to make the display darker) or (¥](to make the display lighter). Press to clear the display. GettingStarted 3 Entering Expressions: Savings Account Example The TI-85 display can show up to eight lines of 21 characters per line. This lets you see each expression or instruction in its entirety as it is entered. Variable names can be up to eight characters. You can enter more than one command on a line; separate them with a: (colon). If you invest $25 at the beginning of each month at 6% annual interest, compounded monthly, how much money will you have at the end of three years? The formula is shown on the right. 1. To store the payment amount ($25) in the variable PMT, press 25 . When you press , the symbol > is copied to the cursor location, and the keyboard is set in ALPHA-lock. This makes each subsequent keystroke an uppercase alpha character. Alpha characters are printed to the right above the keys. . Type PMT. Press to take the keyboard out of ALPHA-lock. . Press [:](the 2nd function of ()) to begin another command on the same line. . Press 3 [x] 12 (STo>) N [ALPHA] to store the number of periods (years +12) in the variable N. The TI-85 evaluates the expression before storing the value. . Press (2nd) [:].06 =] 12 ’ to begin anew command and store the interest per period (rate/12) in the variable |. The entry is more than 21 characters, so it “‘wraps” to the next line. 4 Getting Started (1+ DN+1-(1+1 PMT I 203PNT gore: S#IZ4Ni 66/12 On the TI-85, you enter expressions as you would write them, asshown on the right. 6. To enter the expression for the future value formula, press (:] to begin the next command, press to set the keyboard in ALPHA-lock, and then type PMT : 7. Press CQ (0) 1) PHA) 1D) ©) @cera) NG} 1DIEI C1 (cena) 100) cena) t. 8. Press to store the values in the variables and evaluate the expression. The 12-digit result is shown on the right side of the next line of the display. 9. Press [MODE] (the 2nd function of ) to display the MODE screen. Press (¥ ][>] [>] [=] to position the cursor over the 2. 10.Press (ENTER). This changes the display format to two fixed decimal places. 11.Press [QuIT] (the 2nd function of ), which always returns you to the Home screen. Press (ENTER). The last expression is reevaluated and the result displayed with two fixed decimal places. If you save $25 at the beginning of each month for 36 months, invested at 6%, you will have $988.32, PMT+((1+D4(N+1)-G+D)/ ZOFPNTs StI 23Hi 66/129 TSPMT#CCA+T°CN+19-C1 +19)/1 988, 319637236 ieee acct a 988. 319637236 988. 52 Getting Started 5 Recalling and Editing a Calculation On the TI-85, the Last Entry feature lets you recall the command that was executed when you last pressed (ENTER). If more than one command is entered on a line and separated with a colon, the commands are stored together in Last Entry. The last result is stored in Last Answer. If you continue to invest $25a month for another year, how much will you have? 1. Press {ENTRY]. This recalls the last executed command into the display. The cursor is positioned following the command. 2. Use [aJand [©] to position the cursor over the 3 in the instruction 3+12°N. Type 4. 3. You do not need to be at the end of a command to execute it, so press now. The solution is displayed on the next line. Tf you save $25 at the beginning of each month for 48 months, invested at6%, you will have $1359.21. 4, If you were able to save $50 per month, the amount would double because PMT is directly proportional to the total. Press 2 [x]. Press [ANS]. The variable name Ansis copied to the cursor location. Press (ENTER). You will have $2718.42 if you save $50 per month. 6 Getting Started Z5OPMT? Sel 23h: 06/129 TiPMTeC C141 9“¢Nt19-C1 +134 988, 319637236 988. 32 ZOSPMTs 41 29Ns 667125 TEP CCL4T) CHL) re +1071 aerral 988, 319637236 983, 32 ZOSPMT# 41 25N5 66/123 TEPMT#CC1+19*(N+19-(1 +1))¢1 1359.21 988.32 209PNT? 441 23Ni 86/124 TiPMTacCL+10*CNt1 9-01 +1941 1359.21 2+Ans 2718.42 Graphing on the TI-85 Users familiar with the TI-81 will find that all of the popular Th phing features are also on the TI-85. When you press , the menu keys are labeled with the same graphing options (in the same order) that are on the top row of keys on the TI-81. Graph y=x3—2x and y=2cos x. Determine the solution to x8—2x=2c0s x. 1. Press (GRAPH). The menu keys are Nie labeled on the eighth line of the I: PHT ( ¢ 141 yCNt1I-C1 display with the TI-81 graphing +1997] commands. 