# ti-83 guidebook - Sears Parts Direct

TEXAS |NSTIRUMENTS TI-83 GRAPHING CALCULATOR GUIDEBOOK TI-GRAPH Constant LINK, Calculator-Based Memory, Instruments Windows Laboratory, CBL, CBL 2, Calculator-Based Power Down, APD, and EOS are trademarks Ranger, of Texas Incorporated. IBM is a registered Macintosh Automatic trademark is a registered is a registered © 1996, 2000, 200I of International trademark trademark Texas Business of Apple Computer, of Microsoft Instruments Machines Inc. Corporation. Incorporated. Corporation. CBR, Important Texas Instrtu-nents ilnplied, including inerchantability makes but and no warranty, not lilnited fitness either to any for a particular progralns or book rnateriais solely on an "as-is" basis. and expressed implied rnakes purpose, such or warranties of regarding inateriais any availaMe In no event shall Texas Instrmnents be liable to anyone for special, collateral, ineidentai, or eonsequentiai damages in connection with or arising out of the purchase or use of these inateriais, 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. US FCC Information Concerning Radio Frequency Interference This equiplnent has been tested and found to cornply with the limits for a Class B digital device, pumuant to Pm't 15 of the F(C rules. These limits are designed to provide reasonable protection against harmflfl interference in a residential installation. This equiprnent generates, uses, and can radiate radio frequency enet}4y and, if not installed and used in accordance with the instructions, inay cause hannflll inte_ferenee with radio colnmunications. However, there is no guarantee that inte_ferenee will not occur in a particular instailation. If this equiplnent does cause harrnful interference to radio or telexdsion reception, which can be determined by turning the equipment off and on, you can try to correct the inte_ference by one or inore of the following measures: • Reorient or relocate the receiving • Increase the separation • Connect the equipment into an outlet on a circuit fl_m that to which the receiver is connected. • Consult the dealer or an experienced technician for help. between antenna. the equiplnent and receiver. different radio/television Caution: Any changes or modifications to this equiprnent not expressly approved by Texas Instrulnents may void your authority to operate the equiplnent. Table of Contents This nlanual describes how to use the TI-83 Graphing Calculator, Getting Started is an overview of TI-83 features. Chapter 1 describes how the TI-83 operates. Other chapters describe various interactive features. Chapter 17 shows how to combine these features to solve problems, Getting Started: Do This First! TI-83 Keyboard .......................................... TI-83 Menus ............................................. 2 4 First Steps ............................................... Entering a Calculation: The Quadratic Formula .......... Converting to a Fraction: The Quadratic Formula ........ I)isplaJ_ng ('omplex Results: The Quadratic Formula .... Defining a Function: Box with Lid ....................... Defining a Table of Values: Box with Lid ............... Zooming In on the Table: Box with Lid ................. Setting tile Viewing Window-: Box with Lid ............. I)isplaJ_ng and Tracing the Graph: Box with Lid ....... Zooming In on tile Graph: Box with Lid ................ F) Finding the Calculated Maximum: Box with Lid ........ Other TI-83 Features ..................................... Chapter 1 : Operating the TI-83 Turning On and Turning Off the TI-83 .................... Setting the Display Contrast ............................. The Display .............................................. Entering Expressions and Instructions ................... TI-83 Edit Keys .......................................... 6 7 8 9 10 11 12 13 15 16 17 1-2 1-3 1-4 1-6 1-8 Setting Modes ........................................... Using TI-83 Variable Names ............................. Storing Variable Values .................................. Recalling Variable Values ................................ ENTRY (Last Entry) Storage A_'ea ........................ Ans (Last Pmswer) Storage Pa'ea ......................... TI-83 Menus ............................................. VARS and VARS Y-VARS Menus ......................... 1-9 1-13 1-14 1-15 1-16 1-18 1-19 1-21 Equation Operating System (EOS TM) ..................... Error Conditions ......................................... 1-22 1-24 Introduction iii Chapter 2: Math, Angle, and Test Operations Getting Started: Coin Flip ................................ Keyboard Math Operations .............................. MATH Operations ........................................ Using tile Equation Solver ............................... MATH NUM (Numbe 0 Operations ........................ Entering and Using Complex Nmnbers ................... MATH CPX (Complex) OperatMns ....................... MATH PRB (Probability) Operations ..................... ANGLE Operations ....................................... TEST (Relational) Operations ............................ TEST LOGIC (Boolean) Operations ...................... Chapter 3: Function Getting Started: Graphing a Circle ....................... Defining Graphs ......................................... Setting the Graph Modes ................................. Defining Funetions ...................................... Graphing Graphing Chapter 5: Polar Graphing iv Introduction 3-2 3-3 3-4 3-5 Seleeting and Deseleeting Punetions ..................... Setting Graph Styles for Flmetions ....................... Setting the Viewing Window \Tariahles ................... Setting the Graph Format ................................ 3-7 3-9 3-11 3-13 Displaying Exploring Exploring Exploring 3-15 3-17 3-18 3-20 Graphs ....................................... Graphs with the Free-Moving Cursor .......... Graphs with TRACE ........................... Graphs with the ZOOM Instructions ........... Using ZOOM MEMORY .................................. Using the CALC (Calculate) Operations .................. Chapter 4: Parametric 2-2 2-3 2-5 2-8 2-13 2-16 2-18 2-20 2-23 2-25 2-26 3-23 3-25 Getting Started: Path of a Ball ........................... Defining and Displaying Parametric Graphs .............. Exploring Parametrie Graphs ............................ 4-2 4-4 4-7 Getting Started: Polar Rose .............................. Defining and Displaying Polar Graphs ................... ExNodng Polar Graphs .................................. 5-2 5-3 5-6 Chapter 6: Getting Started: Forest and Trees ........................ Defining and Displaying Sequence Graphs ............... Selecting Axes Combinations ............................ Exploring Sequence Graphs .............................. Graphing Web Plots ...................................... Using Web Plots to Illustrate Convergence ............... Graphing Phase Plots .................................... Comparing TI-83 and TI-82 Sequence Variables .......... Keystroke Differences Between TI-83 and TI-82 ......... Chapter Tables 7: Getting Started: Roots of a Function ..................... Setting Up the Table ..................................... Defining the Dependent Variables ........................ I)isplaying the Table ..................................... 7-2 7-3 7-4 7-5 Chapter DRAW 8: Getting 8-2 Sequence Graphing Operations Started: Drawing a Tangent Line ................. Using the DRAW Menu ................................... Clearing Drawings ....................................... Drawing Line Segments .................................. 8-3 8-4 8-5 Drawing Horizontal and Vertical Lines ................... Drawing Tangent Lines .................................. Drawing Functions and Inverses ......................... Shading Areas on a Graph ............................... Drawing Circles .......................................... Placing Text on a Graph ................................. UsHlg Pen to Draw on a Graph ........................... Drawing PoHlts on a Graph .............................. Drawing Pixels .......................................... StorH N Graph Pictures (Pic) ............................. Recalling Graph Pictures (Pic) ........................... StorHlg Graph Databases (GDB) ......................... Recalling Graph Dadabases (GDB) ....................... Chapter 9: Split Screen (;-2 6-3 6-8 (;-9 6-11 6-12 6-13 6-15 6-16 Getting Started: Exploring the Unit Circle ................ Using Split Screen ....................................... Horiz (Horizontal) Split Screen ........................... G-T (Graph-Table) Split Screen .......................... TI-83 Pixels in Horiz aim G-T Modes ..................... Introduction 8-6 8-8 8-9 8-10 8-11 8-12 8-13 8-14 8-16 8-17 8-18 8-19 8-20 9-2 9-3 9-4 9-5 9-6 v Chapter 10: Matrices Getting Started: Systems of Linear Equations ............ Defining a Matrix ........................................ Viewing and Editing Matrix Elements .................... Using Matrices with Expressions ........................ I)isplaying and Copying Matrices ........................ Using Math Functions with Matrices ..................... Using the MATRX MATH Operations ..................... 10-2 10-3 10-4 10-7 10-8 10-9 10-12 Chapter 11: Lists Getting Started: Generating a Sequence .................. Naming Lists ............................................. Storing and Displaying Lists ............................. Entering List Names ..................................... Attaching Formulas to List Names ....................... Using Lists in Expressions ............................... LIST OPS Menu .......................................... LIST MATH Menu ........................................ 11-2 11-3 11-4 11-6 11-7 11-9 11-10 11-17 Chapter 12: Statistics Getting Started: Pendulum Lengihs and Periods Setting up Statistical Palalyses ........................... Chapter 13: Inferential Statistics and Distributions vi Introduction ......... 12-2 12-10 Using the Stat List Editor ................................ Attaching Formulas to List Names ....................... I)etaehi_lg Fornmlas from List Names .................... Switching Stat List Editor Contexts ...................... Stat List Editor Contexts ................................. STAT EDIT Menu ........................................ 12-11 12-14 12-16 12-17 12-18 12-20 Regression Model Features .............................. STAT CALC Menu ........................................ Statistical Variables ...................................... 12-22 12-24 12-29 Statistical Statistical Statistical 12-30 12-31 12-37 Analysis Plotting Plotting in a Program ......................... ....................................... in a Program ......................... Getting Started: Mean Height of a Population hfferential Star Editors ................................... 8TAT TESTS Menu ...................................... ............ 13-2 13-6 13-9 Inferential Statistics Input Descriptions .................. Test and Interval Output Variables ....................... Distribution Functions ................................... 13-26 13-28 13-29 Distribution 13-35 Shading ..................................... Chapter 14: Financial Functions Getting Started: Finzmeing a Car. ........................ Getting Started: (;omputing Compound Interest .......... Using tile TVM Solver .................................... Using tile Financial Functions ........................... Calculating Time Value of Money (TVM) ................. Calculating (;ash Flows .................................. Calculating Amortization ................................ Calculating Interest Conversion .......................... Finding I)ays between [)ates_)ef'nm N Payment Method ..... Using tile TVM Variables ................................. 14-2 14-3 14-4 14-5 14-6 14-8 14-9 14-12 l '4-13 14-14 Chapter 15: CATALOG, Strings, Hyperbolic Functions Browsing tile TI-83 CATALOG ........................... Entering and Using Strings ............................... Storing Strings to String Variables ....................... String Functions and Instructions in the CATALOG ...... Hyperbolic Functions in the CATALOG .................. 17)-2 15-g 1:)-4 1.5-6 15-10 Chapter 16: Programming Getting Started: Volume of a Cylinder .................... Creating and Deleting Progrmns ......................... Entering Command Lines and Executing Programs Editing Programs ........................................ Copying and Renmning Programs ........................ PRGM CTL (Control) Instructions ....................... PRGM I/O (Input/Output) Instructions ................... ('ailing Other Programs as Subroutines .................. Chapter 17: Applications 16-2 16-4 ...... 16-5 16-6 16-7 16-8 16-16 16-22 Comparing Test Results Using Box Plots ................ Graphing Pieeewise Punetions ........................... Graphing Inequalities .................................... Solving a System of Nonlinear Equations ................ Using a Program to ( reate the Sierpinski Triangle ....... Graphing Cobweb Attractors ............................ Using a Program to Guess the Coefficients ............... Graphing the Unit Circle and Trigonometric (;m_es ...... Finding the Area between Curves ........................ Using Parametric Equations: Ferris Wheel Problem ...... Demonstrating the Fundamental Theorem of Calculus... Computing Areas of Regular N-Sided Polygons .......... Computing and Graphing Mortgage Payments ........... 17-2 17-4 17-5 17-6 17-7 17-8 17-9 17-10 17-11 17-12 17-14 17-16 17-18 Introduction vii Chapter 18: Memory Management {'heeLing Awailable MemolTy"............................. Deleting Items from MemoKy" ............................ Clearing Entries and List Elements ...................... Resetting the TI-8:3 ...................................... 18-2 18-3 18-4 18-5 Chapter 19: Communication Link Getting Started: Sending Variables ....................... TI-83 LINK ............................................... 19-2 19-3 Selecting Items to Send .................................. Receiving Items .......................................... Transmitting Items ....................................... Transmitting Lists to a TI-82 ............................. Transmitting from a TI-82 to a TI-83 ..................... Backing Up MemoKy" ..................................... 19-4 19-5 19-6 19-8 19-9 1%10 Appendix A: Tables and Reference Information TabD Menu Map ............................................... Vm'iables ................................................ Statistical Formulas ..................................... Financial Fommlas ...................................... A-39 A-49 A-50 A-.M Appendix B: General Information BatteKy" Information ...................................... In Case of Difficulty ..................................... En'or Conditions ......................................... B-2 B-4 B-5 of Functions Accuracy hfformation Support and Service Win'rarity Information Index viii Introduction and Instructions ..................... .................................... Infommtion ......................... .................................... A-2 B-10 B-12 B-13 GettingStarted: Do This First! Contents TI-83 Keyboard .......................................... TI-S3 Menus ............................................. First Steps ............................................... Entering a Calculation: The Quadratie Fonuula .......... ('onverting to a Fraction: The Quadratie Formula ........ Displaying Complex Results: The Quadratic Formula .... Defining a Function: Box with Lid ....................... Defining a Table of Values: Box with Lid ............... Zooming In on the Table: Box with Lid ................. Setting tile Viewing Window-: Box with Lid ............. Displaying and Traeing the Graph: Box with Lid ....... Zooming In on tile Graph: Box with Lid ................ Finding the ('aleulated Maximum: Box with Lid ........ Other TI-83 Features ..................................... TEXAS \ X=:I..5:B;!:=I_fiB 13 15 16 17 T1=83 INSTRUMENTS / 2 4 5 6 7 8 9 10 11 12 \. _Y=_;i:.90_;i:_lfi = J STATPLOT TBLSET FORMAT CALC TABLE Getting Started 1 TI-83 Keyboard Generally, keys, the keybom'd advanced Keyboard is dwided function Zones keys, Graphing Editing Graphing Editing allow calculator scientific Keys Scientific Calculator Keys Started keys Scientific standard Keys these access function functions. FuncffonKeys Getting keys Advanced advanced Advanced 2 into and scientific zones: graphing calculator keys, the interactive graphing you to edit expressions keys display keys access calculator. editing keys. menus features. and values. that access the capabilities the of a Using the Color-Coded Keyboard The keys locate on the TI-83 are color-coded to help you easily the key you need. The gray keys are the number keys. The blue keys along the right side of the keyboard are the conunon math functions. The blue keys across the top set up and display graphs. The primaKF function of each key is printed in white on the key. For example, when you press FMA_], the MATH menu is displayed. Using the K_ and @ Keys The secondary function of each key- is pnnted in yellow above the key-. When you press the yellow [_ key, the character, abbreviation, or word printed in yellow above the other keys becomes active for the next keystroke. For example, when you press [_ and then [M#Y_, the TEST menu is displayed. This guidebook describes this keystroke combination as [_ [TEST], The alpha function the key. When you of each key is printed press the green @ in green above key, the alpha character printed in green above the other keys becomes active for the next keystroke. For example, when you press @ and then [MATH],the letter A is entered. This guidebook describes this keystroke combination as @ [A]. The_key accesses the second function printed in yeltow above each key --'_ [email protected] accessesthe alpha function printedin green above each key Getting Started 3 TI-83 Menus Displaying a Menu While using your TI-83, you often to access items from its menus, will need [5+9| When you press a key- that displays a menu, that menu temporarily replaces the screen where you are working. For example, when you press _, the MATH menu is displayed as a full screen. _ After you select an item fronl screen where you m'e working displayed again. 5+9_ Moving Solne from keys One access Menu nlore a menu, usually the is or letter item is highlighted. beyond the screen, replaces the colon than one lnenu. CPX PRB[ CPX PRB 4:_( 5:_ 6:¢Min( 74€Max( When next to the current round( 5:int( _sl_[ 6:Min( 74.max( menu If the menu continues a down arrow ( _ ) ( : ) in the last displayed item. If you scroll beyond the last displayed item, an up arrow ( t ) replaces the colon in the first item displayed.You can select all item in either of two ways. • Press [] or [] to number or letter • Press the key or number or letter Leaving lnove the cursor to the of the item; press [g_. key combination fia" the next to the item. a Menu without Making You can leave a lnenu without selection in ally of three ways. 4 PRB an Item from a Menu The number • Press where • Press screen. • Press CPX to Another you press such a key, the names of all accessible menus are displayed on the top line. When you highlight a menu name, the items in that menu are displayed. Press [] and [] to highlight each menu nalne. Selecting NUM Pao :*Dec [ Getting Started lnenu 4:?Part( 5:int( 5:Min( 74Max( 3tiPar.t( 4:?Part( 5:int( 6:Min( 7:max( MRTH _ 8:fOR( i_lEIgcd( a Selection lnaking a @ to return to the screen you were. [2_] [QUIT] to t_tum to the home a key for another round( 3:iPart( or screen. 15+9_ I First Steps Before starting the sample pr()blems in this chapter, follow the steps on this page to reset the TI-83 to its factotT settings and cleat" all nlenlot_y-. This ensures that the keystrokes in this chapter will produce the illustrated results. To reset the TI-83, follow these steps. FOR] to 1, Press turn on the calculator. 2, Press and release [_, [MEM] (above []). and then press When you press [2_], you access the operation printed in yellow above the next key that you press. [MEM]is the operation of the [] key. RRM... 3:Clear Entries 4:ClrRllLists 5:Reset... The MEMORY menu is displayed. 3. Press 5 to select 5:Reset. The RESET menu is displayed. 4, _MeMoru.., a. DeCaults... Press 1 to select 1:All Memory, The RESET MEMORY menu is displayed. Resettin9 memoru erases all data and PrograMs. 5, Press 2 to select 2:Reset. M1 nlenlot_y- is cleared, and the calculator is reset to the factor T default settings. When you reset the TI-83, the display contrast is reset. | MeM oleared If the screen is vetT light or blank, press and t_lease D_], and then press and hold [] to darken the screen. If the screen is very dark, press and release [2_, and then press and hold [] to lighten the screen. Getting Started 5 Entering a Calculation: Use the quadratic fornmla to solve the quadratic with the equation and 2X 2 - X + 3 = 0, Begin 3 _ @ the coefficient The Quadratic [n] (above 1_]) of the X 2 tenn. Press store 2, Press @ [ : ] (above [_). The colon allows you to enter more than one instruction on a line, 3, Press 6 _ @ [B] (above _) to store the coefficient of the X term. Press @ [ : ] to enter a new instruction on the same line. Press 2 _ @ [c] (above _) to store the constant. 4, Press [NY_ to store the values to the variables A, B, and C. to [] @ [B] [] [A]_ _ [<] @ [B] [c] []17113[] 2 @ [A] [] to enter the expression one of the solutions for the quadratic formula, for - b+ 2a Press _ equation to find one solution 3X 2 + 5X + 2 = 0. for the The answer is shown on the right side of the display. The cursor nloves to the next line, ready for you to enter the next expression. 6 Getting Started 3X 2 + 5X + 2 = 0 3÷R: 5÷B: 2÷C| The last wdue you stored is shown on the right side of the display. The cursor moves to the next line, ready for your next entt3z, D [] 4_ equations 3X 2 + 5X + 2 = 0, 1, Press[] Formula ÷R: 5÷B: 2÷C 2 Converting to a Fraction: You can show the solution 1. Press [_ The Quadratic Formula as a fl'action. to display the MATH lnenu. Pao NUN eo CPX PRB 3:_ 4:_#( 5: *# 6:¢Min( 7¢€Ma× ( Press 1 to select 1:)Frac froln the MATH (-B+#(BZ-4RC))/( 2R) %6666666667 lnenu, When you press 1, AnsJ,Frac is displayed the home screen. Arts is a variable that contains the last calculated answer. Press 1_ fl'action. to convert on the result to a Rns*Fr, ac| (-B+4-(BZ-4RC) 2R) To save keystrokes, you can recall the last expression edit it for a new calculation. Press [2_ [ENTRY](above [gNT_) to recall the fraction conversion entry, and then press Fffffd][ENTRY]again to recall the quadratic-fornmla expression, 2a 5, you entered, )/( and then I-B+E(BZ-4RC))/( R) -.6666666667 Rns*Fpac -2/3 (-B+E(BZ-4RC))/( 2R)| Press [] to nlove the cursor onto the + sign in the fornmla, Press [] to edit the quadratic-fornmla expression to become: 2R) -.6666666667 Rns_Frac (-B-.r(BZ-4RC))/( -2/31 2a 6, Press 1_ the quadratic to find the other solution for equation 3X 2 + 5X + 2 = 0. -1 _R) Getting Started 7 Displaying Now solve mode, Complex the equation the TI-83 Results: The Quadratic 2X 2 - X + 3 = 0. When displays complex Formula you set a+bi complex number results. Press 1_ [] [] [] [] [] [] (6 times), and then press [] to position the cursor over a+bi. Press @ to select a+bi coinplexnumber mode. 2, Press [_ [QU*T] the home screen, cleat" it. Press 2 _ @ _E]) to return to and then press @ to (above [A] @ [: ] [] z G-T 1 [c] F_q. The coefficient of the X 2 term, the coefficient of the X term, and the constant for the new equation are stored to A, B, and C, respectively. Press [_ [ENTRY] to recM1 the store instruction, and then press [_ [ENTRY] again to recall the quadratic-fornmla expression, eR:-leB:3aC 2+R: -1+B:3+C 3 3 2o Press @ to find one solution equation 2X 2 - X + 3 = 0. for the 12+R:-I+B:3+C i25-I. Press [2_ [ENTRY]repeatedly quadratic-fornmla expression until this is displayed: 2a Press @ the quadratic to find the other solution for equation: 2X 2 - X + 3 = 0. 198957881t (-B-g(BZ-4RC))/_ 2R) .25-1.198957881t (-B+E(BZ-4RC))/( 2R) i25+1.198957881t Note: An alternative for solving equations for real numbers is to use the built-in Equation Solver (Chapter 2). 8 Getting Started Defining Take a Function: a 20 enl. x 25 enl. sheet Box with Lid of paper and cut X × X squm'es fronl two comers, Cut X × 12,5 cm. rectangles from the other two corners as shown in the diagram below, Fold the paper into a box with a lid. What value of X would give your box the nlaxinmln volume V? [ _se the table and graphs to determine the solution, Begin by defining a function volunle of the box. From the diagram: Substituting: that describes the 2X + A = 20 2X + 2B = 25 V=ABX V = (21) - 2X) (25/2 - X) X 1. Press [] to display the Y= editor, which is where you define functions for tables and graphing. Press[] volume 20[] 2 _ [] [] 25[] 2[] [] _ [_ to define the function as Y1 in terms of X. lets you enter X quickly, without having to press @. The highlighted sign indicates that Y1 is selected. _ x PloL:L Plot;' B PICL3 ","?t =I \y._= xY_= "_y_= ,..y_= ,,y_= xY?= \'14tB<20-2X) -X)X _Yz=l <25/2 ,..y_= = xYfi= Getting Started 9 Defining a Table of Values: Box with Lid The table feature of the TI-83 displays numeric You can use a table of values fl'om the function an answer to the problem, 1, Press [2_ [TBLSET] (a|)ove _) display the TABLE SETUP menu, to Tb IStart=O aTbl=l Indent: 2, Press [gNT_ to accept TblStart=0. 3. Press 1 [ggY_ to define the table increment ATbI=I. Leave Indpnt: Auto and Depend: Auto so that the table will be generated automatically, 4. Press [2_ [TABLE](above _) the table, Notice that the nlaxilnuln (box's volunm) occurs between 3 and 5. TABLE SETUP Depend: X to display I value when inforlnation about a function. defined on page 9 to estimate for Y1 X is about 91 o 1 Z 207 3_6 _99 hOB 6 3t_ 4, X=O 5, Press and hold [] to scroll the table until a negative result for Y1 is displayed. Notice that the nmxinmm length of X for this problem occurs where the sign of Y1 (box's volume) changes from positive to negative, between 10 and 11, 6, Press[2_ Getting V1 _t2 F B 231 lhh 10 0 X=12 [TBLSET]. Notice that TblStart h_s changed to 6 to reflect the first line of the table as it was last displayed, (In step 5, the first value of X displayed in the table is 6.) 10 X E Started TblStart=6 _Tbl=l IndPn÷: P._ TRBLE SETUP Depend: _. Rsk Zooming In on the Table: Box with Lid You can adjust the way a table is displayed to get lnore inforlnation about a defined function. With smaller values for aTbl, you can zoom in on the table. Press 3 _ to set TblStart. Press [] 1 [gNT_ to set ATbl. This adjusts the table setup to get a nlore accurate estimate of X for lnaxilnuln volunle Y1. 2, Press[2_ 3. [TABLE], X Notice that tile nlaxinluln value for Y1 is 410.26, which occurs at X=3.7. Therefore, nlaxinmln TABLE SETUP Depend: Press [] and [] to scroll the table. the TblStart=3 _Tbl=. 1 IndPnt: r=Rg_t_ occurs where 3.6<X<3.8, r=_r;J_ 91 _.6 4±0.11 :<;' KB _.0.z6 hOg,gtl _ 't0a u06.x9 h0h.3B 2,.9 h09.19 X=4.2 Press [2_ [TBLSET]. Press 3 [] 6 _ to set TblStart. Press [] 01 [gNT_ to set ATbl. Press [2_ [TABLE], and then press [] and [] to scroll the table. Four equivalent nlaxinluln values are shown, 410.60 at X=3.67, 3.68, 3.69, and 3.70. TRBLE SETUP TblStart=3.6 _Tbl=.Ol IndPnt: _ Rsk Depend: Rsk g _ YI K67 3,68 K69 3.? hi0&6 h10,?.6 h10.;':6 h:t0._:6 h:t0.23 X=3, 72 Press [] and [] to inove the cursor to 3.67. Press [] to lnove the cursor into tile Y1 colulnn, Tile value of Y1 at X=3.67 is displayed the bottoln line in full precision as 410.261226. Press [] to display tile other on nlaxinlunls. The value of Y1 at X=3.68 in full precision is 410.264064, at X=3.69 is 410.262318, and at X=3.7 is 410.266. The lnaxilnuln volulne of the box would occur at 3.68 if you could lneasure and cut the paper at .01-eln. increments. X Y_ -_:.6B hlO.Z6 3.69 3.? 3.71 _.72 h10,_':6 hlO,Z6 h10.25 h10.2_ V, =410, X 261226 V_ 3.66 3.6}' h10.2_ K6B K69 h10,?.6 3.7 3.71 2;.72 h10,;':6 h10._:5 ht0.23 V, =410, 264064 Getting Started 11 Setting You also the Viewing can use the graphing Window: features Box with Lid of the TI-83 to find the nlaxinlunl value of a previously defined function. When the graph is activated, the viewing window defines the displayed portion of the coordinate plane. The values the window variables determine tile size of tile xqewing window. WINDOW XMin=-lO XMax=lO Press _ to display tile window editor, where you can view and edit the values of the window variables. The standard window variables define XscI=I VMin=-lO VMax=lO Vscl=l Xres=l the viewing window _ shown. Xmin, Xmax, Ymin, and Ymax define the boundm'ies of :_Ymax Xscl j Xmm the display. Xscl and Yscl define the distance between tick nmrks on the X and Y taxes. Xres controls resolution. 2. Press 0 _ 3. Press 20 [] 2 to define Xmax using an expression. to define Xmin. Xma× iZ Ysd Ymin \ WINDOW Xmin=O 4. Press [g_gO. The expression is evaluated, and 10 is stored in Xmax. Press [gffT_] to accept Xscl as 1. 5. Press 0 [ggggm 500 [ggggm 100 [g_gN 1 [ggggm to define the remaining window variables. 12 Getting Started of XMax=20/2I Xscl=l VMin=-lO YMax=IO Yscl=l Xres=l WINDOW XMin=O Xmax=lO XS61=I VMin=O VMax=500 Yscl=100 Xres=l / Displaying Now that and Tracing you have defined the Graph: the function which to graph it, you can displayfunction using the TRACE feature. 1. to be graphed and explore The graph of Y1--(20 - 2X)(25/2 - X)X is displayed. Press functionill the _viewing to window. graph the selected Press [] to activate the free-moving Box with Lid and the window the graph. I_i/f in You call trace .-_.-_-, Nj Getting Started along a graph cursor, The X and Y coordinate position of the graph on the bottom line. 3. values cursor for the are displayed Press _], [], [], and [] to move the freemoving cm\sor to the apparent nlaxinmln of the function. As you move coordinate the cursor, values the X and Y are updated continually. 13 4. Press _. The trace cursor on the Y1 function. is displayed The function that you are tracing displayed in the top-left corner. is Press [] and [] to trace along Y1, one X dot at a time, evaluating Y1 at each X. You also can enter your nlaxinmln value of ×. 6. estimate ?t: G:'_) - ::"}D_.::'_ / ::"- }{)}: for the t/ [?t:{20-2g:l{2gc'2:-{,l)g Press a [] 8. When you press a number key while in TRACE, the X= prompt is displayed in the bottom-left corner. '¢l=€.RO-l_g)(2g/l_-l{)g 7. Press [gNT_. The trace cursor jumps to tile point on the Y1 function evaluated at X=a.8. Press [] and [] until nlaxinlunl Y wdue. you are on the This is the nlaxinlunl of YI(X) for the X pixel values. The actual, precise nl_kxinlunl may lie between pixel values. 14 Getting Started ?t:G_O-_:8)(2:gd_-R):_ ',.. Zooming In on the Graph: To help identify nlaxinlulns, nlininlulns, you can magnify instructions. the viewing window 1. Press _ Box with Lid roots, to display- the ZOOM lnenu. This menu is a typical TI-83 menu. To select an item, you can either press the number or letter next to the item, or you can press [] until the item number or letter is highlighted, and then press [_. 2. and intersections at a specific location using of functions, tile ZOOM MEMORY In 3:Zoom Out 4:ZOeoiMal 5:ZS_uare 6:ZStandard ?4ZTPig Press 2 to select 2:Zoom In. The graph is displayed again. The cursor has changed to indicate that you m'e using a ZOOM instruction. X=.3.7;_.3LI0_ .Y=_:tl.=90.3;: . With the cm_sor near the nlaxinlunl vMue of the function (as in step 8 on page 14), press [_. The new viewing window is displayed. Both Xmax-Xmin and Ymax-Ymin have been adjusted by factors of 4, the default values for the zoom factors. Press _ settings. to display the new window WINDOW Xmin=2.4734042_. XMax=4.9734042... Xsol=l YMin=348.79032... YMaX=473.79032... Yscl=100 Xres=l Getting Started 15 Finding the Calculated You can use function. a CALCULATE menu Maximum: operation Box with Lid to calculate a local maxinmm Press [2_ [CALC] (above _) to display the CALCULATE menu. Press 4 to select 4:maximum. The graph is displayed Left Bound? prompt, again with a Press [] to trace along the curve to a point to tile left of the nlaxinluln, and then press [N!N. A _ at the top of the screen indicates selected bound. A Right Bound? prompt 3. the is displayed. Press [] to trace along the curve to a point to the right of the nlaxinluln, and then press [g_gm. A _ at the top of the screen indicates selected bound. the A Guess? prompt is displayed. 