1359, 21 2*Ans The Home screen and cursor are still 2718.42 displayed. You do not leave the Home screen and enter the graphing = application until you select a menu ey. tz 2. Press [Fi] to select <y(x)=>, which oi Bx" s-2 x accesses the y(x) editor, where you W282 cos x enter and select functions to graph. Press (you may press [F1] to select <x> instead) 4] 3(€) 2 to enter the equation yl =x‘3-2x. Press 2 to enter y2=2cos x. The highlighted = shows yl and y2are “selected” to be graphed. BIER RANGE 200M LE GkAFH Notice, however, that the TI-85 uses lowercase x and y as its graphing variables, rather than the uppercase Xand Y used by the TI-81. 3. Press [M3] to select <ZOOM>. With the ZOOM instructions, you can easily display the current graph ina different viewing rectangle. LoS ivy ha a Press [F4] to select <ZSTD>. This is the same as the ZOOM Standard option on the TI-81. : Getting Started 7 Graphing on the TI-85 (Continued) 4. Press [F4] to select <TRACE>. Press (e] to trace along function y1, then press [4] to move to function y2. Notice the 1 or 2in the upper right of the display, which indicates which function you are tracing. 5. Press to leave TRACE and display the GRAPH menu. Press [F3] to select <ZOOM>. Press (F2] to select <ZIN>. Move the cursor over the apparent intersection in the first quadrant. Press (ENTER). 6. Press to leave ZIN and display the ZOOM menu. Press (F4] to select <ZSTD> to display the original graph. 7. Toexplore the apparent solution in the second quadrant, press to select <BOX>. Move the cursor to the upper right corner of the area you want to examine more closely. Press (ENTER). Move the cursor to the lower left corner (the box defining the area is shown as you move the cursor). Press (ENTER). 8. If necessary, repeat the procedure for ZIN or BOX to see if the two functions intersect in the second quadrant (they do not). @ Getting Started os, fs, bee Se RE.G349206349 — Iyed 6102375421 KELNEOS7A42ES — y=.G451612903 (The coordinate values may vary depending on the cursor location.) XE". 375661376 . 9=.SS1 50884498 Entering an Equation: Illumination Example On the TI-85, you can explore problems in several different ways. For example, you can solve many problems either by using the SOLVER feature or graphically. The remaining pages in Getting Started present an illumination example to show how to enter equations and explore them both by using the SOLVER and by graphing. The illumination on a surface is: © Proportional to the intensity of the source. e Inversely proportional to the square of the distance. © Proportional to the sine of the angle between the source and the surface. The formula for illumination of a point ona surface is shown on the right. A substitution from trigonometry allows us to define illumination in terms of INTEN (intensity), HEIGHT (height of the pole), and DIST (distance). Appropriate units are ft-c (foot-candles) for illumination, CP (candlepower) for intensity, and ft (feet) for distances. |<——- Base ———+| _ INTEN * sin@ DIST2 HEIGHT DIST ILLUM sin 6 = INTEN +* HEIGHT DIST ILLUM = Assume the height of a light on a pole ina parking lot is 50 ft and the intensity is 1000 CP. Determine the illumination on the surface 25 ft from the pole. 1. Press [MEM] <RESET> <ALL> <YES> to reset the calculator. On the TI-85, you can store an unevaluated expression as an equation variable. From geometry, DIST=V (BASE? + HEIGHT). 2. Press toset ALPHA- lock, type DIST =, and then press to take the keyboard out of Done ALPHA-lock. Press Iv] (ALPHA) (ALPHA) BASE (ALPHA) [x2) (ALPHA) (ALPHA) HEIGHT (ALPHA) [x2] [) J {ENTER}. GettingStarted 9 Entering an Equation in the SOLVER With the SOLVER feature of the TI-85, you can solve an equation for any variable in the equation. In the SOLVER, you can observe the effect that changing the value of one variable has on another and apply “what if” scenarios. This page shows how to enter the illumination equation in the SOLVER. 1. Press (2nd) [SOLVER] to display the leans SOLVER equation entry screen. 