4. Press [] to trace to a point neat" the inaxiinuin, and then press [ggT_q. Or, press 3 [] 8, and then press [ggT_q to enter a guess for the nmxinmm. When you press a number key in TRACE, the X= prompt is displayed in the bottomleft corner. Notice how the values for the calculated nlaxinlunl compare with the nlaxinlunls found with the free-moving cursor, the trace cursor, and the table. Note: In steps 2 and 3 above, you can entervalues directlyfor Left Bound andRight Bound,in the same way as describedin step 4. 16 Getting Started Gu¢_=? X=_.O69i_g9 Y=_06.9_216 of a Other TI-83 Features Getting Started has introduced describes in detail the features other features and capabilities you to basic TI-83 operation. This guidebook you used in Getting Started. It also covers the of the TI-83. Graphing You can store, graph, and analyze up to 10 functions (Chapter 3), up to six parametric functions (Chapter 4), up to six polar functions (Chapter 5), and up to three sequences (Chapter 6). You can use DRAW operations to annotate graphs (Chapter 8). Sequences You can generate sequences and graph thenl over time. Or, you can graph them as web plots or as phase plots (Chapter 6). Tables You can create function functions sinmltaneously Split Screen You can split the screen horizontally to display- both a graph and a related editor (such msthe Y= editor), the table, the stat list editor, or the home screen, Ms(), you can split the screen verticMly to display a graph and its table sinmltaneously (Chapter 9), Matrices You can enter and save up to 10 matrices and perform standard matrix operations on them (Chapter 10). Lists You can enter and save as nlany lists as lllelllOl_y-allows for use in statistical analyses. You can attach fornmlas to lists for automatic computation. You can use lists to evaluate expressions at nmltiple values sinmltaneously and to graph a family of curves (Chapter 11). Statistics You can perform one- and two-variable, list-based statistical analyses, including logistic and sine regression analysis. You can plot the data as a histogram, xyLine, scatter plot, modified or regulm" box-and-whisker plot, or normal probability plot. You can define and store up to three stat plot definitions (Chapter 12). evaluation (Chapter tables to analyze nlany 7). Getting Started 17 Inferential Statistics You can perform 16 hypothesis tests and confidence inte_'als and 15 distribution functions. You can display hypothesis test results graphically or numerically (Chapter 13). Financial Functions You can use tilne-value-of-lnoney (TVM) functions to analyze financial instruments such as annuities, loans, mortgages, leases, and sa_lngs. You can analyze the value of money over equal time periods using cash flow functions. You can amortize loans with the amortization functions (Chapter 14). CATALOG The CATALOG is a convenient, alphal_etieal list of all functions and instructions on the TI-83. You can paste any function or instruction from the CATALOG to the current cursor location (Chapter 15). Programming You can enter and store programs that include control and input!output instructions (Chapter Communication Link The TI-83 has a port to connect and conlnlunieate with another TI-83, a TI-82, the Calculator-Based Laborato_sJ u (CBL 2 CBL System, a Calculator-Based Ranger (CBWM), or a personal computer. The unit-to-unit link cable is included with the TI-83 (Chapter 19). TM, 18 Getting Started TM) extensive 16). TM 1 Contents Operating the TI-83 Turning On and Turning Off tile TI-83 .................... Setting the Display Contrast ............................. Tile Display" .............................................. Entering Expressions and Instructions ................... TI-83 Edit Keys .......................................... Setting Modes ........................................... Using TI-83 Variable Names ............................. Storing Variable Values .................................. Recalling Variable Values ................................ 1-2 1-3 1-4 1-6 1-8 1-9 1-13 1-14 1-15 ENTRY (Last Entry) Storage Area ........................ Ans (Last Answer) Storage Area ......................... TI-8:_ Menus ............................................. VARS and VARS Y-VARS Menus ......................... 1-16 1-18 1-19 1-21 Equation Operating System (EOS TM) ..................... En'or Conditions ......................................... 1-22 1-24 TEXAS TI-83 INSTRUMENTS Sol Eng 123456789 Degree Pol Se_ Dot Si_ul Horiz G-T J STAT PLOT TBLSET FORMAT CALC TABLE Operating tile TI-83 1-1 Turning On and Turning Turning On the Calculator To turn Off the TI-83 on the TI-83, press ION]. • If you previously had turned pressing K_] [OFF], the TI-83 as it was when you last used off the calculator by displays the home screen it and clears any error. • If Automatic Power Down m (APD TM) hal p_eviously turned off the calculator, the TI-83 will return exactly you left it, including the display, cursor, and any em)r. To prolong the life of the batteries, APD turns automatically after about five minutes without Turning Off the Calculator To turn Operating the manually, All settings and memory Constant Memo_y TM. • Any er_)r TI-83 replaceable To replace in memory, 1-2 TI-83 • The Batteries offthe TI-83 condition uses press contents [_ as off the TI-83 any actixqty. [OFF]. are retained by is cleared. four AAA alkaline batteries and has a user- backup lithium batte_Ty- (CR1616 or CR1620). batteries without losing any information stored follow the steps in Appendix B. Setting the Display Adjusting the Display Contrast Contrast You can adjust the display contrast to suit your angle and lighting conditions. As you change the setting, a number from 0 (lightest) to 9 (darkest) top-right corner indicates the current level. You able to see the number if contrast is too light or viewing contrast in the may not be too dark. Note: The T1-83 has 40 contrast settings, so each number 0 through 9 represents four settings. The TI-83 retains turned off. tile To adjust the contrast, 1. Press and release contrast follow setting these in nlenlol_y- when it is steps. the D_] key. 2. Press and hold [] or [], which are below and above contra_t sjnnbol (yellow, half-shaded circle). • [] lightens the • [] darkens the screen. the screen. Note: If you adjust the contrast setting to 0, the display may become completely blank. To restore the screen, press and release _, and then press and hold [] until the display reappears. When to Replace Batteries When the batteries are low, a low-battelT message displayed when you turn on the calculator. Your is battePies ape lou. Recommend change of batteries, To replace the batteries without losing any- information memory, follow tile steps in Appendix B. in Generally-, the calculator will continue to operate for one or two weeks after the low-batte<F message is fil_t displayed. After this period, the TI-83 will turn off automatically and the unit will not operate. Batteries nmst be replaced. All nmmow is retained. Note: The operating period following the first low-battery message could be longer than two weeks if you use the calculator infrequently. Operating the TI-83 1-3 The Display Types of Displays The TI-83 displays both text and graphs. Chapter 3 Home The home screen is the prima_T screen of the TI-83. On this screen, enter instructions to execute and expressions to evaluate. The answers are displayed on the same screen. describes graphs. Chapter 9 describes how the TI-83 can display- a horizontally or vertically split screen to show graphs and text simultaneously. Screen Displaying Entries and Answers When text is displayed, the TI-83 screen can display a nlaxinmm of eight lines with a nmxinmm of 16 characters per line. If all lines of the display are full, text scrolls off the top of the display. If an expression on the home screen, the Y= editor (Chapter 3), or the program editor (Chapter 16) is longer than one line, it wraps to the beginning of the next line. In numeric editors such as the window screen (Chapter 3), a long expression scrolls to the right and left. VC]mn an enhT is executed on the home screen, is displayed on the right side of the next line. Entry Answer io9(2) • 3010299957 The mode expressions the answer settings control and displays the way the TI-83 interprets answers (page 1-9). If an answer, such as a list or matrix, is too long to display entirely on one line, an ellipsis (...) is displayed to the right or left. Press [] and [] to scroll the answer. ILl 1{25.12 874.2 36_ Returning to the Home Screen To return Busy Indicator When the TI-83 is calculating or graphing, a vertical moving line is displayed as a busy indicator in the top-right corner of the screen. When you pause a graph or a program, the busy indicator becomes a vertical moving dotted line. 1-4 Operating [_ the to the honle screen Entry Answer fronl any- other screen, press [QUIT]. TI-83 Display Cursors In most cases, will happen menu item the appearance of the cursor when you press the next to be pasted as a character. indicates key- or select what the next Cursor Appearance Effect of Next Keystroke EntKF Solid • A character is entered at the cursor; any existing character ove_wvritten rectangle Insert Underline A character Second Reverse [] a_TOW A 2nd character (yellow on the keyboard) is entered or a 2nd operation is executed Alpha Reverse [] A Full Checkerboard rectangle iiiiiii An alpha keyboard) executed is inserted in front is of character (green on the is entered or SOLVE is No ently; the lnaxilnuln are entered at a prompt is full ehara('te_ or lnelnory If you press @ during an insertion, the cursor becomes an underlined A (A) ff you p_ss [_ during an insertion, the underline cursor becomes Graphs and editors which are described an underlined sometimes in other display chapters. Operating I' (I'). additional the cursors, TI-83 1-5 Entering Expressions What Is an Expression? and Instructions An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements. An expression evaluates to a single answer. On the TI-83, you enter an expression in the same order _.s you would write it on paper. For exalnple, xR 2 is an expression. You can use an expression on tile home screen to calculate an answer. In most places where a value is required, you can use an expression to enter a value. (i/3) • z 111111111 Entering an Expression I WINDOW Xmin=-10 Xmax=2x [ I To create an expression, you enter numbers, variables, and functions from the keyboard and menus. AI_ expression is coinpleted when you press [gNY_, regardless of the cursor location. The entire expression is evaluated according to Equation Operating System (EOS TM) rules (page 1-22), and the answer is displayed. Most TI-83 functions and operations are s3qnbols comprising several characters. You nmst enter the symbol from the keyboard or a menu; do not spell it out. For example, to calculate the log of 45, you nmst press [UfN 45. Do not enter the letters t., O, and 6. If you enter LOG, the TI-83 inteqorets the enttT as implied nmltiplication of the variables L, O, and G Calculate 3.76 + (-7.9 + _5) + 2 Iog 45. a[E][email protected]@ [d 5DD @21 q 45D 2. 642575252 Multiple Entries on a Line To enter two or more expressions or instructions on a line, separate them with colons (@ [:]). All instructions are stored together in last enttT (ENTRY; page 1-16). 15+R:2+B:R/B 1-6 Operating the TI-83 2.51 Entering a Number in Scientific Notation To enter a number in scientific notation, ff)llow these steps. 1. Enter the part of the number that precedes exponent. This value can be an expression. 2. Press [_ [EE]. E is pasted to the cursor the location. 3. If the exponent is negative, press D, and then exponent, which can be one or two digits. l(19/2) When £-2 you enter enter the .0951 a number in scientific notation, the TI-83 does not automatically display answers in scientific or engineering notation. The mode settings (page 1-9) and the size of the number determine the display- format. Functions A function returns a value. For example, +, -, +, _(, and log( are tlle functions in the example on page 1-6. In general, the first letter of each function is lowercase on the TI-83. Most functions take at least one a_gument, parenthesis ( ( ) following the name. _qui_s one argument, sin(value). as indicated For exalnple, by _m open sin( Instructions An instruction initiates an action. For example, ClrDraw is an instruction that clears any- drawn elements from a graph. Instructions cannot be used in expressions. In general, the first letter of each instruction name is uppercase. Some instructions take more than one argument, as indicated by an ()pen parenthesis ( ( ) at the end of the name. For example, Circle( requires three arguments, Circle(X,Y, radius). Interrupting a Calculation To intetTupt a eMeulation or graph in progress, would be indicated by the busy indicator, press When you interrupt a calculation, • To return • To go to the location When to the home you interrupt screen, the menu select a graph, To return to the home nongraphing key. • To restart graphing, graphing instruction. a partial screen, press is displayed. 1:Quit. of the interruption, • which [_]. select graph press a graphing Operating 2:Goto, is displayed. @ or any key or select the TI-83 a 1-7 TI-83 Edit Keys Keystrokes Result [] or [] [] or [] Moves the cursor within an expression; these keys repeat. Moves the cursor from line to line within an expression occupies more than one line; these key-s repeat. that On the top line of an expression on the honle screen, [] nloves the cursor to the beginning of the expression. On the bottom line of an expression on the home screen, nloves the cursor to the end of the expression. Moves the cursor to the beginning Moves the cursor to the end of an expression. Evaluates an expression of an expression. or executes an instruction. On a line with text on the home screen, On a blank line on the honle screen, home screen. In an editor, clears the expression located; it does not store a zero. Deletes [_ tINS] a character clears the current clears everything or value where line. on the the cursor is at the cursor; this key repeats. Changes the cursor to __ ; inserts underline cursor; to end insertion, [], or []. [] chm'acters in front of the press [2_] [,NS] or press [], [], [_ Changes the cursor to n; the next keystroke performs a 2nd operation (an operation in yellow above a key- and to the left); to cancel 2nd, press [2_] again. @ Changes the cursor to i51;the next keystroke pastes an alpha character (a character in green above a key and to the right) or executes SOLVE (Chapters 10 and 11); to cancel @, press @ or press _, [], [], or []. [_ [A-LOCK] Changes the cursor to r/l;sets alpha-lock; subsequent keystrokes (on an alpha key) paste alpha characters; to cancel alpha-lock, press @; name prompts set alpha-lock automatically. Pastes an X in Func Inode, a T in Par Inode, a O in Pol Inode, or an n in Seq mode with one keystroke. 1-8 Operating the TI-83 Setting Modes Checking Mode Settings Mode settings control how the TI-83 displays and interprets numbers and graphs. Mode settings are retained by the Constant Meln(aTy- feature when the TI-83 is turned off. All numbet_, including elements of matrices and lists, are displayed according to the current mode settings. To display- the mode settings, press [Mff_]. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail. Normal Sci Eng Float 0123456789 Radian Degree Func Par Pol Seq Connected Dot Sequential Simul Real a+b i re^0 i Ful 1 H0ri z G T Changing Mode Settings To change Numeric notation Nulnber of deeilnal places Unit of angle men,sure Type of graphing Whether to connect graph points Whether to plot sinmltaneously Real, rectangular cplx, or polar eplx Full screen, two split-screen modes nlode settings, follow these steps. 1. Press [] or [] to lnove the cm\sor to the line of the setting that you want to change. 2. Press [] or [] to nlove the cursor want. 3. Press Setting a Mode from a Program to the setting you [ggY_, You call set a mode fronl a program by entering the name of the mode as all instruction; for example, Func or Float. Fronl a blank eonlnland line, select the nlode setting fronl the mode screen; the instruction is pasted to the cursor location. PROGRRM: TEST : FuncI I Operating the TI-83 1-9 Normal, Sci, Eng Notation modes only 'affect the way an answer is displayed on the home screen. Numeric answers can be displayed with up to 10 digits and a two-digit exponent. You can enter a number in any- format. Normal notation numbers, with in 12345.67. mode is the usual way we express digits to the left and right of the decimal, as Sci (scientific) notation mode expresses number,s in two pm'ts. The significant digits display- with one digit to the left of the decimal. The app_)priate power of 10 displays to the right of E, t_sin 1.234567E4. Eng (engineering) notation mode is similm" to scientific notation. However, the number can have one, two, or three digits before the decimal; and the power-of-10 exponent is a nmltiple of three, as in 12.34567E3. Note: If you select Normal notation, but the answer cannot display in 10 digits (or the absolute value is tess than .00I ), the TF83 expresses the answer in scientific notation. Float, 0123456789 Float (floating) the sign decimal mode displays up to 10 digits, plus and decimal. 0123456789 (fixed) decimal mode specifies the number of digits (0 through 9) to display to the right of the decimal. Place the cursor on the desired and then press [ENYE_. The decimal setting notation modes. applies The decimM setting applies • • • • • 1-10 Operating the number to Normal, of decimal digits, Sci, and Eng to these numbers: An answer displayed on the home screen Coordinates on a graph (Chapters 3, 4, 5, and 6) The Tangent( DRAW instruction equation of the line, x, and dy/dx values (Chapter 8) Results of CALCULATE operations (Chapters 3, 4, 5, and 6) The regression equation stored after the execution of a regression lnodel (Chapter 12) TI-83 Radian, Degree Angle modes control how the TI-83 inteq)rets angle values in trigonometric functions and polar/rectangular conversions. Func, Par, Pol, Seq Radian mode intelprets display- in radians. angle values as radians. Answers Degree mode interprets display- in degrees. angle vMues as degrees. Answers Graphing modes define the graphing paralneters. 3, 4, 5, and 6 describe these nlodes in detail. Chapters Func (function) graphing mode plots functions, a function of X (Chapter 3). where Y is Par (parametric) graphing mode plots relations, and Y are functions of T (Chapter 4). where X Pol (polar) graphing mode plots functions, function of 0 (Chapter 5). Seq (sequence) Connected, Dot where graphing mode plots sequences r is a (Chapter 6). Connected plotting mode draws a line connecting point eMeulated for the selected functions. each Dot plotting mode plots only the e;flculated selected functions. of the Operating points the TI-83 1-11 Sequential, Simul Sequential graphing-order mode evaluates and plots one function completely before the next function is evaluated and plotted. Simul (sinmltaneous) graphing-order mode evaluates and plots all selected functions for a single wdue of X and then evMuates and plots them for the next value of X. Note: Regardless of which graphing mode is selected, the TI-83 wil! sequentially graph all stat plots before it graphs any functions. Real, a+bi, re^Of Real mode does not display complex results complex numbers are entered as input. Two Full, Horiz, G-T display- a+bi (rectangulm" complex numbers in the form a+bi. • re^0i (polar in the fornl complex re^Oi. Full screen mode or edit screen. uses Each split-screen sinmltaneously. nlode • Operating modes • • 1-12 complex the complex mode) results. displays mode) displays the entire screen displays complex complex to display- numbers a graph two screens Horiz (horizontal) mode displays the the top half of the screen; it displays an editor on the bottom h'alf (Chapter G-T (graph-table) mode displays the the left half of the screen; it displays the right half (Chapter 9). TI-83 unless current graph on the home screen or 9), current graph on the table screen on Using TI-83 Variable Variables and Defined Items Names On the TI-83 you can enter and use several types of data, including real and complex numbe_\s, matrices, lists, functions, stat plots, graph databases, graph pictures, and strings. The TI-83 uses ansigned names for variables and other items saved in nlenlol_yL For lists, you 'also can create your own five-character names. Variable Real Type Complex numbers A, B,..., Z, 0 A, B,..., Z, 0 Matrices [A], [B], [C], . . . , [J] Lists Cl, L2, L3, L4, LS, L6, and userdefined haines Functions Y1, Y2,..., Parametric Polar equations Yg, Yo XIT and YIT, ... functions Sequence , X6T and Y6T rl, r2, r3, r4, r5, r6 functions u, v, w Stat plots Plot1, Plot2, Plot3 Graph GDB1, GDB2,..., databases GDB9, GDB0 Graph pictures Picl, Pic2,..., Pic9, Pic0 Strings Strl, Str9, Str0 System Notes about Variables Names numbers variables Str2,..., Xmin, Xmax, and others • You can create (Chapter 11). • Progranls have user-defined with variables (Chapter 16). • FI_)lll the honle as many screen to matrices (Chapter (Chapter 15), system 1), TblStatt (Chapter 3, 4, 5, and list names nanles and will Mlow share nlenlory or fronl a progranl, you can store 10), lists (Chapter 11), strings variables such me Xmax (Chapter 7), and all Y= functions (Chapters 6), • FI_Olll an editor, you can store Y= functions (Chapter 3). • FI_Olll the store a value • as nlenlo_y- honle to matrices, lists, and sereen_ a progranl, or all editor, you to a lnatrix element or a list element. You can use DRAW STO menu graph datab_kses and pictures items to store (Chapter 8). Operating the can and reeM1 TI-83 1-13 Storing Variable Storing Values in a Variable Values Values are stored to and recalled fronl nlenlol_- using variable names. When an expression containing the name of a variable is evMuated, the vMue of the variable at that time is used. To store a value to a vm'iable fronl the home screen or a program using the _ key, begin on a blank line and follow these steps. 1. Enter the value you want to store. The value can be an expression. 2. Press _. -> is copied to the cursor location. 3. Press @ and then the letter of the variable you want to store the value. to which 4. Press [gg_O. If you entered an expression, it is evaluated. The value is stored to the variable. [5+8_'3÷Q Displaying a Variable Value To display- the value of a vm'iable, enter the name on a blank line on the home screen, and then press IgOr. I° 1-14 Operating 517[ the 5171 TI-83 Recalling Using Recall (RCL) Variable Values To recall and copy location, follow variable these contents steps. to the current To leave 1. Press [2_] ERCL]. Rcl and the edit the bottom line of the screen. Enter the name of the variable are displayed on in any of five ways. Press • Press [g_ [LIST], and then or press [g_ [Ln]. • Press • Press [V_g] to display the VARS menu or _ [] to display the VARS Y-VARS menu; then select the type and then the name of the variable or function. • Press NRgM] [_, and then program (in the program _, variable bottom and then cursor cursor @. • The @ RCk, press the letter and then select name the name the name select editor you selected line and the cursor of the variable. select of the matrix. the name only). is displayed of the list, of the on the disappeat\s. 100+ Rol 0 Press IENTEEI.The variable contents are inserted the cursor w_s located befot_ you began these 1100+517I where steps. I Note: You can edit the characters pasted to the expression without affecting the value in memory. Operating the TI-83 1-15 ENTRY (Last Entry) Using ENTRY (Last Entry) Storage Area When you press [g_ on the holne screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called ENTRY (last ent_T). When you tu_ off the TI-83, ENTRY is retained in lllelllOl_y', To recall ENTRY, press 12_ [ENTRY].The last entry is pasted to the cur_nt cursor location, where you can edit and execute it. On the home screen or in an editor, the current line is clea_d and the last entry is pasted to the line. Because the TI-83 updates ENTRY only when you press [g_, you can recall the previous entry even if you have begun to enter the next expression. 5 [] 7 F_a] [ENTRY] Accessing a Previous Entry 5+7 5 +711 12 The TI-83 retains as many previous entries as possible in ENTRY, up to a capacity of 128 bytes. To scroll those entries, press [_ [ENTRY] repeatedly. If a single ent_T is more than 128 bytes, it is retained for ENTRY, but it cannot be placed in the ENTRY storage area. 2_B I_ I_A [_ [ENTRY] 2+B 1÷1::1 2+BI 12 If you press [[email protected]] [ENTRY] after displaying the oldest stored enttT, the newest stored entry is displayed again, then the next-newest entry, and so on, [ENTRY] 1-16 Operating the TI-83 2eB 1+RII Reexecuting the Previous Entry After you have pasted the last entt'y to the home and edited it (if you chose to edit it), you can entry-. To execute the last ent_T, press [_T_]. screen execute the To reexecute the displayed entry, press _ again. Each reexecution displays an answer on the right side of the next line; the entry- itself is not redisplayed. F_° _ @ @N[][email protected] Multiple Entry Values on a Line N O+N N+I÷N:NZ 0 To store to ENTRY two or more expressions or instructions, separate each expression or instruction with a colon, then press [_T_. All expressions and instructions separated by colons are stored in ENTRY. When you press K_ [ENTRY], all the instructions separated by colons are cursor locatkm. You can edit any of execute all of them when you press expressions and p_sted to the current the entries, and then [_R]. For the equation A=_r 2, use trial and error to find the radius of a circle that covers 200 square centimeters. Use 8 as your first guess. [:][_ [_-]@ R [_7 [_E_ F_ [E.TR¥] [] F_t_q 7 [_ [INS] [] 95 8÷R:_RZ 201.0619298 8÷R:=RZI 8+R:_Rz 201.0619298 7.95+R:_Rz 198.5565097 Continue until the answer is as accurate as you want. Clearing ENTRY Clear Entries (Chapter 18) cleats all data that the TI-83 is holding in the ENTRY storage area. Operating the TI-83 1-17 I Ans (Last Answer) Using Ans in an Expression When Storage an expression Area is evaluated successfully- home screen (Jr from a program, answer to a storage at_a called be a real or complex number, a When you turn off the TI-83, the fronl the the TI-83 stores the Ans (last answer). Ans nlay list, a lnatrix, or a string. value in Ans is t_tained in nlenlol_y. You can use the variable Ans to represent the last answer in most places. Press [2_] tANS] to copy the vm'iable name Ans to the cm'sor location. When the expression is evaluated, the TI-83 uses the value of Ans in the calculation. Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate the yield per square meter if the plot produces a total of 147 tomatoes. 1[]TN4C32 147 [] Continuing an Expression Storing Answers _ [ANS] 1.7.4.2 147/Rn_ 14[ 7 5882s5291 You can use Ans as the first enhTy in the next expression without entering the value again or pressing [_ tANS]. On a blank line on the home screen, enter the function. The TI-83 pastes the vm'iable name Ans to the screen, then the function. s[]2 5/2 _gDg[N_ffl Rns*9.9 To store an answer, store Ans to a variable evMuate another expression. 2.5 24.75 before you Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder of radius 5 meters and height 3.3 meters, and then store the result in the variable V. 1-18 Operating I_ [_]s [] xSZ N3D3 78.53981634 Rns*3.o I __v Rns+U 259.1813939 259.1813939 the TI-83 TI-83 Menus Using a TI-83 Menu You can access lnost TI-83 operations using lnenus. When you press a key or key- combination to display a menu, one or more menu names appear on the top line of the screen. • • • • The menu name on the left side of the top line is highlighted. Up to seven items in that menu are displayed, beginning with item 1, which 'also is highlighted. A number or letter identifies each menu item's place in the menu. The order is 1 through 9, then 0, then A, B, C, and so on. The LISTNAMES, PRGM EXEC, and PRGM EDIT menus only label items 1 through 9 and 0. When the menu continues beyond the displayed items, a down arrow ( $ ) replaces the colon next to the last displayed item. When a menu item ends in an ellipsis, the item displays a secondat7 menu or editor when you select it. To display any or [] until that location within displayed with other menu listed on the top line, press [] menu name is highlighted. The cursor the initial menu is irrelewmt. The menu is the cursor on the first item. Note: The Menu Map in Appendix A shows each menu, each operation under each menu, and the key or key combination you press to display each menu. Scrolling a Menu To scroll down the menu items, press []. To scroll up the menu items, press []. To page down six menu items at a time, press @ []. To page up six menu items at a time, press @ []. The green arrows on the calculator, between [] and [], are the page-down and page-up symbols. To wrap to the last menu item directly fronl the first menu item, press []. To wrap to the first menu item directly fi'om the last menu item, press []. Operating the TI-83 1-19 Selecting an Item from a Menu You can select an item from a menu in either of two ways, • Press the number or letter of the item you want to select. The cursor can be anywvhere on the menu, and the item you select need not be displayed on the screen, • Press [] or [] to move and then press [E6T_. the cursor After you select an item from displays the previous screen, to the item a menu, the TI-83 you want, typically Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT menus, only items 1 through 9 and 0 are labeled in such a way that you can select them by pressing the appropriate number key. To move the cursor to the first item beginning with any alpha character or 6, press the key combination for that alpha character or e. If no items begin with that character, then the cursor moves beyond it to the next item. Calculate Leaving a Menu without Making a Selection 1-20 Operating :_27. You can leave four ways. a menu without making a selection • Press [_] [QUIT] to return • Press @ to return • Press a key or key- combination such as [M_ or [_ [LIST]. for a different menu, • Press a key or key combination such as [] or _ [TABLE], for a different screen, the TI-83 to the home in any- of to the prexdous screen. screen. VARS and VARS Y-VARS VARS Menu You can enter Menus the in an expression haines of functions or store to them and systeln varial>les directly. To display the VARS inenu, press _. All VARS inenu items display secondm:y- menus, which show the names of the system variables. 1:Window, 2:Zoom, and 5:Statistics each access lnore VARS Y VARS i: Window... 2 : Zoom.,. 3: GDB... one secondaYy lnenu, X/Y, T/O, and U/VNV variables ZX/ZY, ZT/ZO, and ZU wuiables Graph database vmiables Picture variables 4:Picture.,. 5:Statistics.,. 6: Table... XY, Z, EQ, TEST, and TABLE vmiables 7: String.., Selecting a Variable from the VARS Menu or VARS Y-VARS Menu than PTS vmiables String variables To display the VARS Y-VARS menu, press _ []. 1:Function, 2:Parametric, and 3:Polar display seconda[3_ menus of the Y= function vmiables. VARS Y VARS i: Yn functions Function... 2: Parametric... 3:Polar... X_?,T,Y'rtT functions rn functions 4:On/Off... Lets you select/deselect functions Note: The sequence variables (u, v, w) are located on the keyboard as the second functions olin, 1%1, and El. To select a variable follow these steps. 1. Display fronl the VARS or VARS Y-VARS menu, the VARS or VARS Y-VARS menu. • Press [_ to display • Press _ [] to display the VARS menu. the VARS Y-VARS lnenu. 2. Select the type of variable, such as 2:Zoom from the VARS menu or 3:Polar froln the VARS Y-VARS menu. secondm:y- menu A is displayed. 3. If you selected 1:Window, 2:Zoom, or 5:Statistics from the VARS menu, you can press [] or [] to display ()the[" secondal_y- lnenus, 4. Select CUrSOr a variable location. name from the menu. Operating It is pasted the TI-83 to the 1-21 Equation Order of Evaluation Operating System (EOS TM) The Equation Operating System (EOS defines the order in which functions in expressions are entered and evaluated on the TI-83. EOS lets you enter numbers and functions in a simple, straightfot_vard sequence. TM) EOS evaluates the functions in an expression in this order: 1 Single-argument argument, such 2 Functions that are entered after the argument, such _ks2, -1, 1, o, r, and conversions 3 Powers 4 Pernmtations 5 Multiplication, division 6 Addition 7 Relational 8 Logic operator 9 Logic operators Within a priority right. functions that precede as ¢(, sin(, or log( and roots, (nPr) such as 2^5 or 5x¢32 and combinations implied the nmltiplication, (nOr) and and subtraction functions, such _ > or < and or and xor level, EOS evaluates functions fronl left to Calculations within parentheses are ewduated first. Multiargument functions, such as nDeriv(A2,A,6), are evaluated as they are encountered. 1-22 Operating the TI-83 Implied Multiplication The TI-83 recognizes implied nmltiplication, so you need not press [] to express nmltiplication in all cases. For example, the TI-83 intel_rets 2_, 4sin(46), 5(1+2), and (2"5)7 as implied nmltiplication. Note: TI-83 implied multiplication rules differ from those of the TI-82. For example, the TI-83 evaluates 1/2X as (1/2)*X, while the TI-82 evaluates 1/2X as 1/(2"X) (Chapter 2). Parentheses All calculations inside a pair of pm'entheses first. For example, in the expression 4(1+2), evaluates the portion inside the pm'entheses, nmltiplies the answer, 3, by 4. 4(1+2) 4.1+2 are completed EOS first 1+2, and then I_ You can omit tile ('lose parenthesis ( ) ) at tile end of an expression. All ()pen parenthetical elements are closed automatic_dly at the end of an expression. This is Mso true for open parenthetical elements that precede the store or display-conversion instructions. Note: An open parenthesis following a list name, matrix name, or Y= function name does not indicate implied multiplication. It specifies elements in the list (Chapter I1) or matrix (Chapter 10) and specifies a value for which to solve the Y= function. Negation To enter a negative number, use the negation key. Press [] and then enter the number. On the TI-83, negation is in the third level in the EOS hierm'chy. Functions in the fil\st level, such as squaring, For example, [ _se parentheses -2z (-2) z ale ewduated -X 2, evaluates to square _ _ before to a negative a negative negation. number (or 0). number. 12->R -AZ 42 ( -A ) z -4 Note:Use the[] key forsubtraction and the[] keyfornegation. If you press [] to enter a negative number, as in 9 [] [] 7, or if you press [] to indicate subtraction, as in !) [] 7, an error occurs. If you press @ A [] @ B, it is interpreted as implied multiplication (A*-B). Operating the TI-83 1-23 Error Conditions Diagnosing Error an The TI-83 detects • • • • errot\s while performing these tasks. Ewduating an expression Executing an instruction Plotting a graph Storing a value VClmnthe TI-83 detects message as a menu title, ERR:DOMAIN. Appendix possible reasons for tile an error, it returns an etTor such _ts ERR:SYNTAX or B describes each error type and etTor. ERR: S_,"NTRX _a[IQuit 2: Goto I • • I If you select 1:OuR (or press [_ [QUIT]or @), then tile home screen is displayed. If you select 2:Goto, then the prexqous screen is displayed with the cut\sot at or neat" the error location. Note: If a syntax erroroccurs in the contentsof a Y= functionduring program execution, thenthe Goto option returnsto the Y= editor, not to the program. Correcting Error an To eotTect an error, follow these steps. 1. Note the error type (ERR:e_9"or type). 2. Select 2:Goto, if it is available. The previous screen is displayed with the cursor at or neat" the error location. 3. Determine the error. If you cannot recognize refer to Appendix B. 4. Correct 1-24 Operating the TI-83 the expression. the error, Math,Angle, Operations and Test Contents Getting Started: Coin Flip ................................ Keyboard Math Operations .............................. MATH Operations ........................................ Using the Equation Solver ............................... MATH NUM (Number) Operations ........................ Entering and Using Complex Nmnbers ................... MATH CPX (Complex) Operations ....................... MATH PRB (Probability) Operations ..................... ANGLE Operations ....................................... TEST (Relational) Operations ............................ TEST LOGIC (Boolean) Operations ...................... '_ TEXAS 2-2 2-3 2-5 2-8 2-13 2-16 2-18 2-20 2-23 2-24 2-26 T1=83 iNSTRUMENTS Q^3+PZ-125=O -Q=4.6415888336... P=5 bound={-50,50} -le_t-rt=O J STAT PLOT TBLSET FORMAT Math, CALC Angle, TABLE and Test Operations 2-1 Getting Getting Started: Started Coin Flip is a fast-paced introduction. Read the chapter for details. Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this sinmlation 40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a coin flip resulting in tails is I).5. 1. Begin on tile home screen. Press [_ [] to display the MATH PRB menu. Press 7 to select 7:randBin( (random Binomial). randBin( is pasted to the home screen. Press 10 to enter the number of coin flips. Press []. Press [] 5 to enter the probability of heads. Press []. Press 40 to enter the number of sinmlations. Press D2. 3. Press _ to evaluate the expression. A list of 40 elements is displayed. The list contains the count of heads resulting from each set of 10 coin flips. The list has 40 elements because this sinmlation was performed 40 times. In this example, the coin came up heads five times in the first set of 10 coin flips, five times in the second set of 10 coin flips, and so on. _andBin(10,.5,40 {5574663_. Press [_ [_ [L1][gNTgmto store the data to the list name L1.You then can use the data for another activity, such as plotting a histogram (Chapter 12). Rgs_L_ 4. Press [] or [] to view the additional counts in the list. Ellipses (...) indicate that the list continues beyond the screen. Note: Since randBin( generates random numbers, your list elements may differ from those in the example. 2-2 10,. 5,40 _andBin( Math, Angle, and Test Operations 4 6 6 3 ... andBin( 10,. 5, 40 5 5 7 4 6 6 3 ,.. ..£._._L_6 5 7 5 ... Keyboard Math Operations Using Lists with Math Operations Math operations that are valid ff)r lists return a list calculated element by element. If you use two lists in the same expression, they nmst be the same length. {1,2}+{3, + (Addition), - (Subtraction), * (Multiplication), / (Division) 4}+5 {9 113 You can use + (addition, E]), - (subtraction, E]), * (nmltiplieation, [_), and / (division, []) with real and complex numbers, expressions, lists, and lnatrices. You cannot use / with matrices. valueA+valueB valueA*valueB Trigonometric Functions valueA valueA - valueB / valueB You can use the trigonometric (trig) functions (sine, [gN]; cosine, [Ugg]; and tangent, _) with real number\% expressions, and lists. The current angle mode setting 'affects tetut]ls interpretation. -.9880316241; sin(value) For example, sin(a0) in Radian mode in Degree mode it returns .5. cos(value) tan(value) You can use the inverse trig functions arccosine, [g_] [c05-t]; and arctangent, real nmnbers, expressions, and lists. mode setting affects interpretation. sin -1(value) (aresine, [g_] [StN-1]; [g_] [TAN-t])with The current angle cos -1(value) tan -1(value) Note: The trig functions do not operate on complex numbers. ^ (Power), 2 (Square), ,[( (Square Root) You can use ^ (power, [_), 2 (square, [77]), and _/( (square root, [g_] [4]) with teal and complex numbers, expressions, lists, and nmtrices. You cannot use _( with matrices. value^power -1 (inverse) value 2 _[(value) You can use -1 (inverse, [] ) with real and complex numbers, expressions, lists, and matrices. The nmltiplieative inverse is equivalent to the reciprocal, l/x. value-1 15' .21 Math, Angle, and Test Operations 2-3 You can use log( (logarithln, FO_), 10^( (power of 10, [_ [10x]), and In( (natural log, @) with real or eolnplex log(, 10^(, In( nulnbers, expressions, log(value) e^( (Exponential) and lists, lO^{power) In(value) e^( (exponential, [2_ [ex]) returns the constant a power. You can use e^( with real or complex expressions, and lists. e raised numbers, to eA(t)owe_ ,') le^(5)148.41315911 e (constant, [g_] [el) is stored as a constant on the TI-83. Press Kfid][el to copy e to the cursor location. In calculations, the TI-83 uses 2.718281828459 for e. e (Constant) e 2.718281828 - (negation, D) returns the negative of value. You can use with real or complex numbers, expressions, lists, and matrices. - (Negation) -value EOS rules (Chapter 1) determine when negation is evaluated. For example, -A2 t_turns a negative nulnber, because squaring is evaluated before negation. Use parentheses to square a negated number, as in (-A)2, 2+R: 2z, ( {-RZ, -2)z} ( -R>a, {-4 4 -4 4} Note: On the TI-83, the negation symbol (-) is shorter and higher than the subtraction sign (-), which is displayed when you press D. (Pi) (Pi, [g_ [_]) is stored calculations, the TI-83 Ix 2-4 Math, Angle, and 3.1415926541 Test Operations as a constant in the uses 3.1415926535898 TI-83, In for _. MATH Operations MATH Menu To display the MATH menu, press [MKTgl. MATH NUMCPX PRB 1 : _Fra c Displays 2:_Dec 3:3 4:3_( 5: x# 6: fMin( 7: fMax( 8:nDeriv( 9: fnlnt( O: Solver.,. _Frac, _Dec the answer as a fraction. Displays the answer as a decimal. Calculates the cube. Calculates the cube root. Calculates the x t;_root. Finds Finds the nlininmln the nlaxinlunl of a function. of a function. (3olnputes the numerical derivative. (Tonlputes tile function integral. Displays the equation solver. _Frac (display at a fraction) displays an answer _L_its rational equivalent. You can use _Frac with real or complex numbers, expressions, lists, and matrices. If the answer cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use _Frac following value. value _Frac _Dec (display as a decimal) displays an answer in decimal form. You can use *Dec with real or complex numbet_, expressions, lists, following value. value and matrices. You can only use _Dec _Dec I/2+I/3_Frac o/61 Ans_Deo .8333333333 Math, Angle, and Test Operations 2-5 3(Cube), 3_r( (Cube 3 (cube) Root) returns or complex nmtrices. the cube numbers, of value. expressions, You can use 3 with lists, real and square value 3 3_( (cube root) returns the cube root of value. 3_( with real or complex numbers, expressions, You can use and lists. 3_(value) {2,3,4,5}3 {8 27 64 125} 3 4 5} _J'(Rns){2 x_ (Root) x_ (xth root) returns the x th root of value. You can use x_ with real or complex numbers, expressions, and lists. xthrootX-_ value 5 N'32 fMin(, fMax( 2 fMin( (function retun_ the value and fMax( (function the local ndninmm nlininlunl) at which nlaxinlunl) or local nmxinmnl value of expression with respect to variable occurs, between/ower and upper values for variable, fMin( and fMax( are not valid in expression. The accuracy" is controlled iE-5), by tolerance (if not specified, the default is fMin(expression,variable,lower,upper[,toleranoe]) fMax(expression,variable,lower, upper[,toleranoe]) Note: In this guidebook, optional arguments and the commas that accompany them are enclosed in brackets ([ ]). f'Min(_in(R), R, -_ -I. 570797171 r_x(sir,(A), R,-:_ • 2-6 Math, Angle, and 1.570797171 Test Operations nDeriv( nDeriv( (numerical derivative) returns an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and e (if not specified, the default is 1E-3). nDeriv( is valid only for real numbers, nDeriv(expression,variable,value[,a]) nDeriv( uses the s:nnmetrie difference quotient which approximates the numerical derivative slope of the secant line through these points. f(x+e)-f(x-e) f'(x) = 2e As e becomes nlore accurate. nDer method, value as the iv(RA3, smaller, the approxinmtion usually- becomes R, 5,. 01 ) 75,0001 nDeriv(R^3o R, 5,. 0001 ) 75 You can use nOeriv( once method used to calculate false derivative fnlnt( value in expression. Because of the nDeriv(, the TI-83 can return a at a nondifferentiable point. fnlnt( (function integral) returns the numerical integral (Gauss-Kronrod method) of expression with respect to variable, given/ower limit, upper limit, and a tolerance (if not specified, the default is 1E-5). fnlnt( is valid only- for real nunlbers. fnlnt(expression,variable,lower, upper[,tolerance]) ?nlnt(A_,R,O&l) •3333330333 Tip: To speed the drawing of integration graphs (when fnlnt( is used in a Y= equation), increase the value of the Xres window variable before you press _. Math, Angle, and Test Operations 2-7 Using the Equation Solver Solver Solver displays the equation solver, in which you can solve for any variable in an equation, The equation is assunled to be equal to zero. Solver is valid only for real numbers. Vcl_en you select Entering an Expression in the Equation Solver Solver, one of two screens • The equation editor (see step 1 picture below) is displayed when the equation wu'iable eqn is empty, • The interactive 2-9) is displayed solver editor (see step 3 picture on page when an equation is stored in eqn. To enter an expression in the equation solver, assunling that the variable eqn is empty, follow these steps. 1, Select 0:Solver from equation editor. EQUATION e_n: 0=| 2, Enter the MATH menu the expression in any of three • Enter the expression solver, directly • Paste lnenu • Press [_ [act_], p_kste a Y= variable VANS Y-VANS lnenu, and press [_, expression is pasted to the equation a Y= vmiable name from to the equation solver, is stored EQURTION SOLVER e_n: O=Q"3+P z-125 | Math, Angle, to display- and Test the SOLVER The expression enter it. 2-8 is displayed. Operations ways, into the equation the VANS Y-VANS to the variable name from The solver. eqn as you the 3, Press _ displayed. or [_. The interactive solver editor is 1%35 -1 5=8 P=8 bound={ • • • • -1 E99, 1... The equation stored in eqn is set equal to zero and displayed on the top line. Variables in the equation are listed in tile order in which they appear in the equation. Any values stored to the listed variables also are displayed. The default lower and upper bounds appeal" in the last line of the editor (bound={-1E99,1E99}). A 4 is displayed in the first colunul of the bottonl line if tile editor continues beyond the screen. Tip: To use the solverto solve an equationsuch as K=.SMV2, enter eqn:0=K-.SMV 2 inthe equationeditor. Entering and Editing Variable Values When you enter or edit a value for a variable in the interactive solver editor, the new value is stored in nlenlol_yto that varialfle. You can enter an expression for a variable value. It is ewduated when you move to the next varialfle. Expressions nmst resolve to real numbers at each step during the iteration. You can store equations to any VAR8 Y-VARS variables, such as Y1 or r6, and then reference the w_riables in tile equation. The interactive solver editor displays all varialfles of all Y= functions referenced in the equation. EQURTION e_n: 8=V., +7SSL_)ER I Y_+7=Obound=C=BR=SX=8 { -i E99, I.,. Math, Angle, and Test Operations 2-9 Solving for a Variable in the Equation Solver To solve for a variable equation has been using stored the equation to eqn, follow solver these after an steps. 1. Select 0:Solver from the MATH menu to display the interactive solver editor, if not already displayed. I% ;P -125=°P=o L. bound={-1E99, 2. Enter Ol" edit tile value of each known variable. variables, except the unknown variable, nmst value. To move the cm\sor to the next wuiable, All contain press INto or _. QQ3;PZ-125=0p=5I 1... bound={ 3. Enter -1 E99, an initial guess for tile variable for which you are solving. This is optional, but it may help find the solution more quickly-. Also, for equations with nmltiple roots, the TI-83 will attempt to display the solution that is closest to your guess, IQ"3+Pp=sQ=4I z- 125=0 bound={ -I E99, 1... (upper+ The 2-10 Math, Angle, and default Test guess is calculated Operations as lower) 2 a 4. Editbound={lower,upper}, lower and bounds between which the TI-83 upper are the searches for a solution. This is optional, but it may help find the solution quickly. The default is bound={- 1E99,1E99}. more 5. Move the cursor to the variable for which you want to solve and press @ [SOLVE](above the [gNTgNkey-). Q_'3+PZ-125=0 I,Q=4.6415888336... P=5 bound={-50,50} leCt-rt=O The solution is displayed next to tile variable for which you solved. A solid square in the fil_t colunm marks the variable for which you solved and indicates that the equation is balanced. An ellipsis shows that tile value continues beyond the screen. Note: When a number continues beyond the screen, be sure to press [] to scroll to the end of the number to see whether it ends with a negative or positive exponent. A very small number may appear to be a large number until you scroll right to see the exponent. The values of the variables are updated in nlenlot'y. left-rt=diffis displayed in the last line of the editor. diffis tile difference between the left and right sides of the equation. A solid square in the first colunm next to left-rt= indicates that the equation has been evaluated at the new value of tile variable for which you solved. Math_ Angle_ and Test Operations 2-11 Editing an Equation Stored to eqn To edit or replace an equation stored to eqn when the interactive equation solver is displayed, press [] until the equation editor is displayed. Then edit the equation. Equations with Multiple Roots Sonle equations have nlore than one solution. You can enter a new initial guess (page 2-10) or new bounds (page 2-11) to look for additional solutions. Further Solutions After you solve for a varialfle, solutions from the interactive you can continue to explore solver editor. Edit the values of one or more varialfles. When you edit any variable value, the solid squares next to the previous solution and left-rt=diff disappear. Move the cursor to the varialfle for which you now want to solve and press @ [SOLVE]. Controlling the Solution for Solver or solve( The TI-83 solves equations through an iterative process. To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds. This will help to find a solution more quickly. Also, it will define which solution you want for equations with nmltiple Using solve( on the Home Screen or from a Program solutions. The function solve( is available only fronl CATALOG or from within a program. It returns a solution (root) of expression for variable, given an initial guess, and lower and upper bounds within which the solution is sought. The default for lower" is -1E99. The default for upper is 1E99. solve( is vMid only for real numbers. soNe(expression,variable,guess[ ,{lower, upper'} ]) expression is assumed equal to zero. The value of variable will not be updated in nlenlory, guess nlay be a value or a list of two values. Values must be sto[_d for eve_Ty"variable in expression, except variable, before expression is evaluated./ower and upper nmst be entered in list format. 4. 641588834 2-12 Math, Angle, and Test Operations MATH NUM (Number) MATH NUM Menu To display Operations the MATH NUM menu, MATH NUM CPX PRB i : ab s ( 2: round( Al_solute Round 3 : i Part ( Integer 4: 5: 6: 7: Fractional part Greatest integer Mininmln value Maxinlunl value f Pa r t ( i nt( mi n ( max ( 8 : ] cm( 9 :gcd ( abs( press [Z], _ value part Legist eonlnlon nmltiple Greatest eonnnon divisor abs( (absolute value) returns complex (modulus) numbers, matrices. the absolute expressions, value of real lists, and or abs(value) abs ( -256 ) 2561, abs( {I.25, -5.67} I {1.25 5.67} Note: abs( is also available on the MATH CPX menu. round( round( returns a nunlber, expression, list, or nlatrix rounded to #decimals (_<9). If #decimals is omitted, value is rounded to the digits that are displayed, up to 10 digits. rou nd(value [,#decimals ]) 123456789012÷C I 1.23456789E111 round (x, 4) 3. 1416 C-round(C) !21 123456789012-Iz3 456789000 Math, Angle, and Test Operations 12 2-13 iPart( (integer iPart(, fPart( or complex part) numbers, returns the integer expressions, lists, part or parts of ++al and matrices. iPart(value) fPart( (fra('tional real or complex paxt) returns the fractional part or p_u'ts of numbe_, expressions, lists, and lnatrices. fPart(value) int( iPart (-23.45) -23 f Part ( -23.45)._ 45 int( (greatest integer) returns the largest integer _<real complex numbers, expressions, lists, and nmtrices. or int(value) lint(-23.45) _241 Note:Fora givenvalue, theresult ofint(isthesame as theresult of iPart( for nonnegative numbers and negative integers, but one integer less than the result of iPart( for negative noninteger numbers. 2-14 Math, Angle, and Test Operations min(, max( min( (ndnimum value) valueB or the smallest returns element the smaller of valueA and in list, If listA and listB are compared, min( returns a list of the smaller of each pair elements, If list and value are compared, min( compares each element in list with value, of max( (n]axin]on] value) returns the larger of valueA and valueB or the largest element in list. If listA and listB are con]pared, max( retm'ns a list of the larger of each pair of elements. If list and value are compared, max( compares each element in list with value, min(valueA,valueB) min(list) min(listA,listB) min(list,value) max(valueA,valueB) max(list) max(listA,listB) max(list,value) r,,in (3,2+2)= 3[ r,,in( {3, 4, _,}, 4) {3 4 4} r,Jax( {4, 5, 6}) I 6 Note: rain( and max( also are available on the LIST MATH menu. Icm(, gcd( Icm( t_tums the least eonlnlon nmltiple of valueA and valueB, both of which must be nonnegative integers, When listA and listB are specified, Icm( retm'ns a list of the lcm of each pair of elements. If list and value are specified, Icm( finds the leln of each element in list and value, gcd( returns the greatest conlnlon divisor of valueA and valueB, both of which must be nonnegative integers, When listA and listB are specified, gcd( t'etun_s a list of the ged of each pair of elements. If list and value are specified, gcd( finds the ged of each element in list and value, Icm(valueA,valueB) Icm(listA,listB) Icm(list,value) gcd(valueA,valueB) gcd(listA,listB) gcd(list,value) 10M(2,5) 10 god( {48, 66}, {64, 122} ) {16 Math, 2} Angle, and Test Operations 2-15 Entering and Using Complex Complex-Number Modes Numbers The TI-83 displays complex numbers in rectangular form and polar forln. To select a complex-nulnber lnode, press [MffffE], and then select either of the two modes. • • a+bi (rectangular-complex lnode) re^0/(polar-colnplex mode) Sci Eng Dot Horiz G-T On the TI-83, complex numbet\s can be stored to variables. Also, complex numbers are valid list elements. In Real mode, COlnplex-nulnber results return an error, unless you entered a complex number as input. For example, in Real mode In(-1) returns an error; in a+bi nlode In(-1) returns an answer. Real a+bi lnode mode lin<-i;,m l I Iln( -l>m 4, ERR-'NONRERL ilBQuit 2: Goto RNS i i Entering Complex Numbers Complex numbers are stored in rectangular form, but you can enter a complex number in rectangulm' form or polar form, regm'dless of the mode setting. The components of complex numbers can be real numbers or expressions that evMuate to reM numbers; expressions m'e evMuated when the connnand is executed. Note about Radian versus Degree Mode Radian mode is reconnnended for conlplex number calculations. Internally-, the TI-83 converts all entered values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic functions. trig In degree mode, complex identities such as e ^ (i0) = cos(0) + i sin(0) are not generally true because the values for cos and sin are converted to radians, while those for e ^ () are not. For example, e^(i45) = cos(45) + i sin(45) is treated internally as e ^ (i45) = cos(_/4) + i sin(x/4). Complex identities are always tree in radian mode. 2-16 Math, Angle, and Test Operations Interpreting Complex Results Complex numbers in results, including list elements, are displayed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction (page 2-19). In the example below, re^0/and Radian modes are set. _2+t)-(le'-(x/4t) 1.325654296e^( .... RectangularComplex Mode Rectangular-complex mode recognizes and displays a complex number in the fore1 a+bi, where a is the ten component, b is the imagimuy component, and i is a constant equM to @'1. -1) lln< 3.141592654tI To enter a complex nulnber in rectangular form, enter the value of a (real component), press [] or [], enter the value of b (imaginary component), and press [_ [i] (constant). Polar-Complex Mode real component(÷ or -)imaginary 14+2t 4+2t cornponenti I Polar-complex mode recognizes and displays a complex number in the form re ^ 0/, where r is the nmgnitude, e is the b_e of the natm'al log, 0 is the angle, and i is a constant equM in(-I) 3.141592654e^ ( I... To enter a complex number of r (magnitude), press [_ enter the value of 0 (angle), then press D. in polar ff)nn, enter the value [ex] (exponential function), press [_ [i] (constant), and ma_dtudeea(anglei) 10e._(n/3t) 10e"(I.04719755... Math, Angle, and Test Operations 2-17 MATH CPX (Complex) MATH CPX Menu To display Operations the MATH CPX menu, press [_ [] [], MATH NUM CPX PRB Returns Returns Returns Returns Returns Displays Displays 1:conj( 2:real( 3:imag( 4:angle( 5:abs( 6:_Rect 7:_Polar con j( the the the the the the the complex conjugate, real part. imaginary part, polar angle. magnitude (modulus), result in rectangular form, result in polar form, conj((conjugate) returns the complex conjugate complex number or list of complex numbers, of a conj(a+bi) returns a-bi in a+bi nlode, conj(re^(0i)) returns re^C0/) in re^ei mode, toni (3+4t) 3-4t1 c°nJ (3e^(4t >> 3e"(2. 28318530?._ real( (real part) returns the real part of a complex or list of complex nmnbers, real( number real(a+bi) returns a, real(f'e^(0i)) returns _"*cos(O). r.eal(3+4t) imag( 3[ real (3e_'(4t >> -I.968938863 imag( (imaginary part) returns the imagining(nonreal) of a complex number or list of complex numbers. imag(a+bi) t_tunls b. imag(re^(Oi)) returns _'_sin(O), Iimag(3+4t ) 2-18 Math, Angle, and Test Operations 41 imag(3e^(4t >-2. 270407486 > part angle( angle( returns the polar angle of a complex number or list of complex numbers, calculated as tan -1 (b/a), where b is the imaginatT part and a is the real part. The calculation adjusted by +x in the second quadrant or -x in the third quadrant. angle(a+bi) returns tan-l(b/a). angle(re^(Oi)) returns 0, where -x<O<x. an91 e ( 3+4t ) • 927295218 abs( abs( (absolute _(real2+imag2) nulnl)ers, value) is an91 e (38^ ( 4i.) ) -2. 283185387 returns the lnagnitude , of a complex nulnber (lnodulus), or list of eonlplex abs(a+bi) returns _ . abs(re^(Oi)) returns r (nmgnitude), labs(3+4t ) _Rect 51 [abs(3e^(4t )) 31 )Rect (display as reetanguhu') displays a complex t_sult in rectangular form. It is valid only at the end of an expression, It is not valid if the result is real, complex result_Rect returns a +bi. _Rec.t 1#(-2_.414213562t1 )Polar )Polar (display as polar) displays a coInplex result in polar form, It is valid only at the end of an expression. It is not valid if the result is real. corr_plexresult_Polarreturnsre ^ (_). #(-2)_PolaP 1.4142135628^(I... Math, Angle, and Test Operations 2-19 MATH PRB (Probability) MATH PRB Menu To display the Operations MATH PRB menu, press _ E}, MATH NUM CPX PRB i: rand Randonl-nunlber generator Number of pernmtations Number of combinations Factorial 2: nPr 3:nCr 4:! 5: randlnt( Random-integer Random # from Random # from 6: randNorm( 7: randBin( rand generator Normal distribution Binomial distribution rand (random number) generates and returns one or more random numbers > 0 and < 1. To generate a list of randomnumbers, specify- an integer > 1 for numt'rials (number of trials). The default for numt'rials is 1. rand [(num trials)] Tip: To generate random numbers beyond the range of Oto I, you can include rand in an expression. For example, rand*5 generates a random number > 0 and < 5. With each rand execution, the TI-83 generates the salne randonl-number sequence for a given seed value. The TI-83 factoFf-set seed value for rand is 0. To generate a different randonl-number sequence, store any nonzero seed value to rand. To restore the factoFy--set seed vMue, store 0 to rand or reset the defaults (Chapter 18). Note: The seedvalue also affectsrandlnt(, randNorm(, and randBin( instructions(page2-22). r'and • 1272157551 1÷rand 2646513087 rand(3) {. 7455607728 2-20 Math, Angle, and Test Operations nPr, nCr nPr (number of permutations) returns the number of pernmtations of items taken number at a time. items and number must be nonnegative integers, Both items and number can be lists. items nPr number nCr (number of combinations) returns the number of combinations of items taken number at a time. items and number nmst be nonnegative integers. Both items and number can be lists. itemsnCrnumb_" 5 5 nCe nPe 2 2 (2_2_i; {2,3> nPP _ 6} ! (Factorial) ! (factorial) returns the factorial of either an integer or a nmltiple of .5. For a list, it returns factorials for each integer or nmltiple of .5. value nmst be _>-.5 and _<69. value! £120 24 720} Note: The factorial is computed recursiveiy using the relationship (n+t)! = n.n!, until n is reduced to either 0 or -1/2. At that point, the definition 0!=I or the definition (-1/2)!=_- is used to complete the calculation. Hence: n!=n*(n-I )*(n-2)* ... *2* I, if n is an integer >0 n!= n*(n-1 )*(n-2)* ....1/2.-_;, if n+1/2 is an integer >O n! is an error, if neither n nor n+I/2 is an integer >0. (The variable n equals value Math, in the syntax Angle, and description Test above.) Operations 2-21 randlnt( (random randlnt( integer) generates and displays a random integer within a range specified by lower and upper integer bounds. To generate a list of random numbers, specify an integer > 1 for numt,Fials (number of trials); if not specified, the default is 1. randlnt(lower,upper[,numtrials]) rand Int ( 1,6)+ra dlnt(1,6) 1,{26, 3)i5} randInt( randNorm( G randNorm( (random Normal) generates and displays a random real number fi'onl a specified Normal distribution. Each generated value could be any real number, but most will be within the intercal [p-3(_), p+3(o)]. To generate a list of random numbers, specify- an integer > 1 for numtrials (number of trials); if not specified, the default is 1. randNorm(p,ol,numtrials]) randNorm(O, 1) .0_7207G175 _ndNo:r,(35,2,10 _34.02r01938 37_. randBin( randBin( (randon] Binomial) generates and displays a random integer from a specified Binomial distribution. numtrials (nmnber of trials) lnust be _>1, prob (probability of success) must be _>0 and _<1. To generate a list of randonl nunlbers, specify an integer > 1 for numsimulations (nmnber of sinmlations); if not specified, the default is 1. randBin(numtrials,prob[,numsimulations]) randBirKS,,2) randBin(7,. 3 4, 10) {3 3 2 5 1 2 2 ... Note: The seed value stored to rand also affects randlnt(, randNorm(, and randBin( instructions (page 2-20). 2-22 Math, Angle, and Test Operations ANGLE Operations ANGLE Menu To display the ANGLE menu, menu displays Radian/Degree interpretation press [_ [ANGLE]. The ANGLE angle indicatot\_ and instruetions. mode setting affects the TI-S3's of ANGLE menu entries. The ANGLE 1: ° 3: r Degree notation DMS minute notation Radian notation 4: ,DMS Displays as degree/lninute/seeond 5: R,Pr( Returns Returns Returns Returns r, given X and Y 0, given X and Y x, given R and 0 y, given R and 0 2:' 6: R_PO( 7: P_Rx( 8: PmRy( DMS Entry Notation DMS (degrees/minutes/seconds) entlT notation comprises the degree sjonbol (°), the minute sjonbol ('), and the second symbol ("). degrees nmst be a real number; minutes and seconds nlust be real numbers _>0. degrees°minutes'seconds For exalnple, enter '' for 30 degrees, 1 minute, the angle nlode is not set to Degree, the TI-83 call interpret the atgulnent and seconds. 23 seconds. If you nmst use ° so that as degrees, minutes, Radian mode Degree mode I sin(30° 1'23") I sin(30° 1'23") -. 98421299951 sin(30 °l 23 o) .5003484441 ° (Degree) •5003484441 ° (degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In Radian nlode, you Call use ° to convert degrees to radians. value ° {value1 ,value2,value3,value_ ,...,value n} ° ° also designates degrees (D) in DMS format. ' (minutes) designates minutes (M) in DMS format. " (seconds) designates seconds (S) in DMS format.. Note: " is not on the ANGLE menu. To enter ", press @ Math, Angle, and Test Operations [-]. 2-23 r (radians) r (Radians) designates an angle regardless of the cmTent angle mode, you can use r to convert or list of angles as radians, mode setting. In Degree radians to degrees. value r Degree mode sin (<_/4.') r ) • 7071067812 sin( {0, ,/2} _) %w.J 1} (x/4> r 45 _DMS _DMS (degree/minute/second) displays answer in DMS format (page 2-23). The nlode setting lnust be Degree for answer to be interpreted as degrees, minutes, and seconds. _DMS is valid only at the end of a line. answe_'_DMS 54°32'30"*2 I 109.08333331 Rns*DMS 10905 0 RI_Pr(converts rectangular coordinates to polar coordinates and returns r, R_PO( converts rectangular coordinates to polar coordinates and returns O.x and y can be lists. R_Pr (, R_,Pe (, P_-Rx(, P*Ry( R*Pr(x,y), R*PO(x,y) I R*Pr(-1,O) e,eo( } ,05 ! I Note: Radian mode is set 14i5926541 PI_Rx( converts polar coordinates to rectangular coordinates and returns x. PI*Ry( converts polar coordinates to reetangulm" coordinates and returns 0 can be lists. y. r and P*Rx(r,_,P*Ry(v,_ P*Rx(I,x) -10 P*R_(I,x) 2-24 Math, Angle, and Test Operations Note: Radian mode is set. TEST (Relational) TEST Menu >_ ->, <,_< Operations To display the TEST menu, [_ This operator... TEST LOGIC Returns 1: = 2: _ 3: > Equal Not equal to Greater than 4: > 5: < Greater than Less than 6: < Less than [TEST]. 