2. Press ILLUM=INTEN (ALPHA) (ALPHA) [ALPHA] HEIGHT (=). Press [F1] to select <DIST> from the menu; the characters DIST are copied to the fort | a Pa | 1 cursor location. 3. Press[*] 3tocomplete theequation feant..H# 4] that defines illumination in terms of intensity and height: ILLUM=INTEN« HEIGHTIDIST 4 3. As you enter the equation beyond 17 characters, it scrolls. Ellipsis marks (...) indicate that not all of the fil 1 1 | 1 equation is displayed on the line. You can use [| and () to scroll the equation. 4. Press (ENTER. The SOLVER edit TLLUN=TNTEN*+HETGHT 0... screen is displayed. heals The equation is displayed on the top HETGHT= line. The variables are listed in the BASE= order in which they appear in the bound=<-1e99, 16993 equation. The variables HEIGHT and BASE, which define the equation IGRAPHARANGED 200M I TRACE PSOLYE| variable DIST, are shown. The cursor is positioned after the = following the first variable. If the variables have current values, the value is shown. bound defines the interval in which the SOLVER searches for a solution. The default values are -1£99 to 1699. 10 Getting Started Solving for a Variable The TI-85 solves the equation for the variable on which the cursor is placed when you select <SOLVE>. Enter values for all known variables, and then solve for the unknown variable. 1. Use (ENTER), [¥), or A]to move the IL cursor between the variables. Enter 1000 as the value for INTEN. Enter 50 as the value for HEIGHT. Enter 25 as the value for BASE. The values of INTEN, HEIGHT, and BASEin memory are updated. JM=TNTEN*HETGHT 0... I { LUM HETGHT=58 BASE=25 2. Press [4]to move the cursor to ILLUM, the unknown variable. 8. Press [F5] toselect <SOLVE> fromthe fT menu. A moving bar is shown in the e IL upper right of the display to indicate IN H that the TI-85 is busy calculating or EIGHT=58 spe bound=¢-1£99, 1699 The solution is displayed. The le pounder Eevaik square dots to the left of ILLUMand left-rt indicate that these are calculated results. The value of ILLUM in memory is updated. left-rtis the difference between the left side and the right side of the equation, evaluated at the current value of the independent variable. If the height is 50 ft and the intensity is 1000 CP, the illumination on the surface 25 ft from the pole is .28621670111999 ft-c. Getting Started 11 Additional Solutions with the SOLVER You can continue to explore solutions to equations with the SOLVER. You can solve for any variable within the equation to explore “what if” questions. If the desired illumination is exactly 0.2 ft-c, and the intensity isstill 1000 CP, at what height on the pole should the light be placed? 1. To change the value of ILLUM to .2, press the key to clear the value on the line quickly and then type .2. The square dots disappear to show that the solution is not current. 2. Move the cursor to HEIGHT. Press toselect <SOLVE>. It is not necessary to clear the value of the variable for which you are solving. If the variable is not cleared, the value is used as the initial guess by the SOLVER. The equation is solved for HEIGHT and the value displayed. The illumination on the surface is .2 ft-c and the intensity is 1000 CP, if the height of the light source is 63.45876324653 ft. The solution is dependent on the initial guess and bound. 12 Getting Started bocnds?-1£99, 1699) leftsrt=a ITLLUN=TNTEN*HEIGHT/D..| TLLUM=, 2 HEIGHT E04 458763246 BASE=25 ™ bound= £71699, L993 8 left-rt=8 Changing the Viewing Rectangle You can graphically examine equations entered in the SOLVER. The viewing rectangle defines the portion of the graphing coordinate plane that is shown in the display. The values of the RANGE variables determine the size of the viewing rectangle. You can display and edit the values of the RANGE variables. 