1 (true) if,.. or equal or equal to to Relational operators compare valueA and valueB and return 1 if the test is true or 0 if the test is false, valueA valueB can be real numbet_, expressions, and _ only, valueA and valueB also can complex numbers. If valueA and valueB nmst have the same dimensions. Relational program operators are often flow and in graphing function over valueA valueA valueA specific =valueB >value B <valueB and or lists. For = be matrices or are matrices, both used in programs to eont_x)l to control the graph of a values. valueA valueA valueA _valueB >valueB <valueB el 25=26 {i'2'3}<3{i Using Tests press 1 0} Relational operatot_ are evMuated after lnathelnatieal functions according to EOS rules (Chapter 1). • The expression 2+2=2+3 returns 0. The TI-83 performs the addition first because of EOS rules, and then it compares 4 to 5. • The expression 2+(2=2)+3 returns 6. The TI-83 performs the relational test first because it is in parentheses, and then it adds 2, 1, and 3. Math, Angle, and Test Operations 2-25 TEST LOGIC (Boolean) TEST LOGIC Menu To display Operations the TEST LOGIC menu, press [_ [TEST] [_. This operator... TEST LOGIC Returns 1: 2: 3: 4: Both values are nonzero (true). At least one value is nonzero (tree), Only one value is zero (false), The value is zero (false). an d 0c x0c n0t ( a 1 (true} if... Boolean Operators Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values. Values are interpreted _ts zero (false) or nonzero (ttlle). and, and, or, and xor (exclusive or) return a value of 1 if an expression is true or 0 if an expression is false, according to the table below, valueA and valueB can be real numbers, expressions, or lists. or_ xor and valueB or valueB xor valueB valueA valueA valueA not( valueA valueB and or xor €0 €0 returns 1 1 0 €0 0 returns 0 1 1 0 €0 returns 0 1 1 0 0 returns 0 0 0 not( returns 1 if value (which can be an expression) is O, not(value) Using Boolean Operations Boolean logic is often used with relational tests. In the following program, the instructions store 4 into C, :If" R=2 and B=3 :Then: 4eC PROGRAM:: 2+R: 3+BBOOLEAN :Else: 5eC :End 2-26 Math_ Angle_ and Test Operations I Contents Getting Started: Graphing a Circle ....................... Defining Graphs ......................................... Setting tile Graph Modes ................................. Defining Funetions ...................................... Selecting and Deseleeting Ftmetions ..................... Setting Graph Styles for Ptmetions ....................... Setting the Viewing Window \Tariables ................... 3-2 3-3 3-4 3-5 3-7 3-9 3-11 Setting the Graph Format ................................ DisNaying Graphs ....................................... Exploring Graphs with the Free-Mo_ng Cursor .......... 3-13 3-15 3-17 Exploring Graphs with TRACK ........................... Exploring Graphs with the ZOOM Instructions ........... Using ZOOM MEMORY .................................. Using the CALC (Calculate) Operations .................. 3-18 _-20 G-23 3-25 _ TEXAS T|=83 INSTRUMENTS J STAT PLOT TIBLSET FORMAT CALC TABLE Fllnction Graphing 3-1 Getting Getting Started: Started Graphing is a fast-paced a Circle introduction. Read the chapter for details. Graph a circle of radius 10, centered on the origin in the standard viewing window. To graph this circle, you nmst enter separate formul_ts for the upper and lower portions of the circle. Then use ZSquare (zoom square) to adjust the display- and make tile functions appear as a circle. In Func mode, press [] to display tile Y= editor. Press _ [_] 100 [] _ [] [] to enter the expression Y=f(100-X2), which defines the top half of the circle. The expression Y=-f(100-X 2) defines the bottom half of the circle. On the TI-83, you can define one function in terms of another. To define Y2=-Y1, press [] to enter the negation sign. Press FqAgg][] to display- the VARS Y-VARS menu. Then press _ to select 1:Function. The FUNCTION seeondatT menu is displayed. Press 1 to select 1:Y1. Press _ 6 to select 6:ZStandard. This is a quick way- to reset the window wu'iables to the standard values. It also graphs the functions; you do not need to press [ggAPH]. Notice that the functions appear as an ellipse in the standard xqewing window. To adjust the display- so that each pixel represents an equal width and height, press 6 to select 8:ZSquare. The functions are replotted and now appear as a circle on the display. To see the ZSquare window variables, press and notice the new values for Xmin, Xmax, Ymin, and Ymax. 3-2 Function Graphing _INOOW Xmin=-15.16129... Xmax=15.161290... XsGI=I Vnin=-lO 9max=lO Vscl=l Xres=l Defining Graphs TI-83--Graphing Mode Similarities Defining a Graph Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-83 graphing mode. Chapters 4, 5, and 6 describe aspects that are unique to paralnetric graphing, polar graphing, and sequence graphing. To define a graph steps. Some steps 1. Press (page in any graphing are not always [ff0_] and set the 3-4). mode, follow necessmT. appropriate graph these mode 2. Press [] and enter, edit, or select one or more in the Y= editor (page 3-5 and 3-7). 3. Deselect 4. stat plots, ifnecessmT Set the graph style ff)r each and define (page function 5. Press (page _ 3-11). 6. Press (page _ [FORMAT] and select 3-13). 3-7). (page the viewing functions 3-9). window the graph variables format settings Displaying and Exploring a Graph After you have defined a graph, press [ffg_] to display- it. Explore the behavior of the function or functions using the TI-83 tools described in this chapter. Saving a Graph for Later Use You can store the elements that define the current graph to any- of 10 graph database variables (GDB1 through GDBg, and GDB0; Chapter 8). To recreate the current graph later, simply recall the graph database to which you stored the original graph. These types of information • Y= functions • Graph • Window • Format style m'e stored in a GDB settings settings settings You can store a picture of the current graph display to any of 10 graph picture variables (Picl through Picg, and Pie0; Chapter 8). Then you can superimpose one or more stored pictures onto the current graph. Function Graphing 3-3 Setting the Graph Checking and Changing the Graphing Mode Modes To display- the mode screen, press [_. settings are highlighted below. To graph nmst select Func mode before you enter window vm'iables and before you enter Sci The default functions, you values for the the functions. Eng Dot Horiz The TI-83 G-T has four • Func (function • Par (parametric • Pol (polar • Seq (sequence graphing modes. graphing) graphing; graphing; Chapter Chapter graphing; 4) 5) Chapter 6) Other mode settings affect graphing describes each mode setting. • Float or 0123456789 (fixed) displayed graph coordinates. • Radian some Setting Modes from a Program or Degree functions. angle decinlal mode Connected or Dot plotting selected functions. mode • Sequential or Simul graphing-order function plotting when nlore than selected. 1 affects interpretation 'affects plotting of of mode affects one function is To set the graphing mode and other nlodes fronl a program, begin on a blank line in the program editor follow these steps. [MO_] to display- the lnode 2. Press [], [], [_, and [] to place that you want to select. 3. Press _ location. The Function Chapter nlode affects • 1. Press 3-4 results. Graphing nlode to paste is changed the Inode when and settings. the cursor name the program to the on the mode cursor is executed. Defining Functions Displaying Functions in the Y= Editor To display the Y= editor, press @. You can store up to 10 functions to tile function variables Y1 through Y9, and YO. You can graph one or more defined functions at once. In this example, functions Y1 and Y2 are defined and selected. PI,'.,LI PloLg Pl,:,t_: -,y1B4"(100-ga:) .,YaB -YI \Y_= ..Y_= ,,y_= ,,y_= -,y_= Defining or Editing a Function To define or edit a function, follow these steps. 1. Press [] to display the Y= editor. 2, Press [] to nlove the cursor to the function you want to define or edit, To erase a function, press @, 3. Enter or edit the expression to define the function. • You lnay use functions and variables (including matrices and lists) in the expression. When the expression ewduates to a nonreal number, the value is not plotted; no error is returned. • The independent variable in the function is X. Func lnode defines _ as X. To enter X, press or press @ [x]. • When you enter the first character, the = is highlighted, indicating that the function is selected. As you enter the expression, it is stored to the variable Yn as a use>defined function in the Y= editor. 4. Press [gNY_ or [] to l:love the cursor to the next function. Function Graphing 3-5 Defining a Function from the Home Screen or a Program To define begin a function on a blank fronl the home line and follow 1. Press @ @ [,], enter [-1 again. 2. Press _. Select cursor 5. Press or a prograln, steps. the expression, 3. Press _ [] 1 to select VARS Y-VARS menu, 4. screen these 1:Function and then press fl'om the the function name, which p_stes the name to the location on the home screen or program editor. _ to complete "expression the instruction. " _ Yn I"X z''÷Vt Donel "J',JtI_IX 2PI':'tt P10t;: Plot, I When the instruction is executed, the TI-83 stores the expression to the designated variable Yn, selects the function, and displays the message Done. Evaluating Y= Functions in Expressions You can calculate specified value Yn(value) Yn({valuel the value ,value2,value3, Pl*tlB. Pl*{2 P10t) \V1 2Xs-2X+6 ,,..z= xV_-= 3-6 Function Graphing of a Y= function of X. A list of values . . .,value I I returns Yn at a a list. n}) Y1 (0) 6 '_1 ._6({0, 4.2 1,2,3,4} 3.6 5.4 ) ... Selecting and Deselecting Selecting and Deselecting a Function You can functkm Functions select and deselect (turn on and turn off) a in the Y= editor. A function is selected when the = sign is highlighted. The TI-83 graphs only the selected functions. You can select any or all functions Y1 through Yg, and Y0. To select or deselect these steps. 1. Press [] a function to display 2. Move the cursor deselect. in the Y= editor, follow the Y= editor. to the function 3, Press [] to place the cursor you want to select on the functkm's 4. Press [gg_g] to change the selection or = sign. status. When you enter or edit a function, it is selected automatically. When you clem' a function, it is deselected. Turning On or Turning Off a Stat Plot in the Y= Editor To view and change the OlVOff status of a stat plot in the Y= editor, use Plot1 Plot2 Plot3 (the top line of the Y= editor). When a plot is on, its name is highlighted on this line. To change the OlgOff status of a stat plot fronl the Y= editor, press [] and [] to place the cursor on Plot1, Plot2, or Plot& and then press [g_N. _lotz Plet_ _ ",YI =. 2X 3-2X+6 \Vz= -Yt J -'1---,_ I ,_.y_=2X+XZ j \Y_= ",us = ",'¢_= J -W= I Plott isturnedon. Plot2 and Plot3 are turned off / Function Graphing 3-7 Selecting and Deselecting Functions from To select or deselect a function fronl the home screen or a program, begin on a blank line and follow these steps. the Home Screen 1. Press _ or a Program 2. Select 4:On/Off to display the ON/OFF secondary [] to display- the VANS Y-VANS menu. menu. 3. Select l:FnOn to turn on one or more functions or 2:FnOff to turn off one or more functions. The instruction you select is copied to the cursor location. 4. Enter the number (1 through 9, or 0; not the variable Yn) of each function you want to turn on or turn off. • If you enter two or more numbers, with eonunas. separate • To turn on or turn off all functions, number after FnOn or FnOff, do not enter a FnOn [function#function#,.,, FnOff[function# function# function function .... them n] n] 5, Press [ggTig], When the instruction is executed, the status of each function in the eutTent mode is set and Done is displayed. For example, in Func mode, FnOff :FnOn 1,3 turns off all functions in the Y= editor, and then turns on Y1 and Y3. FnOff 3-8 Function Graphing :FnOn Dlo3e I Pl<,tl Plo_Z Plot._ ",Y1 B. 2X_-2X+6 _,Y;_= -Y1 ",YsBXZ xy_= xY_= \Y_= ,,y_= Setting Graph Styles for Functions Graph Style Icons in the Y= Editor This table describes the graph graphing. Use the styles to be graphed together, solid line, Y2 as a dotted styles available for function to visually differentiate functions For example, you can set Y1 as a line, and Y3 as a thick line, Icon Style Description ".. Line A solid line connects plotted points; the default in Connected mode "i Thick A thick '_.i Above Shading covers the area a*bove ik Below Shading covet\_ the area below '1! Path A circular the graph cursor traces the and draws a path (! Aidmate A circular the graph cursor without ". Dot A snlall dot represents each plotted this is the default in Dot mode solid line connects plotted this is points the graph the graph leading edge of traces the leading drawing a path edge of point; Note: Some graph styles are not available in all graphing modes. Chapters 4, 5, and 6 list the styles for Par, Pol, and Seq modes. Setting the Graph Style To set the graph style for a function, the Y= editor. 1. Press [] to display 2. Press [] and [] to nlove follow the cut\sor these steps. to the function. 3. Press [] [] to move the cm'sor left, past the = sign, to the graph style icon in the first colunm. The insert cm'sor is displayed. (Steps 2 and 3 are interchangeable.) 4. Press _ repeatedly styles. The seven styles which 5. Press they are listed [], to rotate through the graph rotate in the same order in in the table [], or [] when you have above. selected a style. PlotJ. F'1ot;_P1ot:_ ",Y1B8sin(X) _YzB8cos(X) \Y_= xY_= \Y_= xy_= xy_= Function Graphing 3-9 Shading Above and Below When you select TI-83 rotates • Vertical graph _mor 1;. for two or more through lines four shade shading the first the function with a '_.1or b. style. • Horizontal lines • Negatively sloping • Positively • The rotation returns to vertical lines for the fifth '_.ior i;. function, repeating the order described above. sloping VClmn shaded Note: shade the second. diagonal lines diagonal are_Ls intersect, When _1or h_,is selected lines shade shade for a Y= function the third. the fom'th. the patterns curves, such as Yl={1,2,3}X, the four shading each member of the family of curves. Setting a Graph Style from a Program functions, patterns. overlap. that graphs patterns a family of rotate for To set the graph style fl'onl a program, select H:GraphStyle( from the PRGM CTL menu. To display this menu, press [V_ while in the program editor.function# is the nmnber of the Y= function name in the current graphing mode. graphstyle# is an integer from 1 to 7 that corresponds to the graph style, 1 = ". (line) 4 = 1'.-.(below) (animate) as shown below. 2 = '_i(thick) 8 = ':) (path) 7 = ". (dot) 3 = ,m(above) 6 = (! GraphStyle(fanction#,graphstyle#) For example, when this program is executed GraphStyle(1,3) sets Y1 to '_](above), : OisPGr'aPh 3-10 Function Graphing in Func mode, Setting the Viewing The TI-83 Viewing Window Window Variables The viewing window is the portion of the coordinate plane defined by Xmin, Xmax, Ymin, and Ymax. Xscl (X scale) defines the distance between tick marks on the x-axis. Yscl (Y scale) defines the distance between tick marks on the y-axis. To turn off tick marks, set Xscl=0 and Yscl=0. WINDOW Xmin=-lO XMax=lO Xscl=l Ymin=-lO Ymax=lO Yscl=l XPes=l _Ymax Xsc_ Xmax / _--Yscl Ymir_ N Displaying the Window Variables To display the current window variable values, press _. The window editor above and to the right shows the default values in Func graphing mode and Radian angle nlode. The window variables differ fronl one graphing mode to another. Xres sets pixel resolution only. The default is 1. • • (1 through At Xres=l, functions are evaluated pixel on the x-axis. At Xres=8, functions are evaluated eighth pixel along the x-axis. 8) for function graphs and graphed at each and graphed at every Tip: SmalIXres valuesimprovegraph resolutionbut may causethe TI-83 to draw graphs more slowly. Changing a Window Variable Value To change a window variable editor, follow these steps. value fronl the window 1. Press [] or [] to move the cut\sor to the window variable you want to change. 2. Edit the value, which can be an expression. • • Enter a new wdue, which clears the original value. Move the cursor to a specific digit, and then edit it. 3. Press [g_gff], [], or []. If you entered an expression, TI-83 ewduates it. The new value is stored. the Note: Xmin<Xmax andYmin<Ymax must be true in orderto graph. Function Graphing 3-11 Storing to a Window Variable from the Home To store a value, variable, begin Screen 1, Enter the value 2, Press _. 3, Press _ or a Program 4, can be an expression, line and follow you want to display- to a window these to store, the Func window • Press [] to display the Par and Pol window (T/0 secondm_y- menu). • Press [] [] to display the Seq window (UN/W secondary menu). variables variables variables the window variable to which you want to store The name of the variable is pasted to the current CUrSOr 6, Press steps, the VARS menu. Select 1 :Window to display (X/Y secondmT menu). 5, Select value, AX and AY which on a blank location. _ to complete the instruction. When the instruction value to the window is executed, the TI-83 stores the variable and displays the vMue. J14+Xv,ax 14J The variables AX and AY (items 8 and 9 on the VARS (1:Window) X/Y seeondmT menu) define the distance from the center of one pixel to the center of any adjacent pixel on a graph (graphing accuracy), a× and AY are calculated from Xmin, Xma×, Ymin, and Yma× when you display- a graph. AX = (Xmax - Xmin) 94 AY - (Ymax - Ymin) 62 You can store values to AX and AY. If you do, Xmax and Ymax m'e cMculated from AX, Xmin, AY,and Ymin. 3-12 Function Graphing a Setting the Graph Displaying the Format Settings Format To display- the format settings, default settings are highlighted RectGC CoordOn GridOff AxesOn LabelOff PolarGC CoordOff GridOn AxesOff LabelOn ExprOn ExprOff pl_ss [2_ below. [FORMAT]. The Sets cursor Sets Sets Sets Sets Sets coordinates display on or off. grid off or on. axes on or off. axes label oft" or on. expression display on or off. coordinates. Format. settings define a graph's appearance on the display. Format settings apply to all graphing modes. Seq graphing mode has an additional mode setting (Chapter 6). Changing a Format Setting To change a fornlat setting, follow these steps. 1. Press [_, [}_],[], and [] as necessary- to lnove the cursor to the setting you want to select. 2. Press [ggYgg]to select the highlighted RectGC, PolarGC RectGC (rectangular graphing cursor location _LSrectangular coordinates) coordinates setting. displays the X and Y. PolarGC (polar graphing coordinates) displays tile cursor location as polar coordinates R and 0. The RectGC/PolarGC setting determines which wuiables are updated when you plot tile graph, move the freenloving cursor, or trace. • • RectGC updates X and Y; if CoordOn format is selected, X and Y are displayed. PolarGC updates X, Y, R, and 0; if CoordOn format is selected, R and 0 are displayed. Function Graphing 3-13 CoordOn CoordOn, CoordOff (coordinates on) displays CoordOff (coordinates number or coordinates, GridOff, GridOn Grid points correspond GridOff does AxesOn, the cursor coordinates at the bottom of the graph, If ExprOff format is selected, the function number is displayed in the top-right corner, AxesOff off) does cover the viewing to the tick marks not display grid points. AxesOn displays the This overrides not the display- the function window in rows that (page 3-11) on each axis. grid points. GridOn displays AxesOff does not axes. display- the axes. LabelOff/LabelOn format setting. LabelOff, LabelOn LabelOff and LabelOn determine whether for the axes (X and Y), if AxesOn format ExprOn, ExprOff ExprOn and ExprOff determine whether to display- the Y= expression when the trace cursor is active. This format setting also applies to stat plots. When ExprOn is selected, the expression top-left comer of the graph screen. to display labels is also selected. is displayed in the When ExprOff and CoordOn both are selected, the number in the top-right corner specifies which function is being traced. 3-14 Function Graphing Displaying Graphs Displaying a New Graph To display Pausing or Stopping a Graph V_l_ile plotting Smart Graph the graph of the selected function or functions, press _. TRACE, ZOOM instructions, and CALC operations display- the graph automatically. As the TI-83 plots the graph, the busy indicator is on. As the graph is plotted, X and Y m'e updated. a graph, • Press [ggT_ • Press [ON]to stop; you can to pause; then then press pause press or stop [ggT_ _ graphing. to resume. to redraw. Snlart Graph is a TI-83 feature that redisplays the last graph ilnlnediately when you press _, but only if all graphing factors that would cause replotting have remained the same since the graph was last displayed. If you performed any of these actions since the graph was last displayed, the TI-83 will replot the graph based on new values when you press _. • Changed a mode setting that affects graphs • • • • • • Changed a function in the current picture Selected or deselected a function or stat plot Changed the value of a variable in a selected function Changed a window variable or graph fornlat setting Cleared drawings by selecting ¢lrDraw Changed a stat plot definition Function Graphing 3-15 Overlaying Functions on a Graph On the TI-83, Graphing a Family of Curves If you you can graph one or more new functions without replotting existing functions, For example, store sin(X) to Y1 in the Y= editor and press [_7. Then store cos(X) to Y2 and press _ again. The function Y2 is graphed on top of Y1, the original function, enter a list (Chapter 11) as an element in an expression, the TI-83 plots the function for each value in the list, thereby graphing a family of curves. In Simul graphing-order mode, it graphs 'all functions sequentiMly for the fit.st element in each list, and then for the second, and so on. {2,4,6}sin(X) 6 sin(X). graphs three functions: 2 sin(X), 4 sin(X), and Plot1 PIo_Z Plot_ _.YtB£2, 4, 6}sin(X xy?= \y_,= -.y_= ",y_= -.y_= {2,4,6}sin({1,2,3}X) graphs 2 sin(X), 4 sin(2X), and 6 sin(3X). ".YI B(2, 4, 6}sin( 1,2,3}X) \Yz = \Y_= \Y_= PI_L1 PlOL_: -.y_= ..y_= Plot. _ Note: When using dimensions. 3-16 Function Graphing '_ more than one list, the lists must have the same Exploring Free-Moving Cursor Graphs with the Free-Moving Cursor When a graph is displayed, press [], [], [], or [] to nlove tile cursor around the graph. When you first display- the graph, no cursor is visible. When you press [], [], [], or [], the cursor moves from the center of the viewing window. As you move the cursor around the graph, the coordinate values of the cursor location m'e displayed at the bottom the screen if ¢oordOn format is selected. The Float/Fix decimal mode setting determines tile number of decimal digits displayed for the coordinate wdues. of To display the graph with no cursor and no coordinate values, press @ or [gg_g]. When you press [], [], [], or [], the cursor moves froln the same position. Graphing Accuracy The flee-moving cursor nloves fronl pixel to pixel on the screen. When you move the cursor to a pixel that appears to be on the function, the cursor nlay be neat', but not actuMly on, the function. The coordinate value displayed at the bottom of the screen actuMly lnay not be a point on the function. To lnove the cursor along a function, use (page 3-18). The coordinate values displayed as you move the cursor approximate actuM math coordinates, *accurate to within the width and height of the pixel. As Xmin, Xmax, Ymin, and Ymax get closer together (as in a Zoomln) graphing accuracy ineretkqes, and the coordinate values nlore closely approxinlate the lnath coordinates. Free-moving Function cursor 'on" the curve Graphing 3-17 Exploring Graphs with TRACE Beginning a Trace Use TRACE to move the cursor from one plotted point to the next along a function• To begin a trace, press _. If the graph is not displayed already, press _ to display it. The trace cursor is on the first selected function in the Y= editor, at the middle × value on the screen• The cursor coordinates are displayed at the bottom of the screen if CoordOn format is selected. The Y= expression is displayed in the top-left corner of the screen, if ExprOn format is selected. Moving the Trace Cursor To move the TRACE cursor,., do this: • , , to the previous point, press [] or []. or next plotted •.. five plotted points on a function (Xres affects this), press [g_ [] or K_ []. •.. to any valid X value on a function, enter a value, and then press [KNT_. • fronl one function to another, press [] or []. When the trace cursor nloves along a function, the Y wdue is calculated from the X value; that is, Y=Yn(X). If the function is undefined at an X value, the Y value is blank. '_1='_-_i_*_ J ..... i / _-- -- Trace cursor on the curve ............ g:?,:LB:LLIBgR f:IL:L:LBLIT09 If you nlove the trace cursor beyond the top or bottonl the screen, the coordinate values at the bottom of the screen Moving the Trace Cursor from Function to Function continue Function appropriately. To nlove the trace cursor fronl function to function, press [] and []. The cursor follows the order of the selected functions in the Y= editor• The trace cursor moves to each function at the same × value• If ExprOn format is selected, the expression 3-18 to change of Graphing is updated. Moving the Trace Cursor to Any Valid X Value To move the trace cursor to any valid X value on the current function, enter the value. When you enter the first digit, an X= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the X= prompt. The value nmst be valid for the current viewing window. When you have coinpleted the enttT, press _ to inove the cursor. Zt Note: This feature L;t L...... does not apply to stat plots. Panning to the Left or Right If you trace a function beyond the left or right side of the screen, the viewing window automatically pans to the left or right. Xmin and Xmax are updated to correspond to the new viewing window. Quick While tracing, you can press _ to adjust the viewing window so that the cursor location beconles the center of the new xqewing window, even if the cursor is above or below the display. This allows panning up and down. After Quick Zoom, the cursor remains in TRACE. Zoom When you leave and return to TRACE, the trace cursor is displayed in the same location it was in when you left TRACE, unless Smart Graph has replotted the graph (page 3-15). Leaving and Returning to TRACE Using TRACE a Program in On a blank line in the prograln editor, press _. The instruction Trace is pasted to the cursor location. When the instruction is encountered during program execution, the graph is displayed with the trace cursor on the first selected function. As you trace, the cursor coordinate values are updated. When you finish tracing the functions, press _ to resume program execution. Function Graphing 3-19 Exploring ZOOM Menu Graphs with the ZOOM Instructions To display the ZOOM menu, press _, You can adjust the viewing window of the graph quickly- in several ways. All ZOOM instructions axe accessible fronl programs. ZOOM MEMORY i: ZBox Draws a box to define the viewing window. 2: Zoom In Magnifies the graph around the cursor. 3: Zoom Out Views more of a graph atxmnd the cursor. Zoom Cursor ZBox 4: ZDecimal Sets aX and aY to O. 1. 5: ZSquare 6: ZStandard Sets Sets equal-size pixels on the X and Y m,ces. the standard window variables. 7: 8: 9: 0: Sets the built-in trig window variables. Sets integer values on the X and Y m,ces. Sets the values for current stat lists. Fits YMin and YMax between XMin and XMax. ZTrig Zlnteger ZoomStat ZoomFit When you select 1 :ZBox, 2:Zoom In, or 3:Zoom cursor on the graph becomes the zoom cursor smaller version of the free-mo_dng cursor (+). To define a new viewing window steps, Out, the (+), a using ZBox, follow these 1, Select l:ZBox from the ZOOM menu. The zoom cursor displayed at the center of the screen. is 2. Move the zoonl cursor to any spot you want to define as a cornet" of the box, and then press [N_N. When you lnove the cm_or away- from the first defined corner, a smM1, square dot indicates the spot. 3. Press [_, E], [_, or [_. As you lnove the cursor, of the box lengthen or shorten proportionately screen. Note: To cancel ZBox before you press _, 4. When you have the graph. defined the box, press the sides on the press @. [_ to replot V]\,, ,,/' X:3,:L9J.tlBBq t:! .B2:.t:LIB3B To use ZBox to define repeat steps 2 through 3-20 Function Graphing another box within the new graph, 4. To cancel ZBox, press @. Zoom In, Zoom Zoom cursor location. Zoom Out displays a greater portion of the graph, centered on the cut\sor location. The XFact and YFact settings determine the extent of the zoom. Out In magnifies To zoom the part in on a graph, of the graph follow these 1, Check XFact and YFact (page 2, Select 2:Zoom cursor In from that surrounds the steps. 3-24); change the ZOOM menu. as needed. The zoom is displayed. 3, Move the zoom cut, or to the point center of the new viewing window, that is to be the 4, Press [gNYE_, The TI-83 adjusts the viewing window by XFact and YFact; updates the window variables; and replots the selected functions, centered on the cursor location, 5. Zoonl in on the graph in at the same • To zoom in at a new point, move point that you want as the center window, and then press [_T_]. To cancel Zoom point, select In or Zoom of two press 3:Zoom Out, press ways. [_T_]. the cm\sor to the of the new viewing Out and repeat @. ZDecimal replots the functions inunediately. It updates the window variables to preset values, tks shown below. These values set AX and AY equal to 0.1 and set the X and Y value of each pixel to one decimal place. Xmin=-4.7 Xmax=4.7 Xscl=l ZSquare in either To zoom To zoom out on a graph, steps 3 through 5. ZDecimal again • Ymin=-3.1 Ymax=3,1 Yscl=l ZSquare replots the functions immediately. It redefines the xqewing window based on the cun'ent values of the window variables. It adjusts in only one direction so that AX=AY,which makes the graph of a circle look like a circle. Xscl and Yscl remain unchanged. The midpoint of the current graph (not the intersection of the axes) becomes the midpoint of the new graph. Function Graphing 3-21 ZStandard ZStandard replots window vm'iables Xmin=-lO Xmax=lO Xscl=l ZTrig the functions immediately, It updates to the standm'd values shown below. Ymin=-lO Ymax=lO Yscl=l Xres=l ZTrig replots the functions immediately. It updates the window vm'iables to preset values that are appropriate ffw plotting trig functions. Those preset values in Radian mode m'e shown below, Xmin=-(47/24)_ Xmax=(47/24)_ Xscl=_/2 Zlnteger Ymin=-4 Ymax=4 Yscl=l Zlnteger redefines the viewing window to the dimensions shown below, To use Zlnteger, move the cursor to the point that you want to be the center of the new window, and then press [_T_]; Zlnteger replots the functions, AX=I AY=I Xscl=lO YscI=IO ZoornStat ZoomStat statistical modified ZoomFit ZoomFit replots the functions immediately, ZoomFit recalculates YMin and YMax to include the nlininmm nlmNinlunl Y values of the selected functions between current 3-22 the Function Graphing redefines the viewing window so that all data points m'e displayed. For regular and box plots, only Xmin and Xmax m'e adjusted. and the XMin and XMax. XMin and XMax are not changed. Using ZOOM ZOOM MEMORY Menu MEMORY To display the ZOOM MEMORY menu, ZOOM MEMORY 1:ZPrevious 2:ZoomSto 3:ZoomRcl 4:SetFactors... p_ss _ [_. [ _ses the pre_ious _iewing window, Stores the user-defined window, Recalls the user-defined window. Changes Zoom In and Zoom Out factors. ZPrevious ZPrevious replots the graph the graph that was displayed ZOOM instruction. ZoomSto ZoomSto inunediately stores the cmTent viewing window. The graph is displayed, and the values of the current window variables are stored in the user-defined ZOOM variables ZXres. using the window variables of before you executed the last ZXmin, ZXmax, ZXscl, ZYmin, ZYmax, ZYscl, and These variables apply to all graphing modes. For example, changing the value of ZXmin in Func nlode also changes it in Par mode, ZoomRcl ZoomRcl graphs viewing window. determined instruction. user-defined the selected functions in a user-defined The user-defined viewing window is by the values stored with the ZoomSto The window variables are updated with values, and the graph is plotted. Function Graphing the 3-23 ZOOM FACTORS The zoonl XFact and YFact, are positive factors, numbers (not necessarily intege_\_) greater than or equal to 1, They define the magnification or reduction factor used to Zoom In or Zoom Out around a point, Checking XFact and YFact To display the ZOOM FACTORS screen, where you can t_iew the current values for XFact and YFact, select 4:SetFactors from the ZOOM MEMORY menu. The values shown m'e the defaults. I XFacL=4 ZOOM FRCTORS VFact=4 Changing XFact and YFact Using ZOOM MEMORY Menu Items from the Home Screen a Program You can change XFact and YFact in either of two ways. • Enter a new automatically • Place the cursor on the digit you want to change, then enter a value or press [bE[] to delete it, From the home value. The original value is cleared when you enter the first digit. screen or a program, to any of the user-defined you can store and directly ZOOM vm'iables. or 1-5÷ZXr_in: 5÷ZXr_,a5 From a program, you can select the ZoomSto and ZoomRcl instructions fronl the ZOOM MEMORY menu. 3-24 Function Graphing Using the CALC CALCULATE Menu (Calculate) To display items the CALCULATE on this menu CALCULATE i: value 2: zero 3: minimum 4: maximum nlenu, to analyze press I_ tile current [CALC], Use the graph functions, Calculates a function Y value for a given X, Finds a zero (x-intercept) of a function. Finds a nlininmln of a function, Finds a nlaxinmln of a function. Finds an intersection of two functions, Finds a numeric derivative of a function. Finds a numeric integral of a function, 5:intersect 6:dy/dx 7:ff(x)dx value Operations value evaluates one or more currently for a specified value of X. selected functions Note: Whena value is displayedfor X, press[_ to clear the value. When no value is displayed, press @ to cancel the value operation. To evaluate a selected function at X, ff)llow these steps. 1, Select 1:value froln the CALCULATE menu, The graph is displayed with X= in tile bottom-left corner. 2, Enter a real value, which can be an expression, between Xmin and Xmax. for X 3. Press IE_]. "7i7.J The cursor is on the first selected function in the Y= editor at the X value you entered, and the coordinates are displayed, even if ¢oordOff fornlat is selected. To nlove the cm'sor fl'om function to function at the entered X value, press [] or [], To t_store the free-re(Mug cursor, press [] or []. Function Graphing 3-25 zero zero finds a zero solve(. Functions value; zero finds (x-intercept or root) can have more the zero closest of a function using than one x-intercept to your guess. The time zero spends to find the eotTect zero value depends on the accuracy of the values you specify for the left and right bounds and the accuracy of your guess. To find a zero of a function, 1. Select graph 2:zero froln is displayed follow these the CALCULATE with steps. menu. The current Left Bound? in the bottom-left corner. 2_ Press [] or [] to move the cm\sor which you want to find a zero. onto the function %r 3. Press [] or [] (or enter a value) to select the x-value for the left bound of the interval, and then press I_T_. A indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottom-left corner. Press [] or [] (or enter a value) to select the x-value for the right bound, and then press IT_. A _ indicator on the graph displayed screen shows the right bound. in the bottom-left corner. Press [] or [] (or enter the zero of the function, press [_T_]. a value) between Guess? is then to select a point near the bounds, and then ZCYO The cursor is on the solution and the coordinates are displayed, even if ¢oordOff format is selected. To move to the same x-value for other selected functions, press [] or []. To restore the free-moving cursor, press [] or []. 3-26 Function Graphing minimum, maximum minimum and maximum find a ndninmln or nl3xinlunl of a function within a specified inteP_+al to a tolerance of 1E-5. To find a nlininlunl Or nlaxinlunl, follow these steps. 1. Select 3:minimum or 4:maximum fronl the CALCULATE nlenu. The current graph is displayed. 2. Select the function and set left bound, right bound, and guess _ts described for zero (steps 2 through 4; page 3-26). The cursor is on the solution, and the coordinates ate displayed, even if you have selected CoordOff format; Minimum or Maximum is displayed in the bottom-left c()rner. To nlove to the salne x-value for other selected functions, press [] or []. To restore the free-moving cursor, press [] or intersect []. intersect finds the coordinates of a point at which two or nlore functions intersect using solve(. The intersection nmst appear on the display to use intersect. To find an intersection, follow these steps. 1. Select 5:intersect fi'om the CALCULATE menu. The current graph is displayed with First curve? in the bottom-left corner. c >.J Fit_t ll=0 cul_ve? € * Y=.5 2. Press [] or [], if necessatT, to nlove the cursor to the first function, and then press [gg7_. Second curve? is displayed in the bottom-left corner. 3. Press [] or [], if necessatT, to nlove the cursor to the second function, and then press [gg7_. 4. Press [] or [] to nlove the cursor to the point that is your guess as to location of the intersection, and then press [gfff_. The cursor is on the solution and the coordinates are displayed, even if CoordOff format is selected. Intersection is displayed in the bottom-left corner. To restore the freemoving cursor, press [], [], [], or []. Function Graphing 3-27 dy/dx dy/dx (numerical (slope) derivative) of a function finds at a point, To find a function's slope 1, Select 6:dy/dx from graph is displayed. the numerical with at a point, the follow CALCULATE 2, Press [] or [] to select the function to find the numerical derivative. 3, Press [] or [] (or enter a value) which to calculate the deriwttive, The cursor is on the solution derivative e= 1E-3, these menu. steps, The current for which you want to select the X value at and then press [_TE_. and the numerical derivative is displayed. To move to the same x-value for other selected functions, press [] or [], To _store the free-moving cursor, press [] or ff(x)dx []. j'f(x)dx (numerical integral) finds the numerical integral of a function in a specified inte[w'al, It uses the fntnt( function, with a tolerance of e= 1E-3. To find the numerical derivative of a function, follow these steps. 1, Select 7:jf(x)dx from the CALCULATE menu. The current graph is displayed with Lower LimR? in the bottom-left corner. 2, Press [] or [] to move the cm\sor to the function which you want to calculate the integral. for 3, Set lower and upper limits as you would set left and right bounds for zero (step 3; page 3-26). The integral value is displayed, and the integrated area is shaded. ;'t=X_-3_÷:1. [ J ,,f'I-J, LeLOeV Limit? _= - 1 • _II I, Sf(x)4x=_._Z?_li7 Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or any action that invokes Smart Graph to clear the shaded area. 3-28 Function Graphing 4 Contents Parametric Graphing Getting Started: Path of a Ball ........................... Defining and Displaying Parametrie Graphs .............. Exploring Parametric Graphs ............................ _ TEXAS 4-2 4-4 4-7 TF83 INSTRUMENTS / J STAT PLOT TBLSET FORMAT CALC TABLE Parametric Graphing 4-1 Getting Getting Started: Started Path of a Ball is a fast-paced introduction. Read the chapter for details. Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal from ground level. How fat" does the ball travel? When does it hit the ground? How high does it go? Ignore all forces except gravity. For initial velocity v0 and angle 0, the position has horizontal and vertical components. Horizontal: Vertical: The vertical X1 (t)=tv0cos(0) Y1 (t)=tv0sin(0)and horizontal Vertical vector: Horizontal vector: Gravity constant: vectors of the bali's motion also will be graphed. X2(t)=0 Y2(t)=Yl(t) X3(t)=Xl(t) Y3(t)=0 g=9,8 m/see 2 Press @. Press 30 _ [_ [ANGLE] I (to select °) [] [_ XITin terms of T. 4. 26 [_ to define _ 28 [_ [ANGLE]1 [] [] [] _ to define YIT. The vertical component by X2Tand Y2T. vector is defined Press 0 [ggY_ to define X2T. Press [_ [] to display the VARS Y-VARS menu, Press 2 to display the PARAMETRIC secondmT nlenu, Press 2 [gN?_7to define Y2T, 4-2 Parametric Graphing of time 1 , g gt 2 Press [_3_. Press [] [] [] [] [_ to select Par mode. Press [] [] [] [_ to select 8imul R)r sinmltaneous graphing of all three parametric equations in this example. Press 30 _ 9.8 [] 2 _ of the ball as a function The horizontal component defined by X3Tand Y3T, vector is PI,:,I:t Press [gAg_ [] 2, and then press 1 [gNTgglto define X3T.Press 0 [gNT_ to define Y3T. PI,:,L> PlOI:3 91T B30Tsin (25 ° ) -9.8/2TZ xXzT Be VaT B'¢1T ",X_T BX1T V St 1_10 \X_T Press [] [] [] _ to change the graph style to 5 for X3Tand Y3T. Press [] [gNY_ [gNT_ to change the graph style to .41! for X2Tand Y2T. Press [] [gNY_ [gNT_ to change the graph style to "0for XlT and Y1T. (These keystrokes _tssume that all graph styles were set to "..originally.) Press _. Enter these values for the window variables. Tmin=0 Tmax=5 Xmin=-10 Xmax=100 Ymin=-5 Ymax=15 Tstep=,l Xscl=50 Yscl=10 Press [g_ [FORMAT] [] [] [] [] F_ AxesOff, which turns off the axes. = Plo_t PloLZ Plot3 _XITB30Tcos(25 °) YITB30Tsin(25 -9.8/2TZ _XZT B0 YZT BYI T °) _T _1 T WINDOW STsteP=,l XMin=-lO gMax=100 Xscl=50 Vmin=-5 Vmax=15 Vsol=lO PolarGC CoordO££ GridOn to set xPrO_£ 10. Press _. The plotting action sinmltaneously shows the ball in flight and the vertical and horizontal component vectors of the motion. /---_,. Tip: To simulate the ball flying through the air, set graph style to _)(animate) for XIT and YIT. 1 1. Press _ to obtain numerical results and answer the questions at the beginning of this section. glT=3OTcg¢_;(_ Y1T=30TSin(_:_ Tracing begins at Tmin on the first pm'ametric equation (X1Tand Y1T), As you press [] to trace the curve, the cursor follows the path of the ball over time. The values for X (distance), Y (height), and T (time) are displayed at the bottom of the screen. Parametric Graphing 4-3 Defining and Displaying Parametric Graphs TI-83 Graphing Mode Similarities The steps for defining a parametric graph are similar to the steps for defining a function graph. Chapter 4 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 4 details aspects of parametric graphing that differ from function graphing. Setting Parametric Graphing Mode To display- the mode screen, press NgffE].To graph parametric equations, you nmst select Par graphing mode before you enter window wu'iables and before you enter tile components of parametric equations. Displaying the Parametric Y= Editor After selecting Par graphing _arametric Y= editor. mode, press [] to display the P10L1 Plo_:2 Plot3 _.X1T=11 YtT---- ,,X;_T= 'y';_V= \X_T= y__T= In this editor, you can display and enter both the X and Y conlponents of up to six equations, X1T and Y1T through X6T and YST. Each is defined in terms of the independent variable T. A common application of parametric graphs is graphing equations over time. Selecting a Graph Style 4-4 Parametric The icons to the left of XIT through X6Trepresent the graph style of each parametric equation (Chapter 3). The default in Par mode is "..(line), which connects plotted points. Line, '_i (thick),-(! (path), (!(animate), and ". (dot) styles are available for parametric graphing. Graphing Defining and Editing Parametric Equations To define or edit a parametric equation, • Press • [email protected] the steps in _. [T]. Two components, X and Y, define a single equation. You nmst define both of them. Selecting and Deselecting Parametric Equations follow Chapter 3 for defining a function or editing a function. The independent variable in a paralnetrie equation is T. In Par graphing mode, you can enter the paralnetric variable T in either of two ways. parametric The TI-83 graphs only the selected parametric equations. In the Y= editor, a parametric equation is selected when = signs of both the X and Y components are highlighted. You may select any or all of the equations XIT and YIT through the X6T and Y6T. To change the selection status, move the cursor onto the = sign of either the X or Y colnponent and press [gNYE_. The status of both the X and Y components is changed. Setting Window Variables To display" the window variable values, press _. These vmiables define the viewing window. The values below are defaults for Par graphing in Radian angle mode. Tmin=O Tmax=6.2831853,.. Tstep=.1308996... Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1 Smallest T v'Mue to evaluate Largest T value to evaluate (2x) T value increment (x/24) SmMlest X vMue to be displayed Largest X value to be displayed Spacing between the X tick nlarks SmMlest Y vMue to be displayed Largest Y value to be displayed Spacing between the Y tick marks Note: To ensure that sufficient points are plotted, change the T window variables. Parametric you may want to Graphing 4-5 Setting the Graph Format To display- the current graph format Displaying a Graph When you press _, the TI-83 plots the selected parametric equations, It evaluates the X and Y components for each value ofT (fronl Tmin to Tmax in intel_'als of Tstep), and then plots each point defined by X and Y. The window vm'iables define the viewing window. As the graph is plotted, You can • • perform these actions Access functions by using component of the equation *.5 graphs (Chapter fronl the home 3). screen or a Store • Select parametric Store 1 values 360÷Tnax Graphing equations. "÷Yi TD°neT "÷Xl Done or deselect FR0t'f" • the name of the X or Y as a vm'iable. -, 94. r0916375 "cos(T) "sin(T) Parametric [_ program. NiT 4-6 press X, Y, and T m'e updated. Snlart Graph applies to parametric Window Variables and Y-VARS Menus settings, [FORMAT], Chapter 3 describes the format settings in detail, The other graphing modes share these format settings; $eq graphing mode has an additional axes format setting, \XzT="Xl Bsin(T)yzT=Vin°tIT T Bcos(T)nOtz nots parametric equations, Done Pl0tl =cos(T) ,otz ,,t, ",XlT YiT=sin(T) xXzT= YZT= directly to window 360 variables. I I I Exploring Free-Moving Cursor Parametric The Graphs free-lnoving cursor in Par graphing In RectGC format, nloving X and Y; if CoordOn format displayed. In PolarGC format, format is selected, TRACE works the salne as the cursor updates the values is selected, X and Y are of in Func graphing. X, Y, R, and 0 are updated; R and 0 m'e displayed. if CoordOn To activate TRACE, press _. When TRACE is active, you can nlove the trace cursor along the graph of the equation one Tstep at a time. When you begin a trace, the trace cursor is on the first selected function at Train. If ExprOn is selected, then the function is displayed. In RectGC format, TRACE updates and displays the vMues of X, Y, and T if CoordOn format is on. In PolarGC format, X, Y, R, 0 and T are updated; if CoordOn format is selected, R, 0, and T are displayed. The X and Y (or R and 0) values are calculated from T. To nlove five plotted points at a time on a function, press [] or [2ffd][_. If you nlove the cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately. Quick Zoom is available (Chapter 3). in Par graphing; Parametric panning is not Graphing 4-7 Moving the Trace Cursor to Any Valid T Value To move the trace cursor to any valid current function, enter the first digit, a T= prompt and displayed in the bottom-left enter an expression at the valid for the current _ewing colnpleted the ent_% press T value on the number, When you enter the the number you entered are corner of the screen. You can T= prompt, The wdue nmst be window, When you have [K_Y_ to lnove the cursor. PIoI:I PloL2 Plot_ _.X1 T _sir,(T) YtT_T XIT=S;n(T) XIT=_;ifl(T) T=2 ZOOM _,Ii ( _IT=T T=T } T=;_ ZOOM operations in Par graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window vm'iables are affected. The T window vm'iables (Train, Tmax, and Tstep) are only'affected when you select ZStandard. The MARS ZOOM seeondm_y- menu ZT/Z0 items 1 :ZTmin, 2:ZTmax, and 3:XTstep are the zoom memory variables for Par graphing. CALC 4-8 CALC operations in Par graphing work the same as in Func graphing. The CALCULATE menu items available in Par graphing are 1:value, 2:dy/dx, 3:dy/dt, and 4:dx/dt. Parametric Graphing Polar Graphing Contents Getting Started: Polar Rose .............................. Defining and Displaying Polar Graphs ................... Exploring Polar Graphs .................................. TEXAS 5-2 5-3 5-6 T1=83 INSTRUMENTS J STAT PLOT TBLSET FORMAT CALC TABLE Polar Graphing 5-1 Getting Getting Started: Started Polar Rose is a fast-paced introduction. Read the chapter for details. The polar equation R=Asin(B0) graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B. Press _ to display the mode screen. Press [] [] [] [] [] [gfff_] to select Pol graphing mode. Select the defaults (the options on tile left) for the other nlode settings. Plot:t Plot2 Plot3 _rl B8sin(2.50) \r_:= i_.r_ = Press [] to display- the polar Y= editor. Press 8 NTN2.6 _ [] [g_gO to define %rfi= rl. 3. Press _ 6 to select 6:ZStandard and graph the equation in the standard viewing window. The graph shows only five petals of the rose, and the rose does not appear to be synunetrical. This is because the standard window sets 0max=2= and defines the window, rather than the pixels, as square. 4. Press _ to display the window variables. Press [] 4 [gfi_ [_] to increase value of 0max to 4x. 5, Press _ the graph. the 5 to select 5:ZSquare and plot Repeat steps 2 through 5 with new values for the variables A and B in the polar equation rl=Asin(B0). Observe how the new values 'affect the graph. 5-2 Polar Graphing WINDOW Omin=O OMaX=4X Ostee=,1308996... XMin=-lO Xmax=lO XSCI=I _VMin=-lO Defining and Displaying steps Polar Graphs TI-83 Graphing Mode Similarities The for defining a polar graph are similar Setting Polar Graphing Mode To display- the mode screen, press [M6_]. To graph polar equations, you nmst select Pol graphing mode before you enter values for the window variables and before you enter polar equations. Displaying the Polar Y= Editor After selecting Pol graphing _olar Y= editor. for defining a function graph. Chapter are familiar with Chapter 3: Function details aspects of polar graphing that graphing. PI,:,I:I PloL2 \rl= \i-- 2---M-_ 3:= \1,-, tl = \1.'. _ = \p6= mode, to the steps 5 assumes that you Graphing. Chapter 5 differ from function press [] to display- the Plot3 In this editor, you can enter and display up to six polar equations, rl through r6. Each is defined in terms of the independent variable 0 (page 5-4). Selecting Styles Graph The icons to the left of rl through r6 represent the graph style of each polar equation (Chapter 3). The default in Pol graphing mode is "..(line), which connects plotted points. Line, "i (thick), -(! (path), (! (animate), and ". (dot) styles are available for polar graphing. Polar Graphing 5-3 Defining and Editing Polar Equations Selecting and Deselecting Polar Equations To define or edit a polar equation, follow the steps • Press • [email protected] _. [0]. The TI-83 graphs only the selected polar equations. In the Y= editor, a polar equation is selected when the = sign is highlighted. You nlay select any- or M1 of the equations. To change the selection status, nlove the cursor = sign, and then press [_. Setting Window Variables Ostep=.1308996... Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1 SmMlest 0 value to evMuate Largest 0 vMue to evaluate (2=) Increment between @values (=/24) SmMlest X vMue to be displayed Largest X value to be displayed Spacing between the X tick marks SmMlest Y value to be displayed Largest Y value to be displayed Spacing between the Y tick marks Note: To ensure that sufficient points are plotted, change the 0 window variables. Polar onto the To display- the window variable values, press _. These variables define the viewing window. The values below are defaults for Pol graphing in Radian angle mode. Omin=O Omax=6.2831853,.. 5-4 in Chapter 3 for defining a function or editing a function. The independent vm'iable in a polar equation is 0. In Pol graphing mode, you can enter the polar variable 0 in either of two ways. Graphing you may want to Setting the Graph Format To display the current graph format settings, press [2_] [FORMAT].Chapter 3 describes the forlnat settings in detail. The other graphing lnodes share these format settings. Displaying a Graph When you press _, the TI-83 plots the selected polar equations. It evMuates R for each value of 0 (from 0min to 0max in intervals of 0step) and then plots each point. The window variables define the viewing window. As the graph is plotted, Window Variables and Y-VARS Menus X, Y, R, and 0 are updated. Slnart Graph applies to polm" graphs (Chapter You the can perfornl these actions fronl honle 3). screen or a program. • Access functions wuiable by using the name of the equation rl +r.z • 8 Store polar equations, "51_1"÷1"i • • as a Done \r?:=\rll_5OPl°tl P10t_: Select or deselect polar equations. FnOff Done 1 Plott xr I =50PIotZ Plot_ Store values directly to window IO+Orqih Plot3 I I I variables. OI Polar Graphing 5-5 Exploring Polar Graphs ffee-mo_ing cursor in Pol graphing Free-Moving Cursor The works the same as TRACE To activate TRACE, press _. When TRACE is active, you can nlove the trace cursor along the graph of the equation one 0step at a time. When you begin a trace, tile trace cursor is on the first selected function at 0min. If ExprOn fornlat is selected, then the equation is displayed. in Func graphing. In RectGC fonnat, moving tile cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and 0 are updated; if CoordOn format is selected, R and 0 m'e displayed. In RectGC format, TRACE updates the values of X, Y, and 0; if CoordOn format is selected, X, Y, and 0 are displayed. In PolarGC format, TRACE updates X, Y, R, and 0; if CoordOn format is selected, R and 0 m'e displayed. To nlove five plotted points at a time on a function, press Kffa][] or Kffa][Z]. If you move tile trace cursor beyond tile top or bottonl of the selden, the coordinate values at the bottonl of the screen continue to change appropriately. Quick Zoom is available not (Chapter 3). in Pol graphing mode; panning is Moving the Trace Cursor to Any Valid e Value To nlove the trace cursor to any valid 0 value on the current function, enter the number. When you enter the first digit, a 0= prompt and the number you entered are displayed in tile bottom-left corner of tile screen. You can enter an expression at the 0= prompt. The value must be valid for the current viewing window. When you complete tile enhT, press _ to nlove the cursor. ZOOM ZOOM operations in Pol graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected. The 0 window variables (0rain, 0max, and Ostep) are not 'affected, except when you select ZStandard. The VARS ZOOM seeondmTy- menu ZT/ZO items 4:Z0min, 5:Z0max, and 6:Z0step m'e zoom nlemoKy-varialfles ff_r Pol graphing. CALC 5-6 CALC operations in Pol graphing work the sanle graphing. The CALCULATE nlenu items available graphing are 1:value, 2:dy/dx, and 3:dr/d0. Polar Graphing as in Func in Pol Sequence Graphing Contents Getting Started: Forest and Trees ........................ Defining and Displaying Sequence Graphs ............... Selecting Axes ('ombinations ............................ Exploring Sequence Graphs .............................. Graphing Web Plots ...................................... Using Web Plots to Illustrate Convergence ............... Graphing Phase Plots .................................... Comparing TI-83 and TI-82 Sequence Variables .......... Keystroke Differences Between TI-83 and TI-82 ......... '_ TEXAS 6-2 6-3 6-8 6-9 6-11 6-12 6-13 6-1.5 6-16 T1=83 iNSTRUMENTS u= -.Bu(7_-:1.)+3.6 -,_ I= -% l ........ >'_=:L5 X=l.F_61172 I' .... "_ "%_ i'=1._ _:61172 J STATPLOT TBLSET FORMAT CALC TABLE Sequence Graphing 6-1 Getting Getting Started: Started Forest and Trees is a fast-paced introduction. Read the chapter for details. A small forest of 4,0!)0 trees is under a new forestw plan. Each year 20 percent of the trees will be hmwested and 1,000 new trees will be planted. Will the forest eventually- disappear? Will the forest size stabilize? If so, in how many yeat\_ and with how many trees? Press IM65E].Press [] [] [] [] [] [] IgffTgR] to select Seq graphing mode. Soi Eng 0123456789 Degree ar Pol Press [_ [FORMAT] and select Time axes format and ExprOnformat if neeessatT. 3. Press @. If the graph-style icon is not ". (dot), press [] [], press [g_-gRquntil ". is displayed, and then press [] []. 4. Press [_ [] a to select iPart( (integer pro't) because only whole trees are harvested. After each annual hatw'est, 80 percent (.80) of the trees remain. Press [] 8 [_ [u] [] _ [] 1 [] to define the number of trees after each harvest. Press [] 1000 [] to define the new trees. Press [] 4000 to define the number of trees at the beginning of the program. 5. MW UW PI_I PI_tZ Plot3 _Min=l '..u(_bBiPart(.Bu( _-I)+1000) u(_Min)B4000 ".v(_)= v(_Min)= ".u(_)= Press [_ 0 to set nNin=0. Press [] 60 to set nNax=fi0, nNin and nMax evaluate forest size over 50 years. Set the other window variables. PlotStart=l Xmin=0 Ymin=0 PlotStep=l Xmax=50 Xscl=10 Ymax=6000 Yscl=1000 Press _. Tracing begins at nMin (the start of the foresttT plan). Press [] to trace the sequence year by year. The sequence is displayed at the top of the screen. The values for n (number of years), X (X=n, because n is plotted on the x-axis), and Y (tree count) are displayed at the bottom. When will the forest stabilize? With how many trees? 6-2 UM PolaPGC CoopdO_ GridOn RxesO_ LabelOn Sequence Graphing lu=iPart(.Bu(_-l)+lOO0) I Defining and Displaying Sequence Graphs TI-83 Graphing Mode Similarities The steps for defining a sequence graph are similar to the steps for defining a function graph. Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 6 details aspects of sequence graphing that differ froln function graphing. Setting Sequence Graphing Mode To display- the mode screen, press [M6D_.To graph sequence functions, you nmst select 8eq graphing mode before you enter window wu'iables and before you enter sequence functions. Sequence graphs automatically plot in Simul mode, regardless of the current plotting-order mode setting. TI-83 Sequence Functions u, v, and w The TI-83 has three sequence functions that you can enter from the keyboard: u, v, and w. They are above the [7], [], and [] keys. You call define sequence • • • • functions in terms off The independent variable n The previous term in the sequence function, such as u(n-1) The term that precedes tile previous term in tile sequence function, such as u(n-2) The previous term or the term that precedes the previous term in another sequence function, such as u(n-1) or u(n-2) t_ferenced in the sequence v(n). Note: Statements in this chapter about u(n) are also true for v(n) and w(n); statements about u(n-1) are also true for v(n-1) and w(n-1); statements about u(n-2) are also true for v(n-2) and w(n-2). Sequence Graphing 6-3 Displaying the Sequence Y= Editor After selecting Y= editor. Seq mode, press [] to display- the sequence nMin=l ",.u(n)= u(nMin)= "..v(n)= v(nMin)= "..u(n)= u(nMin)= In this editor, you can display and enter sequences for u(n), v(n), and w(n), Also, you can edit the value for nMin, which is the sequence window variable that defines the nlininluln n value to evaluate. The sequence Y= editor displays the nMin value because of its relevance to u(nMin), v(nMin), and w(nMin), which are the initial values for the sequence equations u(n), v(n), and w(n), respectively. nMin in the Y= editor is the same as nMin in the window editor. If you enter a new value for nMin in one editor, the new value for nMin is updated in both editors. Note: Useu(nMin), v(nMin), or w(nMin) only with a recursive sequence,which requires an initialvalue. Selecting Styles Graph Selecting and Deselecting Sequence Functions The icons to the left of u(n), v(n), and w(n) graph style of each sequence (Chapter 3). $eq mode is ". (dot), which shows discrete "..(line), and "i (thick) styles m'e available graphing. Graph styles m'e ignored in Web The TI-83 graphs only the selected sequence functions. In the Y= editor, a sequence function is selected when the = signs of both u(n)= and u(nMin)= are highlighted. To change move the then press sequence 6-4 Sequence represent the The default in values. Dot, for sequence format. Graphing the selection status of a sequence function, cut\sor onto the = sign of the function name, and [g_. The status is changed for both the function u{n) and its initial value u(nMin). Defining and Editing a Sequence Function To define or edit a sequence function, follow the steps in Chapter 3 for defining a function. The independent vmiable in a sequence is n. In Seq graphing mode, you can enter the sequence in either of two ways. • • vmiable Press _. Press [g67][CATALOG][N]. You can enter the function name from the keyboard. • • To enter the function To enter the function name u, press [gh_][u] (above [_). name v, press [g6_ [v] (above [_). • To enter the function name w, press [g67][w] (above [_). Generally, sequences are either nonrecursive or recursive. Sequences are evaluated only at consecutive integer values, n is always a series of consecutive integers, starting at zero or any positive integer. Nonrecursive Sequences In a nonrecursive sequence, the nth term is a function of the independent variable n. Each term is independent of all other terms. For example, in the nonrecursive sequence below, you can calculate u(6) directly, without fit\_t calculating u(1) or any %exdous terlll, PloL1 PloL2 Plot3 _Hin=l ,.u(_)B2*n u(_Min)B "..v(_)= v(_Min)= "'.u(_)= u(_Min)= The sequence 2, 4, 6, 8,10, equation above returns the sequence . . . for n = 1,2,3,4,5,.... Note: You may leave blank the initial value u(nMin) when calculating nonrecursive sequences. Sequence Graphing 6-5 Recurslve In a reem\Mve Sequences defined in relation to the previous term or the term that precedes the previous term, represented by u(n-1) and u(n-2). A reem\Mve sequence may also be defined in relation to n, as in u(n)=u(n- 1)+n. For example, u(5) without sequence, the nth term in the sequence first calculating plo1:1 PloL2 pl,:a:_: _Min=l "..u(_)B2*u(n-1 ) in the sequence is below you cannot calculate u(1), u(2), u(3), and u(4). I I u(.n[_in)B1 Using an initial value u(nMin) = 1, the sequence returns 1, 2, 4, 8, 16,... above Tip: On the TI-83, you must type each character of the terms. For example, to enter u(n-1), press _ [u] [] _ [] [] lB. Recursive sequences since they reference • require an initial undefined terms. If each term in the sequence pre_dous term, as in u(n-1), value for the first tenn. PloLi plol:._ [-2) u(r_Min)B{l,O term 6-6 Sequence Graphing value sequence is defined in relation to the the previous term, as in u(n-2), you values for the first two terms. Enter a list enclosed in braees ({ }) with the values. Plot3 nMin=l I..u(n)Bu(n-1 The is defined in relation to the you nmst specify an initial 1 )+5 If each term in the term that precedes nmst specify- initial the initial values as commas separating PloI:2 or values, Plot3 nMin=l ..u (n) B. 8u (n0 u(nMin)B100 Plot't value of the first )+u(n } term is 1 for the sequence is 0 and the value u(n). of the second Setting Window Variables To display- the window variables, press _, These variables define the viewing window. The values below are defaults for Seq graphing in both Radian and Degree angle nlodes, nMin=1 nMax:10 PlotStart:1 PlotStepffil Xmin:-10 Xmax=lO Xscl=l Ymin=-lO Ymax=lO Yscl=l Smallest n value to ev'gduate Largest n value to evaluate First term number to be plotted Incremental n value (for graphing only) Smallest X value to be displayed Largest X value to be displayed Spacing between the X tick marks Smallest Y value to be displayed Largest Y value to be displayed Spacing between the Y tick marks nMin must be an integer k O, nMax, PlotStart, and PlotStep nmst be integers _>1, nMin is the smallest n wdue to evaluate, nMin also is displayed in the sequence Y= editor, nMax is the largest value to evaluate. Sequences are evaluated at u(nMin), u(nMin+l), u(nMin+2), ... , u(nMax). n PlotStart is the first term to be plotted. PlotStart=l begins plotting on tile first term in tile sequence. If you want ph)tting to begin with the fifth term in a sequence, for exalnple, set PlotStart=& The first four terms are evaluated but are not plotted on the graph. PlotStep is the incremental n wdue for graphing only. PlotStep does not 'affect sequence evaluation; it only designates which points are plotted on the graph. If you specify PlotStep=2, the sequence is ewduated at each consecutive integer, but it is plotted on the graph only at evew other integer. Sequence Graphing 6-7 Selecting Axes Combinations Setting the Graph Format To display- the current graph Time Web uv vw uw RectGC PolarGC CoordOn CoordOff GridOff GridOn AxesOn AxesOff LabelOff LabelOn ExprOn Setting Axes Format format settings, press [_ [FORMAT], Chapter 3 describes the format settings in detail, The other graphing modes share these format settings, The m,ces setting on the top line of the screen is available only in Seq mode, ExprOff Type of sequence plot (m,ces) Rectangular or polar output Cursor coordinate display mdoff Grid display off or on Axes display on or off Axes label display- off or on Expression display on or off For sequence graphing, you can select fronl five axes formats. The table below shows the values that are plotted on the x-axis and y-m'ds for each axes setting. Axes Setting Time Web uv vw uw x-axis y-axis n u(n), v(n),w(n) u(n-1), v(n-1),w(n-1) u(n), v(n),w(n) u(n) v(n) u(n) v(n) w(n) w(n) See pages 6-11 and 6-12 for nlore information on Web plots. See page 6-13 for more information on phase plots (uv, vw, and uw m,ces settings). Displaying a Sequence Graph To plot the selected sequence functions, press _. graph is plotted, the TI-83 updates X, Y, and n. Snlart Graph applies to sequence 6-8 Sequence Graphing graphs (Chapter As a 3). Exploring Sequence Free-Moving Cursor The TRACE The Graphs free-moving cursor in Seq graphing works the same as in Func graphing. In RectGC fonnat, nloving tile cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC fornlat, X, Y, R, and 0 are updated; if CoordOn format is selected, R and 0 m'e displayed. axes fornlat setting affects TRACE. When Time, uv, vw, or uw axes format is selected, TRACE moves the cursor along the sequence one PlotStep increment at a time. To nlove five plotted points at once, press [_ [] or [_ []. • • When you begin a trace, the trace cursor is on the first selected sequence at the term number specified by PlotStart, even if it is outside the viewing window. Quick Zoom applies to all directions. To center the viewing window on the current cursor location after you have moved the trace cursor, press [_. The trace cursor t_tun_s to nMin. In Web format, the trail of the cursor helps identify points with attracting and repelling behavior in the sequence. When you begin a trace, the cursor is on the x-axis at the initial wdue of the first selected function. Tip: To move the cursor to a specified n during a trace, enter a value for n, and press _. For example, to quickly return the cursor to the beginning of the sequence, paste nMin to the n= prompt and press Moving the Trace Cursor to Any Valid n Value To nlove the trace cursor to any valid n vMue on the current function, enter the number. When you enter the first digit, an n = prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the n = prompt. The value nmst be valid for the current viewing window. When you have completed the entKy-,press [gfff_ to move the cursor. U=U(:O-1)+U(:O-Z) I . , . :": " ;o=_: "" Sequence Graphing }1=5"I_ ?