1. Press [F2] to display the RANGE editor. You display and edit the values of the RANGE variables on this screen. The values shown are the standard default values. The RANGE variables define the viewing rectangle as shown. xMin, xMax, yMin, and yMax define the boundaries of the display. xSel and yScl define the tick marks on the x and y axes. . Graph the illumination example using new values for the RANGE variables, as shown. xMin Use [yor to move the cursor to each value and then type over the existing values to enter the new value. To enter -1, press (@], not EJ, and then press 1. yMax E xScl pe i | xMax yMin Getting Started 13 Finding a Solution from a SOLVER Graph The graph plots the variable on which the cursor is placed as the independent variable on the x axis and left-rt as the dependent variable on the y axis. Solutions exist for the equation where the function intersects the x axis. 1. 14 Press [F1) to select <GRAPH>. The graph plots HEIGHT on the x axis and left-rt on the y axis in the chosen viewing rectangle. The calculation for left-rt in this case is shown on the right. Notice from the graph that this problem has at least two solutions; we found the solution for HEIGHT at the larger value, 63.45876324653. . Tosolve for the other value of HEIGHT, we must supply anew initial guess or alter the bound. You can select a new initial guess with the graph cursor. Use [<] and [©] to position the cursor near where the function crosses the axis at the smaller value. As you move the cursor, the coordinate values are displayed. . Press to select <SOLVE>. The value of HEIGHT identified by the cursor is used as the new initial guess. The busy indicator is displayed during the calculation. The solution screen is displayed again, with another solution for HEIGHT, 3.2022212466711. The illumination on the surface is .2ft-c and the intensity is 1000 CP, if the height of the light source is either 3.2022212466711 ft or 63.458763246530 ft. Getting Started lefertetm- _INTEN: HEIGHT V (BASE? + HEIGHT2)5 4 Nee HEIGHT=3.1746031746 eFt=-rt=0 ILLUM=.2 INTEN=1600 #HE IGHT=3, 2022212466... BASE=25 bound={@, 196} pleft-rt=1e-14 Defining Functions to Graph On the TI-85, functions are graphed for x and y when x is the independent variable and y=y(x). You can store unevaluated expressions with the = symbot (ALPHA function of the key). This page shows how to enter the illumination problem for a graphic solution. Graph the illumination equation and find the height that provides the maximum illumination for a base of 25 feet and an intensity of 1000 CP. 1. Press [quit] to return to the Home screen. 2. Press HEIGHT= tostore the unevaluated expression x inan equation variable, HEIGHT. Use to enter x quickly. INTEN and BASE still contain 1000 and 25. 3. Press to display the GRAPH menu. Press [F1] to select <y(x)=>. The display shows the name of the first function, y1. 4. Press [RCL]. The cursor is positioned after Rel on the sixth line. The RCL feature lets you recall the expression stored in an equation variable to the cursor location. In the SOLVER, the illumination equation was stored in the equation variable eqn. 5. Press [alpha] to change to lowercase alpha-lock and typeeqn (ENTER). The equation is copied to the cursor location. 6. Press (4) to move the cursor to the beginning of the expression quickly. Press six times to delete ILLUM=. DIST="(BASE* +HETGHT Done HE ITGHT=x Done wi= BIRWER RANGE 200M TRACE GRAFH | x f » TINS F bebe | BIQWER RANGE ZODM TRACE GRAFH eee Be a Getting Started 15 Displaying the Graph After you have created and setected the function to graph and entered the appropriate viewing rectangle, you can display the graph. 1. Press [M5] to select <GRAPH> to graph the selected functions in the viewing rectangle. (2nd) accesses the menu items on the seventh line.) Because HEIGHT is replaced by x, the current value of x is used each time a point is plotted. The graph of the function for 0 < x < 100is plotted. 2. The graph shows that there is likely one maximum value of ILLUM fora height between 0 and 100. Press [=] once to display the graphics cursor just to the right of the center of the display. The line xs50,793650794 y=0 above the menu shows the x and y Pex): IRANGED 200M | TRACE GRAFH M display coordinate values for the cursor position (x,y). 3. Using the cursor-movement keys (), ©), (2), and (¥)), move the cursor until it is positioned at the apparent maximum of the function. As you move the cursor, the x and y display coordinate values are updated continually withthecursor = [y=47.46031746 —_-y=.64290322584 position. = The free-moving cursor shows (xMax — xMin) maximum illumination o