=3 6-9 ZOOM ZOOM operations in Seq graphing work the same as in Func graphing, Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected. PlotStart, PlotStep, nMin, and nMax are only affected when you select ZStandard. The VARS Zoom secondary lnenu ZU items 1 through 7 are the ZOOM MEMORY variables for Seq graphing. CALC The only CALC operation Evaluating u, v, and w is value. When Time axes format is selected, u(n) value) for a specified n value. • When Web axes format is selected, value draws the web and displays Y (the u(n) value) for a specified n value, • When uv, vw, or uw axes format is selected, value displays X and Y according to the axes format setting. For example, for uv axes format, X represents u(n) and Y represents v(n), value displays Y (the To enter the sequence names u, v, or w, press [2_] [u], [v], or [w], You can evaluate these names in any- of three ways, Calculate the nth value in a sequence. Calculate a list of values in a sequence. Generate a sequence with u(nstart,nstop[,nstep]), is optional; default is 1. "nz"+u:u(3) u({1,3,5,7,9}) {i 9 25 49 u(1,9,2) {1 9 25 49 Sequence in Seq graphing • • • • 6-10 available Graphing 9 81} 81} nstep Graphing Web Plots Web axes To select Valid Functions for Web Plots V_l_en Web axes format is selected, a sequence graph properly or will generate an error. Displaying the Graph Screen format, press [FORMAT] [] Graphing a Web Plot [_ [E_], A web plot graphs u(n) versus u(n-1), which you can use to study long-term behavior (convergence, divergence, or oscillation) of a reeursive sequence. You can see how the sequence lnay change behavior as its initial value changes. • It must (u(n-1) be recursive with but not u(n-2)). • It cannot reference n directly. • It cannot reference any defined only one recursion In Web format, press _ The TI-83: • Draws • Plots the independent will not sequence level except itself. to display the graph screen. a y=x reference line selected sequences variable. in AxesOn with format. u(n-1) as the Note: A potential convergence point occurs whenever a sequence intersects the y=x reference line. However, the sequence may or may not actually converge at that point, depending on the sequence's initial value. Drawing the Web To activate the trace cursor, press _. The screen displays the sequence and the emTent n, X, and Y values (X represents u(n-1) and Y represents u(n)). Press [] repeatedly to draw the web step by step, starting at nMin. In Web format, the trace cursor follows this course. 1. It starts on the x-axis PlotStart=l). 2. It lnoves vertically 3. It lnoves horizontally 4. It repeats continue this vertical to press []. at the initial (up or down) value u(nMin) (when to the sequence. to the y=x reference and horizontal Sequence line. movenlent Graphing as you 6-11 Using Web Plots to Illustrate Convergence Press [] in Seq mode to display the sequence Y= editor. Make sure the graph style is set to ". (dot), and then define nMin, u(n) and u(nMin) as shown below. Example: Convergence u(_Min)B{-4} "-.v(n)= _Min=lPl_l PloL_ v(nMin)= PloL_ )+ ".uO?)= 2. Press [_ 3. Press [_ nMin=l nMax=25 PlotStart=l [FORMAT] _ to set Time axes and set the variables Xmin=0 Xmax=25 Xscl=l ff)rmat, as shown below. Ymin=-10 Ymax=l 0 Yscl=l PlotStep=l 4. Press [g_ 5, Press [_ 6. Press [_ Xmin=-10 7. Press [g_ to graph the sequence. [FORMAT]and select the Web axes setting. and change the variables Xmax=10 below. to graph the sequence. 8. Press _, and then press [] to draw the web. The displayed cursor coordinates n, X (u(n-1)), and Y (u(n)) change accordingly. When you press [], a new n value is displayed, and the trace cursor is on the sequence. When you press [] again, the n value remains the same, and the cursor moves to the y=x reference line. This pattern repeats as you tra_'e the web. u=-.au(._._-:t:,*_:.e N'--_.?_:EII?2 6-12 Sequence Graphing t.-* I?=1,?_:El172 Graphing Phase Plots Graphing with uv, The phase-plot m,ces settings uv, vw, and uw show vw, and uw relationships between two sequences. To select a phase-plot axes setting, press [_ [FORMAT],press [] until the cursor is on uv, vw, or uw, and then press [_. Example: Predator-Prey Model Axes Setting x-axis y-axis uv u(n) v(n) vw v(n) w(n) uw u(n) w(n) Use the predator-prey model to determine the regionM populations of a predator and its pt_y that would maintain population equilibrium for the two species. This example uses the model to determine the equilibrium populations of wolves and rabbits, with initial populations of 200 rabbits (u(nMin)) and 50 wolves (v(nMin)). These are the wu'iables (given values are in pm'entheses): R M K W = = = = number of rabbits rabbit population growth rate without wolves rabbit population death rate with wolves number of wolves G D n Rn = = = = wolf population growth rate with rabbits wolf population death rate without rabbits time (in months) Rn_I(I+M-KWn_I) W, = W,_I(I+GRn_I-D (.05) (.001) (.0002) (.03) ) 1, Press [] in Seq mode to display the sequence Y= editor. Define the sequences and initial wdues for Rn and Wn as shown below. Enter the sequence Rn as u(n) and enter the sequence Wn as v(n). Plot:l. Plot::" F'lot2, l nMir,=l I ".l.l(_) BM(_- 1 )*( 1+1 • 05-. 00 l*v(n-1 ) )l -.u (n) By (_- 1 )*( 1+ • 0002.u (n-1)-. 03 )v(nMin)B{50} ".t0(n)= u_(r_Min)= Sequence Graphing 6-13 2, Press _ [FORMAT] _ 3, Press _ nMin=O nMax=400 PlotStart=l to select and set the variables Xmin=O Xmax=400 Xscl=100 Time axes format, as shown below. Ymin=O Ymax=300 Yscl=100 PlotStep=l 4, Press [ghT_] to graph the sequence, 5, Press _ [] to individually trace the number rabbits (u(n)) and wolves (v(n)) over time (n), Tip: Press a number, 6, Press [g_] format, 7. Press _ below. Xmin=84 Xmax=237 Xscl=50 Press _. the number [FORMAT] and then press _ [] [] and change of to jump to a specific n to select uv axes _ these variables as shown Ymin=25 Ymax=75 Yscl=lO Trace both the number of rabbits (X) and of wolves (Y) through 400 generations, Note: When you press [_, the equation for u is displayed in the top-left corner. Press [] or [] to see the equation for v. I g=160.LIB_.=:B y=6;',66;'BLI9 6-14 Sequence Graphing Comparing Sequences and Window Variables TI-83 and TI-82 Sequence Refer to the table shows TI-83 well as their if you are familim" sequences and sequence TI-82 counterparts. with the TI-82. window It vm'iables, as TI-82 TI-83 In the Variables Y= editor: u(n) Un u(nMin) U nStart v(n) Vn v(nMin) VnStart w(n) not available w(nMin) not available In the window (window variable) (window vm'iable) editor: nMin nStart nMax nMax PlotStart nMin PlotStep not available Sequence Graphing 6-15 Keystroke Differences Between to the table TI-83 and TI-82 Sequence Re%r Keystroke Changes conlpares TI-83 sequence-name sy_tax and variable sy_tax with TI-82 sequence-name syntax and variable syntax. if you are familiar with the TI-82. It TI183 / TI-82 On TI183, press: On TI-82, n/ n _ _ [,] u(n) / Un _ _ [Y-VARS] [] [u] press: [] D_D v(n) / vn _ w(n) _ [i r_ [¥-VARS][] [] [w] not available D_D D_D u(n-1)lUn-1 _ [u] _ [Un-l] v(n-1)/vn-1 I_ [v] I_ [vn-_] w(n-1) _ [w] not available D_DmD I]]_E]mD []_•mD 6-16 Sequence Graphing Tables Contents Getting Started: Roots of a Function ..................... Setting Up the Table ..................................... Defining the Dependent Variables ........................ Displaying the Table ..................................... '_ TEXAS T1=83 iNSTRUMENTS X 0 1 2 Y_ 0 "1 h 21 _ 11_ h 5 7-2 7-3 7-4 7-5 Y2 0 "_ 0 15 hE 10_ X= -1 J STAT PLOT TBLSET FORMAT CALC TABLE Tables 7-1 Getting Getting Started: Started Roots of a Function is a fast-paced introduction. Read Evaluate the function Y = X :_- 2X at each integer many sign changes occur, and at what X values? 1. 2. the chapter between for details. -10 and Press _ [] [] [] FENY_to set Func graphing mode. Press @. Press _ Then press [] 2 _ function Y1=X3- 2X. _ 3 to select 3 to enter the Press [_ [TBLSET] to display- the TABLE SETUP screen. Press [] 10 _ to set TblStart=-10, Press 1_ to set ATbI=I. Press _ to select Indpnt: Auto (automatically generated independent values). Press [] [gNT_ to select Depend: Auto (automatically generated dependent values). Press [_ screen. [TABLE]to display the table Plol:l Press [] until you see the sign changes in the value of Y1. How many sign changes occur, and at what X values? TABLE SETUP TbIStart= -10 _Tbl=l Indent: _ Ask Depend: X _ Y_ "9 "B "? "6 "7tl "h96 "329 "_.Oh "_: "Jig "h "gtl X "2 "1 0 1 X=3 Tables Pl_l:_ P1*{_ -.Y1BX x-2X ,,yz= b.Y_= •,.y _ = \Yg= ".YG= \YT= X= -10 7-2 10. How YI "h 1 0 "t h Ask Setting Up the Table TABLE SETUP Screen TodisplaytheTABLESETUPscreen, TblStart=O _Tbl=lSETUP TRBLE IndPnt: Depend: i TblStart, ATbl press[_[TBLSET]. Rsk Rsk TblStart (table start) defines the initial value for the independent variable. TblStart applies only when the independent variable is generated automatically (when Indpnt: Auto is selected). ATbl (table variable. step) defines the increment for the independent Note: In Seq mode, both TblStart and ATbl must be integers. Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask Setting Up the Table from the Home Screen or a Program Selections Table Characteristics Indpnt: Auto Depend: Auto Values are displayed automatically the independent-variable colunm dependent-variable colunms. Indpnt: Ask Depend: Auto The table is empty; when you enter a value for the independent variable, all corresponding dependent-variable values are cah:ulated and displayed automatically. Indpnt: Auto Depend: Ask Values are displayed autonmtically for the independent variable; to generate a value for a dependent variable, move the cursor to that cell and press [E_. Indpnt: Ask Depend: Ask The table is empty; enter values for the independent variable; to generate a value for a dependent variable, move the cm:sor to that cell and press [EN_, in both and in all To store a value to TblStart, ATbl, or TblInput from the home screen or a program, select the variable name from the VARB TABLE seconda[w menu. TblInput independent-variable values in the cmTent is a list of table. When you press [2_ [TBLSET] in the program editor, can select IndpntAuto, IndpntAsk, DependAuto, and DependAsk. Tables you 7-3 Defining the Dependent Variables Defining Dependent Variables from the Y= Editor In the Y= editor, enter the functions that define the dependent vmiables. Only functions that are selected in the Y= editor are displayed in the table. The current graphing mode is used. In Par mode, you nmst define both components of each parametric equation (Chapter 4). Editing Dependent Variables from the Table Editor To edit a selected these steps. Y= function fronl the table editor, follow 1. Press [_ [TABLE]to display" the table, then press [] or [] to move the cursor to a dependent-variable column. 2. Press [] until the cursor is on the function name at the top of the colunm. The function is displayed on the bottonl line. 5G 20't Vt BX_-2X 3, Press [ggT_. The cursor the function. X moves to the bottonl X ml o I .-, o "t it 2t _6 I15 20_ LI _; I_ 71BII_-2X line. Edit m o t o "1 6 20_ V1BX:-4X Press [ggT_ or []. The new values are calculated. The table and the Y= function are updated automatically. X "3 Y1 Yt =O Note: defines 7-4 Tables You also can use this feature a dependent variable without to view the function having that to leave the table. Displaying the Table The Table To display- the table, press [_q [TABLE]. Current cell Independentvariable values to X _ 1 4, _ in the first column lZ 13 -h?.eB -_:Z.BE -_Z.I_6 -6Z.eE 11 "hh.86 9"_ "_ "_'.gB 1_ 1 1h Yz -_9.iz Dependentvariable values in "_:h.86 "G6.98 "E.q.Z 16 "6h._:B "?h,59 Y1 = -39, 173120459 _. -- -- the second and third columns T Current cell's full value Note: The table abbreviates the values, if necessary. Independent Dependent Variables and Clearing the Table from the Home Screen or a Program The current graphing lnode determines which independent and dependent varial)les are displayed in the table (Chapter 1). In the tal)le above, for example, the independent variable X and the dependent wuiables Y1 and Y2 are displayed because Func graphing mode is set. Graphing Mode Independent Variable Dependent Variable Func (function) X Y1 through Y0 Par (parametric) T X1T/Y1T through X6T/Y6T Pol (polar) 0 rl through Seq (sequence) n u(n), v(n), and w(n) Yg, and r6 From the home screen, select the CIrTable instruction the CATALOG. To clear the table, press [ggY_. fronl From a program, select 9:CIrTable from the PRGM I/0 menu or from the CATALOG. The talfle is cleared upon execution. If IndpntAsk is selected, 'all independent and dependent varialfle values on the table are cleared. If DependAsk is selected, all dependent variable values on the talfle are cleared. Tables 7-5 Scrolling IndependentVariable Values If Indpnt: Auto is selected, you can press [] and [] in the independent-variable colunm to display more wdues. As you scroll the colunm, the corresponding dependentvariable values also are displayed. All dependent-variable values may not be displayed if Depend: Ask is selected. X YI Yz 1 z "t 4 "_ ¢ 4 5 6 _6 115 204 4B 105 192 X=O X 1 .3 YI "t 4 21 Yz I "_ io 1_: 18.r. X= -1 Note: You can scroll back from the value entered for TblStart. As you scroll, TblStart is updated automatically to the value shown on the top line of the table. In the example above, TblStart=0 and ATbI=I generates and displays values of X=0,..., 6; but you can press [] to scroll back and display the table for X=-I,..., 5. Displaying Dependent Variables Other If you have defined more than two dependent variables, the first two selected Y= functions are displayed initially-. Press [] or [] to display dependent variables defined by other selected Y= functions. The independent wuiable always remains in the left colunm, except during a trace with Par graphing nlode and G-T split-screen nlode set. X "_ "2 "1 O 1 Z Yz Y_ "6 "6 "4 _ G :L=I ":LB "10 "LI O 2 ;L Y_= -28 Tip: that and For the 7-6 Tables To simultaneously display on the table two dependent variables are not defined as consecutive Y= functions, go to the Y= editor deselect the Y= functions between the two you want to display. example, to simultaneously display Y4 and Y7 on the table, go to Y= editor and deselect Y5 and Y6. 8 Contents Dnrs Wuction s Getting Started: Drawing a Tangent Line ................. Using the DRAW Menu ................................... Clearh]g Dra,_lngs ....................................... Drawing Line Segments .................................. Drawing Horizontal and Vertical Lines ................... Drawing Tangent Lines .................................. Drawing Functions and hwerses ......................... Shading Areas on a Graph ............................... Drawing ('ircles .......................................... Plaeing Text on a Graph ................................. Using Pen m Draw on a Graph ........................... Drawing Points on a Graph .............................. Drawing Pixels .......................................... Storing Graph Pictures (Pies) ............................ Recalling Graph Pictures (Pics) .......................... Storing Graph Databases (GDBs) ........................ Recalling Graph Databases (GDBs) ...................... 4_ TEXAS INSTnUMENTS STAT PLOT TBLSET FORMAT 8-2 8-3 8-4 8-5 8-(; 8-8 8-9 8-10 8-11 8-12 8-1:3 8-14 8-16 8-17 8-18 8-19 8-20 T1=83 CALC T._,B L E DRAW Instructions 8-1 Getting Getting Started: Started Drawing is a fast-paced a Tangent introduction. Suppose you want to find the equation function Y = sinX. Read the chapter of the tangent Before you begin, select Radian and Func mode from the mode screen, if necessaw. 1. Press [] to display- the Y= editor. Press [g_ _ [] to store sin(X) in Y1. 2. Line Press _ 7 to select 7:ZTrig, which graphs the equation in the ZOOlll Trig window. Press [g_ [DRAW] 6 to select 6:Tangent(. The tangent instruction is initiated. line at X = _2 P1,'.,tl Plot_ /-7--,. "..>" [4] 2[] [] 2. Pl(,t3 /-7_ /-7\ ".,_i_1 ?=0 /2"-.. -,_i_1 4=,r(2)/211 8-2 DRAW Instructions -,,_i__ _ tl=sih((X) _.--.. Press [ggg_. The tangent line is drawn; the X value and the tangent-line equation are displayed on the graph. ".L/ tl==in(:4) 1{=0 Press_ for the ".Y1Bsin(X) %yz= ",Yx= -.y_= -,y_= ,,y_= xY_'= /-7_. 4. for details. _ [// ",2/ Using the DRAW Menu DRAW Menu To display the DRAW menu, press [DRAW]. The [_ TI-S3's interpretation of these instructions depends on whether you accessed the menu fronl the honle screen or the program editor or directly- from a graph. DRAW POINTS STO 1 : C1 rDraw Clears 2: Line( 3: Horizontal 4: Vertical 5: Tangent( 6: DrawF elements. a line segment between a horizontal line. a vertical line. 8: Drawlnv 9: Circle( O: Text( Draws text on a graph Activates the free-form A: Pen The DRAW instructions draw on top before you use the DRAW instructions, you want 2 points, Draws a line segment tangent to a function. Draws a function. Shades an area between two functions. Draws the inverse of a function. Draws a circle. 7: Shade( Before Drawing on a Graph all drawn Draws Draws Draws to perform one or more • Change the mode • Change • Enter or edit functions • Select or deselect • Change • Turn stat • Clear existing the fornlat of graphs. consider settings tool. Therefore, whether of the following on the mode actions, screen, on the format screen. in the Y= editor, functions the window plots settings screen. drawing variable in the Y= editor. values. on or off. drawings with ClrDraw (page 8-4). Note: If you draw on a graph and then pedorm any of the actions listed above, the graph is reptotted without the drawings when you display the graph again. Drawing on a Graph You can use any DRAW menu instructions except Drawlnv to draw on Func, Par, Pol, and Seq graphs. Drawlnv is valid only in Func graphing. The coordinates for all DRAW instructions ate the display's x-coordinate and y-coordinate values. You can instructions to identify instructions use most DRAW menu and DRAW POINTS menu to draw directly on a graph, using the cursor the coordinates. You also can execute these from the home screen or from within a progranl. If a graph is not displayed DRAW menu instruction, the home when screen you select a is displayed. DRAW Instructions 8-3 Clearing Drawings Clearing Drawings When a Graph Is Displayed All points, Clearing Drawings from the Home Screen or a Program To clem' drawings on a graph fronl the holne screen or a program, begin on a blank line on the home screen or in the program editor. Select 1 :CIrDraw from the DRAW menu. The instruction is copied to the cursor location. Press instructkms lines, and shading drawn on a graph with DRAW are temporm'y. To elem' drawings from the currently displayed graph, select 1 :ClrDraw from the DRAW menu, The current graph is replotted and displayed with no drawn elements, When CIrDraw is executed, it clears 'all drawings from the current graph and displays the message Done. When you display the graph again, all drawn points, lines, circles, and shaded areas will be gone. ClrOraw Done Note:Beforeyou cleardrawings,you can store them withStorePic (page 8-17). 8-4 DRAW Instructions Drawing Line Segments Drawing a Line Segment Directly on a Graph To draw is displayed, follow 2. Place the cursor on the point where you want segment to begin, and then press [_E_. the line these a line segment when a graph steps. 1. Select 2:Line( from the DRAW menu. 3. Move the cursor to the point where you want the line segment to end. The line is displayed _s you move the cursor. Press [ggY_. R=5,3191_Bgl/I=_.qSi_t_9 To continue drawing line segments, To cancel Line(, press @. Drawing a Line Segment from the Home Screen or a Program repeat steps 2 and 3. Line( also draws a line segment between the coordinates (X1 ,Y1) and (X2,Y2). The values nlay be entered ZLS expressions. Line(X1,Y1,X2,Y2) Line (0, To erase Line(2, 0, 6, 9)11 a line segment, 3, 4, 6, 0)11 enter Line(X1,Y1,X2,Y2,0) /, DRAW Instructions 8-5 Drawing Horizontal Drawing a Line Directly on a Graph and Vertical Lines To draw a horizontal or vertical displayed, follow steps. 1, Select these 3:Horizontal line is displayed line when or 4:Vertical that nloves from [_ To continue To cancel 8-6 DRAW Instructions to draw drawing is the DRAW menu. as you nlove 2. Place the cm'sor on the y-coordinate lines) or x-coordinate (for vertical you want the drawn line to pass. 3. Press a graph the cursor. (for horizontal lines) through which the line on the graph. lines, repeat steps 2 and 3. Horizontal or Vertical, press @, A Drawing a Line from the Home Screen or a Program Horizontal (horizontal line) y can be an expression but draws a horizontal line at Y=y. not a list. Horizontal y Vertical (vertical line) draws an expression but not a list, Vertical line, tile TI-83 to draw more separate each instruction Ho_-izor,÷_al t_al line at X=x, x can be _" To instruct vertical a vertical than one horizontal with a colon or ( : ). 7: Vet 4: Vertical ...................... DRAW Instructions 8-7 Drawing Tangent Drawing a Tangent Line Directly on a Graph Lines To draw these a tangent line when a graph is displayed, follow steps, 1, Select 5:Tangent( fron] the DRAW nlenu. 2. Press [] and [] to move the cm_or to the function for which you want to draw the tangent line. The cmTent graph's Y= function is displayed in the top-left corner, if ExprOn is selected. 3. Press [] a_d [] or enter a number to select the point on the function at which you want to draw the tangent line. 4. Press [E_. In ffunc mode, the X value at which the tangent line wa_ drawn is displayed on the bottom of the screen, along with the equation of the tangent line. In all other nlodes, the dy/dx value is displayed. X=i,gt;_: Tip: Change the fixed decimal setting on the mode screen to see fewer digits displayed for X and the equation for Y. Drawing a Tangent Line from the Home Screen or a Program Tangent( (tangent line) draws a line tangent to expression in terms of X, such as Y1 or X2, at point X=value. X can be an expression, expression is interpreted as being in Func nlode, Tangent(expression,value) Tangent 8-8 if you want DRAW Instructions ('gi, 3)| Drawing Drawing a Function Functions and Inverses DrawF (draw function) draws expression at a function in terms of X on the current graph, When you select 6:DrawF froln the DRAW menu, the TI-83 returns to the home screen or the program editor, DrawF is not interactive, DrawF expression [Ir.at0F t?1-5 II Note: You cannot Drawing an Inverse of a Function use a list in exp'_vssion ...... ./_-.._ .(_. to draw a family ..... of curves. Drawlnv (draw inverse) draws the inverse of expression by plotting X values on the y-axis and Y values on the x-axis. V_lmn you select 8:Drawlnv from the DRAW menu, the TI-83 returns to the home screen or the program editor. Drawlnv is not interactive. Drawlnv works in Func mode only. Drawlnv expression Drato Inv '.?ill . [email protected]__SI. Note: You cannot use a list ine_pression to draw a family of curves. DRAW Instructions 8-9 Shading Areas Shading a Graph on a Graph To shade an area on a graph, select 7:Shade( fronl the DRAW menu. The instruction is pasted to the home screen or to the program editor. Shade( draws loweffune and uppeffunc in terms of X on the current graph and shades the area that is specifically above lowerfane and below uppe_2fune. Only the areas where lowerfane < uppeffunc are shaded. Xleft and Xright, if included, specify- left and right boundaries for the shading. Xleft and Xright nmst be numbers between Xmin and Xmax, which axe the defaults. patte_ specifies one of four shading pattern= 1 pattern= 2 pattern= 3 pattern=4 patres specifies patterns. vertical (default) horizontal negative--slope 45 ° positive--slope 45 ° one of eight shading patres= 1 patres=2 patres=3 patres=4 patres=5 patres=6 patres=7 patres=8 shades shades shades shades shades shades shades shades resolutions. every pixel (default) evetF- second pixel every third pixel eve_- fourth pixel every fifth pixel eve_Ty-sixth pixel evetsz seventh pixel every eighth pixel Shade(lowerfanc,uppe_:func[._left._right,patte_,patres]) Shade(X_-8X, 8-10 DRAW Instructions X-2), ....... ____...;.:( Drawing Circles Drawing a Circle Directly on a Graph To draw cursor, 1, Select 2, Place draw. a circle follow directly these 9:Circle( on a displayed graph using the steps, fronl the DRAW menu. the cursor at the center Press [NTEN. of the circle you want 3. Move the cursor to a point on the circumference. [ggTE_ to draw the circle on the graph. to Press Note: This circle is displayed as circular, regardless of the window variable values, because you drew it directly on the dispiay. When you use the Circle( instruction from the home screen or a program, the current window variables may distort the shape. To continue drawing cancel Circle(, press Drawing a Circle from the Home Screen or a Program circles, @. repeat Circle( draws a circle with center values can be expressions. steps 2 and 3, To (X,Y) and radius. These Circle(X,Y, radius) Ciwcle(O, 0, 7)1 Tip: When you use Circle( on the home screen or from a program, the current window values may distort the drawn circle. Use ZSquare (Chapter 3) before drawing the circle to adjust the window variables and make the circle circular. DRAW Instructions 8-11 Placing Text on a Graph Placing Text Directly on a Graph To place follow text these 1, Select 2, Place on a graph when the graph is displayed, steps, 0:Text( from the cursor the where DRAW menu. you want the text to begin. 3, Enter the characters. Press @ or [_ [A-LOCK] to enter lettet\s and 0. You nlay enter TI-83 functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the graph. To cancel Placing Text on a Graph from the Home Screen or a Program Text(, press @, Text( places on the current graph the chara('ters comprising value, which can include TI-83 functions and instructions. The top-left corner of the first character is at pixel (row,column), where row is an integer between 0 and 57 and column is an integer between 0 and 94. Both row and colnft_firt can be expressions. Text(row,column,value,value.. ,) value can be text enclosed in quotation marks ( " ), or it can be an expression. The TI-83 will evaluate an expression and display the result with up to 10 characters. Text(42,50,"Vt=. 2XX-2X+6 Split Screen 8-12 ..... ...... )| On a Horiz split screen, the nlaxinlunl On a G-T split screen, the nlaxinlunl and the nlaxinlunl value for column DRAW Instructions I ?'I=._:X_-_:X+G value for row is 25, value for ro_t_)is 45, is 46, Using Pen to Draw on a Graph Pen draws directly Pen from the home on a graph screen To draw on a displayed 1. Select A:Pen from only, You cannot graph, follow these [_ to turn steps. the DRAW menu, where you want on the pen, 3. Move the cursor. As you move the cursor, the graph, shading one pixel at a time, 4. Press execute or a progranL 2. Place the cursor on the point drawing. Press [_ to turn to begin you draw on off the pen, For example, Pen was used to create the arrow the local minimunl of the selected function. ..... Using Pen to Draw on a Graph pointing to E.,dL I To continue drawing on the graph, nlove the cursor to a new position where you want to begin drawing again, and then repeat steps 2, 3, and 4. To cancel Pen, press @. DRAW Instructions 8-13 Drawing Points on a Graph DRAW POINTS Menu To display- the DRAW POINTS menu, press [_a] [DRAW] [_. The TI-83's interpretation of these instructions depends whether you accessed this nlenu froth the home screen the program editor or directly froth a graph. DRAW POINTS ST0 i : Pt On( 2: Pt Off( 3: 4: 5: 6: Drawing Points Directly on a Graph with Pt-On( Turns on apoint. Turns off a point. Toggles a point on or off. Turns on a pixeL Turns off a pixel. Toggles a pixel on or off, Returns 1 if pixel on, 0 if pixel off, Pt Change( Pxl On( Pxl Off( Pxl Change( 7: pxl Test( To draw a point on a graph, follow these steps. 1, Select 1 :Pt-On( from the DRAW POINTS menu, 2. Move the cursor the point. to the position where you want to draw 3. Press [ggY_ to draw the )oint. o R:Ll,_6e0mgl y:LI.BM]?O.:I? To continue drawing points, repeat cancel Pt-On(, press @. 8-14 on or DRAW Instructions steps 2 and 3. To Erasing Points with Pt-Off( To erase (turn off) a drawn point on a graph, follow these steps, 1. Select 2:Pt-Off( (point off) from the DRAW POINTS nlenu, 2. Move the cursor 3. Press _ you want points, repeat steps 2 and 3. To cancel To change (toggle on or off) a point on a graph, %llow these steps. 1. Select 3:Pt-Change( (point change) POINTS menu. 2. Move the cursor 3. Press I_ from the DRAW to the point you want to change. to change the point's To continue changing points, t_peat cancel Pt-Change(, press @. Drawing Points from the Home Screen or a Program to erase. to ertkse the point. To continue ertLsing Pt-Off(, press @. Changing Points with Pt-Change( to the point on/off status. steps 2 and 3. To Pt-On( (point on) turns on the point at (X=x,Y=y). Pt-Off( tutlls the point off. Pt-Change( toggles the point on or off. mark is optional; it determines the point's appearance; specify 1, 2, or 3, where: 1 = • (dot; default) Pt-On(x,y[,mark]) Pt-Off(x,y[ ,mark Pt-Change(x,y) 2 = [] (box) 3 = + (cross) ]) Pt.-0n ( 2, 5, 2> :Pt,- .. Note: If you specified mark to turn on a point with Pt-On(, you must specify mark when you turn off the point with Pt-Off(. Pt-Change( does not have the mark option. DRAW Instructions 8-15 Drawing Pixels TI-83 Pixels A pixel is a square dot on the TI-83 display. The Pxl- (pixel) instructions let you turn on, turn off, or reverse a pixel (dot) on the graph using the cursor. When you select a pixel instruction from the DRAW POINTS menu, the TI-83 retm'ns to the home screen or the program editor. The _ixel instl_ctions are not interactive. p; Turning On and Off Pixels with Pxl-On( and Pxl-Off( jq PxI-On( (pixel on) turns where row is an integer integer between PxI-Off( turns and off. on the pixel at (row,column), between 0 and 62 and column is an 0 and 94. the pixel off. Pxl-Change( toggles the pixel on Pxl-On(row,column) Pxl-Off(row,column) Pxl-Change(_'ow,column) Using pxI-Test( pxI-Test( (pixel test) returns 1 if the pixel at (row,column) is turned on or 0 if the pixel is tunled off on the curl_nt graph, row nmst be an integer between 0 and 62. column nmst be an integer between 0 and 94. pxI-Test(row,colu'rnn) Split Screen On a Horiz split screen, the maxinmm value for row for PxI-On(, PxI-Off(, Pxl-Change(, and pxI-Test(. is 30 On a G-T split screen, the nlaxinlunl value for row is 50 and tile nlaxinlunl value for column is 46 for PxI-On(, PxI-Off(, Pxl-Change(, 8-16 DRAW Instructions and pxI-Test(. Storing Graph Pictures DRAW STO Menu (Pics) To display the DRAW STO menu, press [g_ [DRAW] [_, When you select an instruction fronl the DRAW STO menu, the TI-83 returns to the home screen or the program editor. The picture and graph database instructions are not interactive. DRAW POINTS STO 1:StorePic 2:RecallPic 3:StoreGDB 4:RecalIGDB Storing a Graph Picture Stores Recalls Stores Recalls the current picture. a saved picture. the current graph datal)ase. a saved graph database. You can store up to 10 graph pictures, each of which is an image of the cmTent graph display-, in picture wuialfles Pie1 through Picg, or PicO.Later, you can superimpose the stored picture onto a displayed graph from the home screen or a program. A picture includes drawn elements, plotted functions, axes, and tick marks. The picture does not include axes labels, lower and upper bound indicators, prompts, or cursor coordinates. Any parts of the display- hidden by these items m'e stored with the picture. To store a graph picture, follow these steps. 1. Select 1:StorePic fronl the DRAW STO menu. StorePic is DL_ted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the picture variable to which you want to store the picture. For example, if you enter 3, the TI-83 will store the picture to Pic3. 5tor.ePio 3 Note: You alsocan select a variable from the PICTURE secondarymenu (_ 4). The variable is pasted next to 8torePic. 3. Press [ggTE_ to display- the current picture. graph and store the DRAW Instructions 8-17 Recalling Graph Pictures Recalling a Graph Picture To recall a graph (Pics) picture, 1. Select 2:RecallPic is pasted ffonl to the current follow these steps, the DRAW STO menu, cursor RecallPic location, Enter the number (from 1 to 9, or 0) of the picture varial)le from which you want to recall a picture. For example, if you enter 3, the TI-83 will recall the picture stored to Pic3. Reoal IPio 3 Note: You also can select a variable from the PICTURE secondary menu (_ 4). The variable is pasted next to RecallPic. 3, Press I_ to display- the current picture superimposed on it, graph with the Note: Pictures are drawings. You cannot trace a curve that is part of a picture. Deleting a Graph Picture 8-18 To delete graph pictures from MEMORY DELETE FROM menu DRAW Instructions memo[3z, (Chapter use the 18). Storing Graph Databases What Is a Graph Database.'? A graph database (GDB) contains the set of elements that defines a pm'ticular graph. You can recreate the graph froln these elements. You can store up to 10 GDBs in variables GDB1 through GDB9, or GDB0 and recall them to recreate graphs. A GDB stores • • • • • five elements of a graph. Graphing mode Window variables Format settings All functions in the Y= editor and the selection each Graph style for each Y= function GDBs do not Storing a Graph Database (GDBs) To store a graph is pasted StoreGDB from to the current the number to which example, GDB7, drawn database, 3:StoreGDB 1, Select 2. Enter contain (from items or stat follow the these plot of definitions. steps. DRAW STO menu. cursor status StoreGDB location, 1 to 9, or 0) of the GDB variable you want to store the graph database. For if you enter 7, the TI-83 will store the GDB to 7 Note: You also can select a variable from the GDB secondary menu ([_ 3). The variable is pasted next to $toreGDB. 3, Press 1_ specified to store the current GDB variable. database to the DRAW Instructions 8-19 Recalling Graph Databases Recalling a Graph Database (GDBs) CAUTION: When you recall a GDB, it replaces all existing Y= functions. Consider storing the cutTent Y= functions to another database before recalling a stored GDB. To recall a graph database, follow these steps. 1. Select 4:RecalIGDB from the DRAW STO menu. RecalIGDB is pasted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the GDB variable from which you want to recall a GDB. For example, if you enter 7, the TI-83 will recall the GDB stored to GDB7, Reoal IGDB 7 Note: You alsocan select a variable from the GDB secondary menu (_ 3). The variable is pastednext to RecalIGDB. 3, Press [_ to replace the current GDB with the recalled GDB. The new graph is not plotted. The TI-83 changes the graphing mode automatically, if necessat T. Deleting a Graph Database 8-20 To delete a GDB fronl nlemo_T, use the MEMORY DELETE FROM menu (Chapter 18). DRAW Instructions Screen Split Contents Getting Started: Exploring tile Unit Circle ................ Using Split Screen ....................................... Horiz (Horizontal) Split Screen .......................... G-T (Graph-Table) Split Screen .......................... TI-83 Pixels in Horiz and G-T Mode ...................... '_ TEXAS T1=83 INSTRUMENTS ','t==in_)J oX _'.', l .._,75 1.2,_3 _, X=.BO:_h7:_O h ?=.7190761B 9-2 9-3 9-4 9-5 9-6 I oY 1 1.07 1.1177_: 2.337 .97:_9 1.605 .ggg4 J STATPLOT TBLSET FORMAT CALC TABLE Split Screen 9-1 Getting Getting Started: Started Exploring is a fast-paced the Unit Circle introduction. Read the chapter for details. Use G-T (graph-table) split-screen mode to explore the unit circle and its relationship to the numeric values for tile connnonly used trigonometric angles of 0°, 30 °, 45 °, 60 °, 90 °, and so on. Press [g6m to display the mode screen. Press [] [] [] [g_ to select Degree mode. Press [] [] [g_ to select Par (parametric) graphing mode. Press [] [] [] [] [] [] [g_ to select G-T (graph-table) split-screen mode. Press [_ [FORMAT]to display" the format screen. Press [] [] [] [] [] [] [g_ to select ExprOff. Press [] graphing [ggg_] to [] to display" the Y= editor for Par mode. Press [g6_ _ [] store cos(T) to XIT, Press [gF_ _ to store sin(T) to YIT. Press _ editor. Enter variables. Train=0 Tmax=360 Tstep=l 5 to display the window these values for the window Xmin=-2.3 Xmax=2.3 Xscl=l Ymin=-2.5 Ymax=2.fi Yscl=l Press _. On the left, the unit circle is graphed parametrically in Degree mode and the trace cursor is activated. When T=0 (from the graph trace coordinates), you can see from the table on the right that the value of XlT (cos(T)) is 1 and YIT (sin(T)) is 0. Press [] to move the cursor to the next 15° angle increment. As you trace around the circle in steps of 15° , an approximation of the standard value for each angle is highlighted in the table. 9-2 Split Screen li X1, i V1T 0 .g .Bfl6 .zsne ._ss_ T=_O g:.BSfi02B_ 0 1 Using Split Screen Setting a SplitScreen Mode To set a split-screen lnode, press [MO0_,and then nlove the cursor to tile bottol:l line of the l:lode screen. • • Select Horiz (horizontal) to display- the graph screen and another screen split horizontally. Select G-T (graph-table) to display the graph screen and table screen split vertically. Sci Eng Sci Eng Dot The split screen is activated when you press any key that applies to either half of the split screen. Sonle screens m'e never displayed +is split screens. For example, if you press _ in Roriz or G-T inode, the inode screen is displayed as a full screen. If you then press a key that displays either half of a split screen, such as _, the split screen returns. VC]mnyou 6-7 mode, which that the cursor displayed. the half in press a key or key combination in either Horiz or the cursor is placed in the half of the display- for key applies. For example, if you press _, is placed in the half in which the graph is If you press [g_ [TABLE],the cursor is placed in which the table is displayed. The TI-83 will remain in split-screen change back to Full screen mode. lnode until you Split Screen 9-3 Horiz (Horizontal) Horiz Mode Split Screen In Horiz (horizontal) split-screen lnode, a horizontal splits tile screen into tc ) and bottom halves. line \ViBsin(X z) ,.YzBcos(XZ ) \Y._= The top half displays the graph. The bottom • • • • • Moving from Half to Half in Horiz Mode half displays Home screen (four lines) Y= editor (four lines) Stat list editor (two rows) Window editor (three settings) Table editor (two rows) To use the top half of tile split screen: • • Press [g_ or _. Select a ZOOM or CALC operation. To use tile bottonl Full Screens in Horiz Mode any of these editors. half of tile split screen: • Press any key or key combination home screen. • • • • Press Press Press Press that displays the [] (Y= editor). [gT_ [g_ (stat list editor). _ (window editor). [2_ [TABLE](table editor). All other screens are displayed split-screen mode. as full screens in Horiz To return to the Horiz split screen from a full screen when in Horiz mode, press any- key or key combination that displays the graph, home screen, Y= editor, stat list editor, window editor, or table editor. 9-4 Split Screen G-T (Graph-Table) G-T Mode Split Screen In G-T (graph-table) split-screen mode, a vertical tile screen into left and right halves. X line splits Y1 Io ,2: X=Bgq. The left half displays the graph. The right half displays the table. Moving from Half to Half in G-T Mode To use the left half of the split screen: • • Press [g_ or _. Select a ZOOM or CALC operation. To use tile right half of the split screen, Using _ G-T Mode in press [:_ [TABLE]. As you lnove tile trace cursor along a graph in the split screen's left half in G-T mode, the table on the right half autolnatically scrolls to match tile current cursor values. x_ g=.B0ZtlTZ0h Y=,7190761B X Vi 1.07 .B77_ 1._7_7 ,97:'9 t,l_0g .999h Note: When you trace in Par graphing mode, both components of an equation (XnT and YnT) are displayed in the two columns of the table. As you trace, the current value of the independent variable T is displayed on the graph. Full Screens in G-T Mode All screens other than the graph and the table are displayed as full screens in G-T split-screen mode. To return to the G-T split screen from a full screen when in G-T mode, press any key or key combination that displays the graph or the table. Split Screen 9-5 TI-83 Pixels in Horiz and G-T Modes "*. Horiz and G-T Modes (o,0.', l .(°._.h.)?l €,30,0) 1 o0,9_)_, _ X lg 30 _g 60 TI-Sa Pixels in "i I=o Note: Each set of numbers in parentheses above represents the row and column of a corner pixeI, which is turned on. DRAW POINTS Menu Pixel Instructions For PxI-On(, PxI-Off(, Pxl-Change(, • In Horiz mode, • In G-T mode, row row nmst nmst and pxI-Test(: be _<30; column nmst be _<50; column nmst be _<94. be _<46. Pxl-On(row,column) DRAW Menu Text( Instruction For the Text( instruction: • In Horiz mode, • In G-T mode, row row nmst nmst be _<25; column must be _<45; column nmst be _<94. be _<46. Text(row,column,"text") PRGM I/O Menu Output( Instruction For the Output( • In Horiz mode, • In G-T mode, instruction: row row Output(row,column, Setting a Split-Screen Mode from the Home Screen or a Program nmst nmst nmst nmst be _<16. be _<16. "text") To set Horiz or G-T from 1. Press [M0_] while program editor. be _<4; column be _<8; column a program, the cursor follow is on a blank these steps. line in the 2, Select Horiz or G-T, The instruction is pasted to the cursor location. The mode is set when the instruction is eneountered during program execution. It remains in effect after execution. Note: You also can paste Horiz or G-T to the home screen or program editor from the CATALOG (Chapter 15). 9-6 Split Screen 10 Contents Matrices Getting Started: Systems of Linear Equations ............ Defining a Matrix ........................................ Viewing and Editing Matrix Elements .................... Using Matrices with Expressions ........................ Displaying and Copying Matrices ........................ Using Math Functions with Matrices ..................... Using the MATRX MATH Operations ..................... '_ TEXAS T1=83 iNSTRUMENTS MRTRIX[R] 10-2 10-2 10-4 10-7 10-8 10-9 10-12 8 x4 r_ -_.:l.h_: 1:_ E "1 ro r 0 E 1.B r 0 [0 _:.1h11_ 0 0 0 .8571h 0 0 0 BB 0 0 2 i, i=3.141592653 J STATPLOT TBLSET FORMAT CALC TABLE Matrices 10-1 Getting Getting Started: Started Systems is a fast-paced of Linear Equations introduction. Read the chapter for details. Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-83, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using rref( to obtain the reduced row-echelon form. 1. Press [_. Press [] [] to display- the MATRX EDIT menu. Press 1 to select 1: [A], 2. 3. Press 2 [_ 4 [_ to define a 2x4 matrix. The rectangular cursor indicates the current element. Ellipses (...) indicate additional eolunms beyond the screen. Press 1 [_ to enter the first element. The rectangular cursor nloves to the second colunm of the first row. MATRIX[R] [0 2 x4 0 1_1=0 MATRIX[R] [0 0 2 x4 0 I_Z=0 4. Press 2 [g_ 3 [g_ 3 [g_ to complete the first mw for X + 2Y + 3Z = 3. 5. Press 2 [_ 3 [_ 4 [_ 3 [_ to enter the second row for 2X + 3Y + 4Z = 3, Press [_ [QUIT] to return to the home screen. If necessary, press @ to clear the home screen. Press _ [] to IMRTRIX[A] 2 x4 rre?(| display the MATRX MATH menu. Press [] to wrap to the end of the menu. Select B:rref( to copy rref( to the home screen. Press [_ 1 to select 1: [A] from the MATRX NAMES menu. Press [] FENTERI. The reduced row-echelon form of the matrix is displayed and stored in Ans. iX- 1Z=-3 1Y+2Z=3 10-2 Matrices so so X=-3+Z Y=3-2Z rref'([Al ) -31 [[1 18 213 ]l Defining a Matrix What Is a Matrix? A matrix is a two-dimensional alTay. You can display', define, or edit a matrix in the matrix editor. Tile TI-83 h_s 10 matrix variables, [A] through [J]. You can define a matrix directly in an expression. A matrix, depending on available nlelnolT, may have up to 99 rows or colunms. You can store only real numbers in TI-83 matrices. Selecting a Matrix Before you can define or display a matrix in the editor, you first nmst select the matrix name. To do so, follow these steps. [] to display the MATRX EDIT menu. The of any previously defined lnatrices are 1. Press _ dimensions displayed. MATH [el [D] [El [F] [G] 2, Select screen the matrix you want is displayed. MATRIX[B] ro Accepting or Changing Matrix Dimensions to define. The MATRX EDIT I xl I The dimensions of the matrix displayed on the top line. The are 1 xl, You nmst accept or time you edit a matrix, When (row x column) are dimensions of a new matrix change the dimensions each you select a matrix to define, the cursor dimension. highlighLs the row the row • To accept • To change the row dimension, (up to 99), and then press [_. dimension, press enter [_. the number of rows The cursor moves to the eolunm dimension, which you must accept or change the same way you accepted or changed the row dimension. When you press [_, the rectangular cursor moves to the first matrix element. Matrices 10-3 Viewing and Editing Displaying Matrix Elements Matrix Elements After you have set the dimensions of the matrix, you can view the matrix and enter values for the matrix elements. In a new matrix, 'all values are zero. Select the matrix from the MATRX EDIT menu and enter or accept the dimensions. The center portion of the matrix editor displays up to seven rows and three eolunms of a matrix, showing the values of the elements in abbreviated form if necessary. The full vMue of the current element, which is indicated by the t_ctangular cursor, is displayed on the bottonl line. "t _:.tht6 MRTRIX[R] 0 8 0 x4 i i,i=3. 141592653 This is an 8 x 4 matrix. Ellipses in the left or right colunm indicate additional columns, i' or _ in the right column indicate additional rows. Deleting 10-4 a Matrix Matrices To delete matrices fronl nlenlory, FROM seconding- menu ((;hapter use the MEMORY DELETE 18). Viewing a Matrix The matrix editor has two contexts, viewing and editing, In viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the highlighted element is displayed on the bottom line, Select the inatrix fl'oin the MATRX EDIT menu, and then enter or accept the dimensions. ":1, }.:DI:I.I_ 0 MRTRIX[R] 8 x4 2 I,I=3. 141592653 Viewing-Context Keys 1 Key Function [] or [] Moves the rectangular current row. [] or [] Moves the rectangular cursor within the current coluinn; on the top row, [] moves the cursor to the colunm dimension; on the coluinn dimension, [] moves the cursor to the row dimension. [gNT_ Switches to editing context; activates edit cursor on the bottom line. @ Switches to editing context; value on the bottoin line. Any entry character Switches to editing context; clears the value on the bottoln line; copies the character to the bottom line. [_ [ggn [INS] cursor within the the clears the Nothing Nothing Matrices 10-5 Editing a Matrix Element In editing context, an edit cursor is active on the bottom line. To edit a lnatrix element value, follow these steps. 1. Select the matrix from the MATRX EDiT menu, and then enter or accept the dimensions. 2. Press [], [], [], and [] to nlove the cursor element you want to change. 3. Switch to editing context an entw key-. by pressing to the lnatrix [ggT_, @, or 4. Change the value of the tnatrix element using the editing-context keys described below. You nlay enter an expression, which is evaluated when you leave editing context. Note: You can press @ _ to restore the value at the rectangular cursor if you make a mistake. 5. Press IgOr, [], MRTRIX[RI or [] to Inove to another element. 8 ×4 r :Ll_ntG ":kl_ 13 [ 0 [ :t.B 0 0 BII 0 [ 0 .BgT:th 0 [0 0 3.1_I_ ").1ill MRTRIX[R] 1_ 8 x4 i 3, i=2Xz+3| Editing-Context Keys Key Function [] or [] Moves the edit cursor within the value, [] or [] Stores the value displayed on the bottom line to the nlatrix element; switches to xqewing context and nloves the rectangular cut.or within the colunm. [g_Tgm Stores the value displayed on the bottom line to the nlatrix element; switches to viewing context and moves the rectangular cm'sor to the next row element. @ Clears the value on the bottom Any entrycharacter Copies the character to the location edit cursor on the bottom line. [_ [INS] [DE[] 10-6 Matrices Activates line. of the the insert cursor. Deletes the character on the bottonl line. under the edit cursor Using Matrices Using a Matrix in an Expression with Expressions To use a matrix in an expression, following. • • • Entering a Matrix in an Expression you can do any of the Copy the name from the MATRX NAMES menu. Recall the contents of the lnatrix into the expression with [_ [RCL] (Chapter 1). Enter the matrix directly (see below). You can enter, edit, and store a matrix in the nlatlJx You also can enter a nlatrix directly in an expression. in an expression, follow these editor. To enter a nlatrix steps. 1. Press [2_] [ [ ] to indicate the beginning of the nlatrix. 2. Press [2_] [ [ ] to indicate the beginning of a row. 3. Enter a value, which can be an expression, for each element in the row. Sepm'ate the values with conlnlas. 4. Press 5. Repeat 6. Press [2_] [] ] to indicate steps 2 through the end of a row. 4 to enter [2_] [] ] to indicate all of the rows. the end of the nlatrix. Note: The closing ]] are not necessary at the end of an expression or preceding -'>. The resulting matrix is displayed in the form: [[elementl,l,._,elementl,_l,...,[element.,,_,l,...,element,,_,_]] Any expressions executed. are evaluated when the enttsz is 2.[11 [1,2,31[[_ 418"1014'5'161211 Note: The commas that you must enter to separate elements are not displayed on output. Matrices 10-7 Displaying and Copying Displaying a Matrix Matrices To display- the contents of a matrix on the home screen, select the nmtrix from tile MATRX NAMES menu, and then press [_. lEA, El; 711 Ellipses in the left or fight eolunm indicate additional colunms. I' or 4 in the right colunm indicate additional rows. Press [_, [], [], and [] to scroll the lnatrix. 46.0000 I ...116. 0000 ...49. 0000 --62. (_iiiI -96.8...I %88oo65.00...I i::47'. 0000 ...3, 0000 Copying One Matrix to Another -69.04, 136,0... To copy a matrix, 1. Press [_ follow these steps. to display the MATRX NAMES menu. 2. Select the name of the lnatrix you want to copy. 3. Press _. 4. Press _ again and select the name of the new nmtrix to which you want to copy the existing matrix. 5. Press [_ Accessing a Matrix Element to copy the lnatrix to the new lnatrix On the home screen or fronl within a program, you can store a vMue to, or recM1 a value from, a matrix element. The element nmst be within the currently defined matrix dimensions. Select matrix from the MATRX NAMES menu. [matrixl(row,column) 0-:* [BI (2, 3)-" [BI [[7 8 91 [B1(2,3)[3 10-8 Matrices nalne. 2 0110 Using Math Functions with Matrices Using Math Functions with Matrices You can use many of the math functions on the TI-83 + (Add), (Subtract), * (Multiply) To add ([_) or subtract ([_) matrices, the dimensions must be the same, The answer is a matrix in which the elements are the sum or difference of the individual corresponding elements. keybom'd, tile MATH menu, tile MATH HUM MATH TEST menu with matrices. However, nmst be appropriate. Each of the functions new matrix; the original matrL, c remains the matrixA matrixA +matrixB - mat)_ixB To nmltiply dimension matrixB. matrixA menu, and tile the dimensions below creates a same. ([_) two matrices together, the colunm of matrixA nlust match the row dimension of *mat_qxB Multiplying a matrix by a value or a value by a matrix returns a matrix in which each element of matrix is nmltiplied by value, matrix*value value*matrix - (Negation) Negating of evetN a matrix (D) returns a matrix element is changed (reversed), in which the sign -matrix -ira [RI -41 [[212; 41-211] Matrices 10-9 abs( (absolute value, MATH NUM menu) returns a matrix containing the absolute value of each element of matrix. abs( abs(mat_qx) [°] 14,69' abs([Cl_[2512369]14] round( round( (MATH NUM menu) returns a matrix. It rounds every element in matrix to #decimals (<_9), If #decimals is olnitted, the elements are rounded to 10 digits, rou nd(mat)qx[ ,#decimals MAT IX[m 2 ×2 1 [ 3,662 -I (Inverse) I,'15_ ]) [[1.26 2.331 Pound([A],2) [3.66 4.121 [ Jse the -1 function ([_ ) to invert a matrix valid), matrix nmst be square. The determinant equal ] ("-1 is not cannot zero. matrix-1 MRTRIX[R] El E_ _z 2 x2 ] l[m-, [[-2 [1.5 1-.51 ] ] To raise a lnatrix to a power, matrix lnust be square. You can use 2 (_), 3 (MATH menu), or ^power (D) for integer power between 0 and 2S& Powers matrix matrix 2 3 matrix^power [[37 54 ] [81 1181 MRTRIX[R]_ _ 10-10 Matrices 2 x2 ] [R]_,5 [R]_ [[1069 [2337 15581 i 34061 Relational To compare Operations and _ (TEST menu), they must have the sanle dimensions, = and _ compare mat_ixA and mat_ixB on an element-byelement basis. The other relational operations are not valid with matrices. two matrices matri._'A=matrixB returns t_tums 0 if any comparison using the relational operations 1 if eveFy" comparison is false. = is true; matrixA_matrixB t_tums 1 if at least one comparison false; it returns 0 if no comparison is false, it is [RI#[B] [R]=[B] iPart(, fPart(, int( iPart( (integer part), fPart( (fractional part), and (greatest integer) are on the MATH NUM menu, iPart( returns a matrix element of matrix, containing the integer int( part of each fPart( returns a matrix containing the fractional part of each element of matrix. int( returns a matrix containing the greatest integer of each element of matrix, iPart(matrix) fPart(matrix) int(matrix) 100.5 47. 151 [[1 3 1 [100 471 ¢PaPt([D]) iPaPt([D1) [[.25 .3331 i [.5 .15 ] Matrices 10-11 Using the MATRX MATRX MATH Menu MATH Operations To display NAMES i: the MATH det( MATRX MATH menu, EDIT Calculates 2: T [_, _ the determinant. Transposes the matrix, Returns the matrix dimensions. Fills all elements with a constant. 3: dim( 4: Fill( 5:identity( Returns Returns 6: randM( 7:augment( the identity matrix. a random matrix. Appends two matrices. Stores a matrix to a list. Stores a list to a matrix. Returns the eunmlative sums of a matrix. Returns the row-echelon form of a matrix. Returns the reduced row-echelon form. 8: Matr*list( 9: List*matr( O: cumSum( A: ref( B: rref( Swaps two rows of a matrix. Adds two rows; stores in the second Multiplies the row by a number. Multiplies the row, adds to the second C: rowSwap( D: row+( E: *row( F: *row+( det( press det((determinant) of a squm'e matrix. returns the determinant row. row. (a real number) det(matrix) T (Transpose) T (transpose) returns a matrix in which each element colunm) is swapped with the corresponding element (colunm, row) of matrix. matrix T [R] [R]T 11 [[1[32 2 311 Accessing Matrix Dimensions with dim( dim((dimension) ({rows columns} [3 11 returns a list containing ) of mat_qz. the dimensions dim(matrix) Note: dim(mat'rix)->Ln:Ln(1) returns the number of rows. dim(mat'rix)->Ln:Ln(2) returns the number of columns. dim( 3,111 10-12 Matrices (row, [_2,7,11[ -8, {2 3} dim([l>+Li:L1 3,111 Creating a Matrix with dim( Use dim( with _ dimensions rows to create x columns a new matrixname of with 0 _Lseach element. {rows,columns}_dim(mat_xname) {2,2}+di_([E]) [E] Redimensioning a Matrix with dim( Fill( [ I I [0 01 [0 011 Use dim( with _ to redimension an existing matrixname to dimensions rows x columns, The elements in the old matrixname that m_ within the new dimensions are not changed. Matrix elements deleted. Additional created elements are zeros. that m'e outside the new dimensions are {rows,columns}-> dim(matrixname) Fill(storesv_uetoeve_ elementin mat_xname. Fill(v_ue,mat_xname) FilI(5,[E]) [El identity( Done [[5[5 5] 51] identity( returns the identity dimension colunms. matrix of dimension rows x identity(dimension) randM( randM( (create random matrix) returns a rows x columns random matrix of integers _>-9 and _<9, The seed value stored to the rand function controls the values (Chapter 2), randM(rows,eolumns) I÷r-and: PahdM(2,2 I [ [0 -71 [88 1] Matrices 10-13 augment( appends matrixA to matrixB as new colunms. matrixA and mahqxB both nlust have tile sanle number of augment( [_)WS. augment(mat) qxA,matrixB) [ [5,61 [7,811+[BI _a,.,gr,,ent([Rl,[B[ [1,21 [[1[3,41256]]+JR] ] [3 Mats,list( 7 811 4 MatrHist( (lnatrix stored to list) fills each listname with elements from each colunm in mahqx. MatrHist( ignores extra listname arguments. Likewise, MatrHist( ignores extra matrix colunms. MatrHist(matrix,listnomeA,._,listname MatP_lis[4 5 611 "* [[R] [[1 It( 2 31 ,Li,LI) [Rl,LiDone n) Lz i_ {I ii {3{25} MatrHist( also fills alistname with elements fronl a specified column# in matrix. To fill a list vdth a specific colunm from matrix, you lnust enter column# _ffter matrix. Mat_list(matrix,column#,listnome) [R] It1 2 31 I 5 6111 "* [a Lt {3 6} Matr_list( Lt ) Listymatr( JR]Done ,3, List)matr( (lists stored to matrL, c) fills matrixna,me colunm by colunm with the elements fronl each list. If dimensions (ff MI lists are not equal, Cist_matr(fills each extra matrixna,r_w row with O.Conlplex lists are not valid. List_matr(listA,._,list n,mah_xname) List.*matP( 10-14 Matrices {1'2'3}+L_I 2 3} {4'5'6]'+L_4 5 _ IX, LB,[CI) ... [C] L_", I O°nel' [[1 _ _ll]l cumSum( cumSum( returns cumulative sums of the elements in mat_'ix, starting with tlle first element. Each element cumulative sum of the colunm from top to bottom. is the cumSum(mat,_ix) [0] [[1151361412]] °ur_Su'_([Dl_[9[46212]]]] Row Operations MATRX MATH menu items A th['ough F m'e row operations. You can use a row operation in an expression, Row operations do not change matrix in nlenloi_yL You can enter all row numbers and values as expressions. You can select the matrix fronl the MATRX NAMES menu, ref(, rref( ref( 0"ow-echelon fornl) returns the row-echelon if)rill of a real mat'_i:c. The number of columns must be greater than or equal to the number of _'ows. ref(mat,_ix) rref( (reduced echelon form be greater row-echelon ff)rm) ret, umls the reduced rowof a _al matrix', The number of colunms must than or equal to the number of rows, rref(mat,_ix) [7 [B] [ [4 8 9] 5 6] ] re?([B]) [[1 1.142857143_3 [0 1 ... rre?([B]) [[1 0 -1] [0 1 2 ]] Matrices 10-15 rowSwap( rowSwap( returns a matrix, It swaps rowA and rowB of matrix, rowSwap(matrix, rowA,rowB) PowSwaP ( [F] [F] row+( [2 [[2[6 ,2,4>[ I 5 1 O] _ 46 3 8 51 791] row+( (row addition) returns a lnatnx. rowB of matrix and stores the results It adds rowA and in rowB. row+(mat_x,rowA,rowB) [[2,5,7118,9,411 +[O] [[2[8 5 9 71 41 * row( row+{[D],l,2)[1012 514711111 *row( (row nmltiplieation) returns a matrix. It nmltiplies row of matrix by value and stores the results in row. * row(value,matrix,row) *row+( (row nmltiplication and addition) returns a nlatdx, It nmltiplies rowA of matrix by value, adds it to rowB, and stores the results in rowB. * row+( *row+(value,matrix,rowA,rowB) *Pow+(3, [[1 10-16 Matrices [E], 1,2) 21 3511 I 11 Contents Lists Getting Started: Generating a Sequence .................. Naming Lists ............................................. Storing and Displaying Lists ............................. Entering List Names ..................................... Attaching Fornmlas to List Names ....................... Using Lists in Expressions ............................... LIST ©PS Menu .......................................... LIST MATH Menu ........................................ '_ TEXAS I I-2 11-3 11-4 11-6 11-7 11-9 11-10 11-17 T1=83 iNSTRUMENTS cunSu_,( {1,2, 3, 4, 5} ) {1 6 18 15} J STATPLOT TBLSET FORMAT CALC TABLE Lists 11-1 Getting Getting Started: Started Generating is a fast-paced a Sequence introduction. Read the chapter for details. Calculate the first eight terms of the sequence i/k-'. Store the results to a use> created list. Then display the results in fraction form. Begin this example on a blank line on the home screen. 1, Press [gfi_ [LIST] [] nlenu, to display MRTH the LIST OPS 3:dim( 4:Fill( 5:se_( 8:cumSu_( 7$_List( 2. Press 6 to select 6:seq(, which pastes the current cursor location. 3. Press l [] @ [A] [] [] @ [] 8 [] 1 [] to enter the sequence. seq( to [A] [] l 4. Press F_, and then press [_ @ to turn on alpha-lock. Press [s] [E] [Q], and then press @ to turn off alpha-lock. Press 1 to complete the list name. 5. Press F_ to generate the list and store it in SEQ1. The list is displayed on the home screen. An ellipsis (...) indicates that the list continues beyond the viewing window. Press [] repeatedly- (or press and hold [_) to scroll the list and view all the list elements. Press [gfi_ [LIST] to display the LIST NAMES menu. Press FENTEm to p_Bte LSEQ1 to the current cursor location. (If SEQ1 is not item 1 on your LIST NAMES menu, move the cursor to SEQ1 before you press F_.) se_(I/RZ,R,1,8,1 i;S_ _IOPS .1111111... MRTH 7. Press [_ to display the MATH menu. Press 1 to select 1:*Frac, which pastes *Frac to the current cursor location. Ise_(i/Ri,R,1,8,1 )+SEQI {i .25 .1111111._ LSEQI*Frac 8. _I 11-2 Press F_ to show the sequence in fraction form. Press [] repeatedly (or press and hold [_) to scroll the list and view all the list elements. Lists 1/4 1,'9 Ix16_. Naming Lists Using TI-83 List Names L1 through L6 The TI-83 Creating a List Name on the Home Screen To create has six list names in nlenlol_-: L1, L2, L3, L4, L5, and L6. The list names L1 through L6 are on the keyboard above the numeric keys [] through [_. To paste one of these names to a valid screen, press E_], and then press the appropriate key. L1 through L6 are stored in stat list editor colunms 1 through 6 when you reset nlenlory, a list name on the home screen, follow these steps. 1. Press [_] [ { ], enter one or more list elements, and then press [_ [ }]. Separate list elements with conunas. List elements can be real nulnbe_\s, complex numbers, or expressions. I<1'2'3'4> I 2. Press _. 3. Press letter @ [letter from of the name. 4. Enter zero to four A to Z or 0] to enter letters, 0, or numbers the first to complete the nanle. [<10203,4}+TEST I 5, Press [E_, The list is displayed on the next line. The list name and its elements are stored in memory. The list name becomes an item on the LIST NAMES menu. _:I,2,3,4]'+TEST{I 2 3 4} 21TEI2_""_OPS MRTH I Note: if you want to view a user-created list in the stat list editor, you must store it in the stat list editor (Chapter 12). You also call create a list nalne ill these in the stat four places, • At the blame= prompt • At an Xlist:, Ylist:, or Data List: Dxnnpt editor • At a List:, List1:, List2:, Freq:, Freql:, Freq2:, XList:, or YList: prompt in the inferential stat editors • On the home screen using You can create as many has space to store. list editor in the stat plot SetUpEditor list names as your TI-83 memo[3z Lists 11-3 Storing and Displaying Storing Elements to a List You can • store Use braces {4+2t, • The Lists list elements and _ in either of two ways. on the home screen. 5-3t } _k G {4+2t _,-3t } Use the stat maxinmm list editor (Chapter 12). dimension of a list is 999 elements. Tip: When you store a complex number to a list, the entire list is converted to a list of complex numbers. To convert the list to a list of real numbers, display the home screen, and then enter real(listname)->listname. Displaying a List on the Home Screen To display" the elements of a list on the home selden, enter the name of the list (preceded by L if neeessa_77; see page 11-16), and then press FEET'. An ellipsis indicates that the list continues beyond the viewing repeatedly (or press and hold []) all the list elements. _IDRTR {2. 154 11-4 Lists {2 5 _0} 50,47 .... window. to scroll Press [] the list and view Copying One List to Another To copy a list, store it to another list. LTEST÷TEST2 LTEST {123:}} {123 Accessing Element a List You can store a value to or recall a value fronl a specific list element. You can store to any element within the current list dimension or one element beyond. listname(element) {1'2'3}÷L_I 23} 4÷L_(4){L_234 L:_ (z.) }2 Deleting a List from Memory To delete lists fronl nlenlol_, including L1through L6,use the MEMORY DELETE FROM secondatF- menu (Chapter 18). Resetting nlenlory restores L1through L6. Removing a list from the stat list editor does not delete it from nlenlol_L Using Lists in Graphing You can use lists to graph a family of creates (Chapter Lists 3). 11-5 Entering List Names Using the LIST NAMES Menu To display- the LIST NAMES menu, press [_ [LIST]. item is a user-created list name. LIST NAMES menu Each items m'e sorted automatically in alphanumerieal order. Only the first 10 items are labeled, using 1 through 9, then 0. To jump to the first list name that begins with a particulm" alpha character or 0, press @ [letter from A to Z or 0]. T _ IOF'S I MRTH Tip: From the top of a menu, press [] to move to the bottom. From the bottom, press [] to move to the top. Note: The LIST NAMES menu omits list names I_1through 1.6. Enter L1 through L6 directly from the keyboard (page 11-3). When you select the list name • Entering a UserCreated List Name Directly from the LIST NAMES menu, to the cmTent cursor location. The list name symbol, precedes a list nmne when the name is pasted where non-list name data also is valid, such as the home screen. LTEST • a list name is pasted (I 2 3 4} The L symbol does not precede a list name when the name is pasted where a list name is the only valid input, such as the stat list editor's Name-- p_x)mpt or the stat plot editor's XList: and YList: prompts. To enter an existing 1. Press [_ list nmne [LIST] [] directly-, follow these steps. to display" the LIST OPS menu. Select B:L, which pastes L is not always necessary L to the current (page 11-16). NRMES [_]_R MRTH 61"CMFISL, Ir'l ( 7: _List( 8: Selec.t( 9: augrqent( 81List*F, ate( R: Mate* 1 ist( cursor location. Note: You also can paste L to the current cursor location from the CATALOG (Chapter I5). =11, 3. Enter the characters ILT123I 11-6 Lists that conlprise I the list name. Attaching Formulas Attaching a Formula to a List Name to List Names You call attach element attached a formula to a list name is a result of the fornmla. When formula nmst resolve to a list. V_llen anything in the attached which the fornmla is attached so that each executed, list the formula changes, the list to is updated automatically. • When you edit an element of a list that is referenced in the fornmla, the corresponding element in the list to which the fornmla is attached is updated. • When you edit the fonnula itself, to which the fornmla is attached all elements are updated. in the list For example, the fit\st screen below shows that elements are stored to L3, and the fornmla L3+10 is attached to the list name LADD10, The quotation lnarks designate the formula to be attached to LADD10. Each element of LADD10 is the sum of an element in L3 and 10. {I°2'3}÷L_I 2 3}[ "L_+IO"+ LADD10 La+IB I LRDD10 {11 12 13} The next screen shows another list, L4.The elements of L4 are the sum of the same formula that is attached to L3. However, quotation marks are not entered, so the fornmla is not attached to L4, On the next line, -6->L3(1):L3 changes to -6, and then redisplays L3. the first element in L3 I {II 12 13}I -6÷Li(1):Li {-6 2 3} W+IO+L4 Tile last screen shows that editing L3updated LADD10, but did not change L4. This is because the formula L3+10 is attached to LADDIO,but it is not attached to L4. LRDDIO {4 L4 {Ii Note: 12 13} 12 13} To view a formula that is attached to a list name, use the stat list editor (Chapter12). Lists 11-7 Attaching a Formula to a List on the Home To attach Screen 1. Press @ [.], enter a list), and press @ or in a Program home a ff)rnmla screen from to a list name or from a program, a blank follow the formula [-] again. these (which line on the steps. must resolve to Note: When you include more than one list name in a formula, each list must have the same dimension. 2, Press _. 3. Enter the name the fornmla. of the list to which • Press [_, and then through ks. • Press [_ [LIST] and select a usm_created from the LIST NAMES menu. • Enter a use_created 11-16). Press enter you want a TI-83 list name to attach list name kl list name directly- using t (page ITNt_RI. {4, 8, "5*LI 9}÷L_4 8 9} '% tLIST 5.LI LLIST {28 40 45} Note: The stat list editor displays a formula-lock symbol next to each list name that has an attached formula. Chapter 12 describes how to use the stat list editor to attach formulas to lists, edit attached formulas, and detach formulas from lists. Detaching a Formula from List a You can detach (cleat') any- of tht_e ways. an attached Lists fron] a list in • Enter ""Olistname on the home screen. • Edit any element attached. • Use the stat of a list to which list editor Note: You also can use ClrList from a list (Chapter 18). 11-8 fornmla (Chapter a fornmla is 12). or ClrAIIList to detach a formula Using Lists in Expressions Using a List in an Expression You can use lists in an expression in any- of three When you press [NY_, any expression each list element, and a list is displayed. • Use L1-Ls or any user-created ways. is evaluated list name for in an expression. 5 16} 20/L1 • Enter {10 4 2} the list elements 20/{2, • directly (step 1 on page 11-3). 5, 10} {10 4 2} Use [_ [RCL] to recall the contents of the list into expression at the cursor location (Chapter 1). Rcl Lt an "* {2,5,10}I{4 25 i00} Note: You must paste user-created list names to the Rcl prompt by selecting them from the LIST NAMES menu. You cannot enter them directly using L. Using Lists with Math Functions You can use a list to input functions. Other chapters a list is valid. The function element, several values ff)r some math and Appendix A specify whether is evaluated for each list and a list is displayed. When you use a list with a function, the function lnust be valid for every element in the list, In graphing, an invalid element, such as -1 in _({1,0,-1}), is ignored, 14"({1,O,-1}) I F'loti Plot_: \VIBx,r( {1, F'lot3 O, -I} ) This returns an error. Thisskips graphsX*_(1) but X*_(-1). and X*_(O), When you use two lists with a two-argulnent function, the dimension of each list must be the same, The function is evaluated for corresponding elements. {5 5,7 6} 9} {i, 2, 3}+{4, When you use a list and a value with a two-argument function, the value is used with each element in the list. {1'2'3}+4{5 6 7} Lists 11-9 LIST OPS Menu LIST OPS Menu To display NAMES OPS the LIST OPS menu, [LIST] [_. Sorts lists in _Lscending order. Sorts lists in descending order. Sets the list dimension, Fills 'all elements with a constant. Creates a sequence, Returns a list of cunmlative sums, Returns difference of successive elements, Selects specific data points, Concatenates two lists, Stores a list to a nlatrix. Stores a lnatrix to a list. Designates the list-name data type, 2:SortD( 3:dim( 4:Fill( 5:seq( 6:cumSum( 7:aList( 8:Select( 9:augment( O:List_matr( A:Matr_list( B:L SortD( [_ MATH 1:SortA( SortA(, press SortA( (sort ascending) sorts list elements fron] low to high values, SortD( (sort descending) sorts list elements from high to low values. Complex lists are sorted based on magnitude (modulus). With one list, SortA( and SortD( sort the elements listnome and update the list in nlenloi_. SortA(listname) of SortD(listname) Sor.tR(L_ ) Done L_ {4 5 6} {6 With two or more lists, SortA( and SortD( sort keylistname, and then sort each dependlist by placing its elements in the same order as the corresponding elements in keylistname. All lists nmst have the same dimension, SortA(k¢ylistname,deperwllistl[,depe_wllist2,...,depe_wllist SortD(k¢ylistname,deperwllistl[,depe_wllist2,...,depe_wllist {5'6'4}÷L_5 6 {1,2,3},L_I 2 4} S°rtR(k_'L_>Done _ 3} n]) n]) {4 5 6} {3 1 2} Note: In the example, 5 is the first element in L4, and 1 is the first element in L5. After SortA(L4,Ls), 5 becomes the second element L4, and likewise, 1 becomes the second element of L5. of Note: SortA( and SortD( are the same as $ortA( and SortD( on the STAT EDIT menu (Chapter 12). 11-10 Lists Using dim( to Find List Dimensions dim((dimension) of list. returns the length (number of elements) dim(list) diM({1,3,5,7}) Using dim( to Create a List 4 You can use dim( with _ to create a new listname with dimension length from 1 to 999. The elements are zeros. length_ dim(listname) 3÷diFKLz Lz Using dim( to Redimension a List You can listnome • ) {0 0 0_ use dim with to dimension The elements new in the old listname dimension • Extra • Elements dimension [gg_] to redimension an existing length from 1 to 999. that are within the are not changed. list elements are filled in the old list that are deleted. by 0. are outside the new length_ d im(listname) {4'8'6}÷L_4 4÷dim(L1 LI Fill( Fill( replaces 8 6 ) {4 8 6 0} each element 3÷diM(L1 L1 in listnome with ) {4 8 6_ value. Fill(value,listname) {3'4'5}÷L_3 4 5} FilI(8,L_) Done L_ {8 8 8} Fill(4+3t,Li_one Li {4+or 4+3t 4+3t} Note: dim( and Fill( are the same as dim( and Fill( on the MATRX MATH menu (Chapter 10). Lists 11-11 seq((sequence) seq( returns a list in which each element is the result of the evaluation of expression with regard to variable for the values ranging from begin to end at steps of increment, variable need not be defined in memory. increment can be negative; the default value for increment is 1. seq( is not valid within expression. seq(expression,variable,begin,e_l[,increment]) se_(AZ, {I cumSum( R, 1,11,3) 16 49 100} cumSum( (cunmlative sunl) returns the cunmlative the elements in list, starting with the first element, elements can be real or complex numbers. sunls of list cumSum(list) c.umSum( {i,2, 3,4, 5}){I 3 6 10 15} AList( aList( returns a list containing the differences between consecutive elements in list. AList subtracts the first element in list from the second element, subtracts the second element from the third, and so on. The list of differences is always one element shorter than the original list. list elements can be a real or complex numbers. AList(list) {20,30, 45., 70}÷ LD IST I {20 30 45 70} aList(LDIST) {10 15 25} Select( Select( selects one or more specific data points fronl a scatter plot or xyLine plot (only), and then stores the selected data points to two new lists, xlistname and ylistname. For example, you can use Select( to select and then analyze a portion of plotted CBL 2/CBL or CBR data. Select(xlistname,ylistname) Note: Before you use Select(, you must have selected (turned on) a scatter plot or xyLine plot. Also, the plot must be displayed in the current viewing window (page 11-13). 11-12 Lists Before Using Select( Before using Select(, follow these steps. 1. Create two list names and enter the data. 2. Turn on a stat plot, select Le: (scatter plot) or [_- (xyLine), and enter the two list names for Xlist: and Ylist: (Chapter 12). 3. Use ZoomStat to plot {1,2, 3, 4, 5,6,7,8] ,9,9.5,10}+DIST I I{i 2 3 4 5 6 7 ...I 1{15, 15, 15, 13, ll,I IEg,?,5,3,2,2)÷TIM I I{15 15 15 13 11...I t Using Select( to Select Data Points from a Plot the data (Chapter _DOnO_z _1*t_ el. TgPe: I If"_ _ i_ _ Xlist.:oIsm YlisL:TIME Mark: [] ÷ • J To select data points fronl a scatter follow these steps. 3). . °o " . . ° ° %. plot or xyLine plot, 1. Press [2_] [LIST][] 8 to select 8:Select( from the LIST OPS menu. Select( is pasted to the home screen. 2. Enter xlistname, press [], enter ylistname, and then press [] to designate list names into which you want the selected data to be stored. I ISeleot(L1,Cz)l 3. Press [g_-gm. The graph screen is displayed Left Bound? in the bottom-left corner. a LeFtBound? u with iI 000 Press [] or [] (if more than one stat plot is selected) to move the cursor onto the stat plot from which you want to select data points. Press [] and [] to move the cursor to the stat )oint that you want as the left bound. keFt BOLIhd? plot data _ ua Lists 11-13 6. Press [NER]. A _ indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottonlleft corner. P i:BIST.,TIH{ o a a _ u U a U uua RiZlht _OUnd? Press [] or [] to nlove tile cursor to the stat plot point that you want for the ri ht bound, and then press [ENY_. PI:DIST_TIHE : a i aa_ a Ri_htBound? m u a " o u u"_ u " [] u The x-values and y-values of the selected points stored in xlistname and ylistname. A new stat ._:listname and ylistname replaces the stat plot which you selected data points. The list names updated in the stat plot editor. are plot of from are 11 9 7 s 3 ]91ist:Lz Mark: [] ÷ . Note: The two new lists (xlistnanw and ylistname) willinclude the points you select as left bound and right bound. Also, left-bonnd x-volne 11-14 Lists < "l_ight-bound x-value must be true. augment( augment( concatenates the elements of listA and listB. The list elements can be real or complex numbers. augment(listA,listB) {1,17,21}+L_ {1 1721} augment.(L_o{a5,3 8,41}) -, {1 17 21 25 o0 ... List_matr( List*matr( (lists stored to matrix) fills matrixname colunm by colunm with the elements from each list. If the dimensions of all lists are not equal, then List_matr{ fills each extra matrixname row with O. Complex lists are not valid. List*matr(listl,list2, {l'2'3}+LX1 . . . ,list n,mat_xname) 2 3} List*matt( LB, 1C1 ) LX, Lists L'_J, I Oone[ 11-15 MatrHist( MatrHist( (matrix stored to lists) fills each listname with elements from each colunm in mahqx. If the number of listname argulnents exceeds the number of colunms in matrix, then MatrHist( ignores extra listr_ame arguments. Likewise, if the number of colunms in matrix exceeds the number of listr_ame arguments, then MatrHist( ignores extra matrix colunms. Mat_list(mat_x,listnamel,listname2 [4 Matr_li_t( ,Lz,L_) 5 6111 -- .... Lz [RI,L1 Done ,listnamen) {2 5} {3 Math.list( also fills a listname with elements fronl a specified column# in matrix. To fill a list with a specific colunm from matrix, you nmst enter a column# after matrix. Mat_list(matrix,column#,listnome) IN] [[1 2 31 [ 5 6111 -- L1 {3 6} Matt*list( LI) [R1,3, Done t preceding one to five characters identifies those characters _ts a use>created listname, listname may comprise letter\% 0, and numbers, but it nmst begin with a letter fi'onl A to Z or 0. Llistname Generally, L must precede a user-created list name when you enter a use>created list name where other input is valid, for example, on the home screen. Without the t, the TI-83 may misinterpret a use>created list name as implied nmltiplication of two or more characters. t need not precede a use>created list name where a list name is the only valid input, for example, at the Name= prompt in the stat list editor or the Xlist: and Ylist: prompts in the stat plot editor. If you enter • where it is not necessary, the TI-83 will ignore the enttT. 11-16 Lists LIST MATH LIST MATH Menu min(, max( Menu To display the LIST MATH menu, press [_ [LIST] E], NAMES OPS MATH i: min( Returns 2: max( Returns Returns 3: mean( Returns 4: median( Returns 5: sum( nnninmm element of a list. nl_ximum element of a list. mean of a list, median of a list, sum of elements in a list. 6: prod( 7:stdDev( 8: variance( product of elements in list, standard deviation of a list, the variance of a list, Returns Returns Returns min((nlininlunl) and max((nlaxinlunl) retul]l the smallest or largest element of listA. If two lists are compared, it returns a list of the snmller or larger of each pair of elements in listA and listB. For a complex list, the element with snmllest or largest magnitude (modulus) is returned. min(listA [,listB ]) max(listA[,listB]) mir,({lo2,3},{3,21 ,i}> {I 2 I}II max({l,2,3}, ,i}> {3 2{3'23} Note: min( and max( are the same as min( and max( on the MATH NUM menu. mean(, median( mean( returns the mean value of list. median( returns the median value of list. The default value forfreqlist is 1. Eachfreqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid. mean(list[ #¢reqlist]) median(list[ dreqlist ]) mean( {1,2,3}, {3, 2, I} > I. 666666667 _'_ed ian ({i, 2, 3} )2 Lists 11-17 sum(, prod( sum((sununation) returns the sunl of the elements start and end are optional; they specify a range elements, list elements can be real or complex in list, of numbers. prod( _tma_s the product of all elements of list. start and end elements are optional; they specify- a range of list elements, list elements can be real or complex nmnbers. sum(list[,start,ef_l]) prod(list[,start,ef_l]) L_ {I 2 5 sur_(L_ ) 8 10} 26 su_KLI,3,5) Sums and Products of Numeric You can 23 colnbine 2 5 8 ) 10} 400800 Prod(Li,3,5) sum( or prod( with upper Sequences k_ {I Prod(L1 seq( to obtain: upper expression(x) x=lower To evaluate x=lower Z 2 (N 1)fl'Oln N=I to 4: sur_(se_ (2" (N- I ), N, 1,4, I)) stdDev(, variance( 15 stdDev( retrains the standard deviation of the element._ The default value forfreqlist is 1, Eachfreqlist element counts the number of consecutive occurrences of the con'esponding element in list. Complex in list. lists m'e not valid. variance( returns the variance of the elements in list, The default value forfreqlist is 1, Eachfreqlist element counts the number of consecutive occmTences of the corresponding element in list. Complex list.s are not valid. stdDev(list[freqlist]) stdOev( ,3, 11-18 Lists vadance(list[freqlist]) {i, 2, 5, -6 -2}) 3. 937003937 variance( -6,3, -2}) {i, 2,5, 15.5 2 Contents Statistics Getting Started: Pendulum Lengihs and Periods ......... Setting Up Statistical Analyses ........................... Using the Stat List Editor ................................ Attaching Fornmlas to List Names ....................... Detaching Formulas from List Names .................... Switching Stat List Editor Contexts ...................... Stat List Editor Contexts ................................. STAT EDITMenu ........................................ Regression Model Features .............................. STAT CALC Menu ........................................ Statistical Variables ...................................... Statistical Analysis in a Program ......................... Statistical Plotting ....................................... Statistical Plotting in a Program ......................... TEXAS 12-2 12-10 12-11 12-14 12-1(; 12-17 12-18 12-20 12-22 12-24 12-2(.) 12-30 12-31 12-37 TI-83 INSTRUMENTS p Z:LI_RE:VIn D 0 M 0 M 0 0 g=Nl.g Y='.OZ7001 J STAT PLOT TBLSET FORMAT CALC TABLE Statistics 12-1 Getting Getting Started: Started Pendulum is a fast-paced A group of students is between the length of pendulum). The group then suspends it from of 12 string lengths.* Press [_DE] [] [] graphing mode. 2. Press [g_g] SetUpEditor screen. introduction. and Periods Read the chapter for details. attempting to determine the lnathelnatical relationship a pendulum and its period (one complete swing of a makes a simple pendulum froln string and washers and tile ceiling. They record the pendulum's period for each Length 1. Lengths (cm) Time 6.5 0.51 11.0 0.68 13.2 0.73 15.0 0.79 18.0 0.88 23.1 0.99 24.4 1.01 26.6 1.08 30.5 1.13 34.3 1.26 37.6 1.28 41.5 1.32 (sec) [] [g_gg] to set Func 5 to select 5:SetUpEditor. is pasted to the honm Press [gfff_. This relnoves lists fronl stat list editor colunms 1 through 20, and then stores lists L1through L6 in eolunms 1 through 6. SetUeEditof Done[ Note: Removinglists from the stat list editor doesnot deletethem from memory. 3. Press [gf_] 1 to select 1:Edit fronl the STAT EDIT menu. The stat list editor is displayed. If elements are stored in 1-1 and I_2,press [] to move the cursor onto 1_1,and then press @ [gNT_ [] [] @ [gg7_ to clear both lists. Press [] to move the rectangular cut\sor back to the first row in 1_1. L1(1)= *This example is quoted and adapted from Contempo'_mT P'recal(vdns Th'mugh Applications, by the North Carolina School of Science and Mathematics, by permission of Janson Publications, Inc., Dedham, MA. 1-800-322-MATH. © 1992. Aft rights reserved. 12-2 Statistics 4. Press 6[] 6 _ to store the first pendulum string length (6.5 cm) in 1.1. The _ctangular cursor nloves to the next row. Repeat this step to enter each of the 12 string length values in the table on page 12-2. Press [] to inove the rectangular to the first row in 1.2. cursor Press [] 61 _ to store the first time measurement (.51 sec) in 1.2. The LI .Z L_: 1 .Z L_: Z 26,6 37.ti L1(1_) = Lt 26.6 t.0B 3LI.:_ 3?.tl t.Ztl J..ZB rectangulm" cursor moves to the next row, Repeat this step to enter each of the 12 time wdues in the table on 6. page 12-2. Press [] to display- Plot1 PloLZ Plot:_ \V1 =11 the Y= editor. If necessm'y, press @ to clem" the fm_ction Y1. As necessmy, press [], [E_, and [] to turn off Plot1, Plot2, and Plot3 from the top line of the Y= editor (Chapter 3). As necessmy, press [], [_, and [_ to deselect functions. ".Yz= _.y_= xy_= "_y_= xY_;= \Y?= Press [_ [STAT PLOT] 1 to select 1:Plot1 fi'om the STAT PLOTS menu. The stat plot editor is displayed for plot 1. Press _ to select On, which turns on plot 1. Press [] _ to select ,,'." (scatter plot). Press [] _ [L1] to specify- ×list:1.1 for plot 1. Press [] [L2] to specify- Ylist:1.2 for plot 1. Press [] [] _ to select + _ksthe Mark for each data point on the scatter plot. _peO Plo_2 P1o_:_ +-,._ liar-k: . [] • Press _ 9 to select 9:ZoomStat fronl the ZOOM menu. The window variables are adjusted automatically, displayed. This is a scatter time-versus-length data. ÷ + ÷ and plot 1 is plot of the ÷ ÷ ++ + +÷+ + Statistics 12-3 Since thescatter plotoftime-versus-length dataappears tobeapproxhnately linear, fit a line to the data. 10. Press _ [] 4 to select (linear regression nlodel) CALC menu, kinReg(ax+b) tile home screen. 11. Press [_ [L1] [] 1 to display 4:LinReg(ax+b) fronl the STAT is pasted to LinReg(ax+b) | _ [L2] [_. Press the VARS Y-VARS [] FUNCTION secondmT menu, and then D_ss 1 to select 1:Y1. Lt L2, and Y1 are pasted to the home screen as arguments to LinReg(ax+b). 12. Press [_ to execute LinReg(ax+b). The lineal" regression for the data in L1 and L2 is calculated. Values for a and b are displayed regression Residuals on the home screen. The linear equation is stored in Y1, are calculated and stored automatically in the list name RESID, which becomes an item on the LIST NAMES menu, 13. Press _. The regression scatter plot are displayed. 12-4 Statistics line and the LinReg 9=_x+b a=.0230877122 b=.4296826236 Theregression lineappears tofit thecentral portionofthescatter plotwell. However, aresidual plotmayprovide moreinformation about thisfit. 14.Press [g_g] 1 to select 1:Edit. The stat list editor Press L3. E2; 11 is displayed. [] and [] to lnove Press [_ displayed shift right prompt is alpha-lock the cursor onto [INS]. An unnamed colunm is in colunm 3; 1.3, k4, L5, and 1_6 one colunm. The Name= displayed in the entry line, and is on. 15. Press [2_ [LIST] to display NAMES menu. the 1_; 18 ;:3.1 2h.h NaMe=_ 2;1 ._8 ,79 ,8B .99 1,01 LIST If necessatT, press [] to inove the cursor onto the list name RESID. 16. Press _ to select RESID and paste it to the stat list editor's Name= pt_mlpt. Lt .2 &5 ,B1 11 13.2 ,l_B .73 2h.h 1.01 1_: 1B .2_:.1 17. Press IgOr. RESID is stored in colunm of the stat list editor. Press [] repeatedly residuals. to examine the _ .79 .EB .99 3 I_.B ,51 ".06911 11 .6B ".0036 13.2 ,73 ".OOhh 1_: .79 .01h 1E .BE .03h?h ?._:.1 .99 .0Z699 2h._ 1.=31 .0lEgit eCSZD= £ -. 0697527... Notice that the first three residuals are negative. They cotTespond to the shortest pendulum string lengths in L1. The next five residuals are positive, and three of the last four are negative. The latter correspond to the longer string lengths in L1. Plotting the residuals will show this pattern more clearly. Statistics 12-5 18. Press [2_] [STAT PLOT] 2 to select 2:Plot2 from the STAT PLOTS menu. The stat plot editor is displayed for plot 2. 19. Press [[email protected]] plot 2. to select On, which turns on Press [] FEffEEN to select _ (scatter plot). Press [] [2_] [L1] to specify Xlist:L1 ff)r plot 2. Press [] [R] [E] [S] [I] [D] (alpha-lock is on) to specify Ylist:RESID for plot 2. Press [] FEflT_]to select [] as the mark for each data point on the scatter plot. 20. Press [] to display the Y= editor. Press [] to nlove the cursor onto the = sign, and then press [g_ to deselect Y1. Press [] [g_ to turn offplot 1. 21. Press _ 9 to select 9:ZoomStat fl'oln the ZOOM menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals. Pl*t:[O_ P10t? _uPe: m k:2 dt_ Xlist:L1 YI ist: RESIO [] * Mark: PI*L1 _ Statistics Pl*t_ xY1 =. 02308771216 587X+. 4296826135 7287 xYz= xY?= xY_= \Y_= D Eli= Notice the pattern of the residuals: a group of negative residuals, of positive residuals, and then another group of negative residuals. 12-6 . then a group Theresidual patternindicates acm5Tature associated withthisdatasetfor whichthelinearmodeldidnotaccount. Theresidual plotemphasizes a downward curvature, soamodelthatcm_'es downwiththedatawouldbe moreaccurate. Perhaps afunction suchassquare rootwouldfit.TFFapower regression to fit a function of the form y = a * xt'. 22. Press [] to display the Y=editor, Press @ to clear tile linear regression equation from Y1,Press [] [ggY_ to turn on plot 1, Press [] [g_gO to turn off plot 2. ",Yz= ,.Y_= _.y_= -,y_= _.y_= \y;_= 23. Press _ 9 to select 9:ZoomStat froin the ZOOM menu. The window variables ÷ + ÷ + are adjusted automatically, and the original scatter plot of time-versuslength data (plot 1) is displayed. _+ ÷ ÷÷÷ ÷ 24. Press Fgg_ [] @ [A] to select A:PwrReg from the STAT CALC menu. PwrReg is pasted to the home screen. PuPReg L1,Lz,Yi| Press [g_ [L1][] [g_ [L2][]. Press [] 1 to display the VARS Y-VAR$ FUNCTION secondmT menu, and then press 1 to select 1:Y1.1.1, 1_2,and Y1 are pasted to the home screen as arguments to PwrReg. 25. Press [g_gm to calculate the power regression. Values for a and b are displayed on the home screen. The power regression equation is stored in Y1. Residuals are calculated and stored automatically in the list name RESID, 26. Press _. The regression scatter plot are displayed. PwrReg _=a*x^b a=.1922828621 b=.5224982852 line and the Statistics 12-7 The new function y=.192x _"- appears t( fit the data well. To get nlore information, examine a residual plot. 27. Press [] to display Pl*tl the Y= editor. _ Pl*t3 19228286213 ".,Y 1 ----. Press [] _ to deselect 552X% Y1. Press [] [NY_ to turn offplot [] [ggY_ to turn on plot 2. 1. Press Note: Step 19 defined plot 2 to plot residuals (RESID) versus string length (11). 28. Press _ 9 to select 9:ZoomStat froln the ZOOM menu. The window variables are adjusted automaticMly, and plot 2 is displayed. This is a scatter plot of the residuMs. 5224982852 \y_= \Y_= D [] a El The new residual plot shows that the residuals are random in sign, with the residuals increasing in magnitude as the string length increases. To see the magnitudes of the residuals, continue with these steps. 29. Press _. Press [] and [] to trace the data. Observe the values for Y at each point. With this model, the largest positive residual is about 0.041 and the smallest negative residual is about -0.027. All other residuals are less than 0.02 in magnitude. 12-8 Statistics P ;':LI_F;E$'r II/:_1.5 B [] Y:'.OZ?OOJ. Nowthatyouhaveagoodmodelfortherelationship between lengthand period, youcanusethemodeltopredict theperiodforagivenstringlength. Toprediet theperiods forapendulum withstringlengths of20cmand50cm, continue withthesesteps. 30.Press [_ [] 1todisplaytheVARS Y-VARS FUNCTION seconda[w menu, and thenpress1toselect 1:Y1. Y1ispasted tothehomescreen. _1 31.Press [] 20 20 [] to enter a string length II of enl, Press _ to calculate the predicted time of about 0.92 seconds. Based on the residual expect the prediction seconds to be within of the actual value. 32. Press _ [ENTRY] anMysis, we would of about 0.92 about 0.02 seconds to recall Press [] [] [] 6 to change length to 51) enL the Last EnbTy'. the string 33. Press _ to calculate the predicted time of about 1.48 seconds. I. 484736865 _11(50)(28!9198781364 Since a string length of 50 cnl exceeds the lengths in the data set, and since residuals appear to be increasing _ string length increases, we would expect more etTor with this estimate. Note: You also can make predictions using the table with the TABLE SETUP settings Indpnt:Ask and Depend:Auto (Chapter 7). Statistics 12-9 Setting Up Statistical Analyses Using Lists to Store Data Data for statistieM Setting Up a Statistical Analysis To set up a statistical chapter for details. 1. Enter 2. Plot is stored 4. data in lists, which you stat list editor. The TI-83 h_ks L1 through L6, to which you calculations. Also, you call you create (Chapter 11). analysis, the statistical follow into these steps. one or more Read the lists. the data. 3. Calculate Graph the statistical the regression 5. Graph Displaying the Stat List Editor analyses can create and edit using the six list vadal_les in lnelnory, can store data ff_r statistical store data to list names that the residuals vm'iables equation or fit a model to the data for the plotted list ff)r the given data. regression model. The stat list editor is a table where you can store, edit, and xqew up to 20 lists that are in nlenlol_yL Also, you Call create list nalnes fronl the stat list editor. To display- the stat list editor, press [g_T], and then select 1:Edit fronl the STAT EDIT menu, CRLC TESTS L1 mmm L_: ._ 1 SortO( ClrList SetUeEditor LI(I)= The top line displays list names. L1 through colunms 1 through 6 after a lnelnolT reset. the current colunm is displayed L6 are stored in The number of in the top-right The bottom line is the entry line. All data entry this line. The characteristics of this line change to the current context (page 12-17). corner. occurs on according The center area displays up to seven elements of up to tht_e lists; it abbreviates wdues when neeessalT. The enttT line displays the full value of the curt_nt element. 12-10 Statistics Using the Stat List Editor Entering a List Name in the Stat List Editor To enter a list name in tile stat list editor, follow these steps. 1. Display the Name= prompt in the entt T line in either of two ways. • Move the cursor onto the list name in the colunm whet_ you want to insert a list, and then press [_ [iNS]. Nil unnamed colunm is displayed and the remaining lists shift right one colunm. • Press [] until the cut\sor is on the top line, and then press [] until you reach the unnamed colunm. Note: If list namesare storedto all 20 columns,you mustremove a list name to makeroomfor an unnamedcolumn. The Name= prompt LI L:;" is displayed and alpha-lock is on. 1 qame=_ 2. Enter a valid list name in any of four ways. • Select a name fl'onl file LIST NAMES menu (Chapter • • Enter Cl, C2, Ca, L4, ks, or C6fronl the keyboard. Enter an existing user-created list name directly from the key! Joard. Enter a new user-created list name (page 12-12). • I I,Iamo=RBC I 11). I I 3. Press [ggtgN or [] to store the list name and its elements, if any-, in the cutTent colunm of the stat list editor. Lt k:;" t To begin entering, scrolling, or editing list elements, []. The rectangular cursor is displayed. Note: If the another stat move to the names shift press list name you entered in step 2 already was stored in list editor column, then the list and its elements, if any, current column from the previous column. Remaining list accordingly. Statistics 12-11 Creating a Name in the Stat List Editor To create 1, a name in the stat list editor, ff)llow these steps, Follow step 1 on page 12-11 to display- the Name= prompt. 2, Press [letter from A to Z or 0] to enter the first letter of the name. The first character cannot be a number. 3, Enter zero to four letters, O, or numbers new user-created list name. List names five characters to conlplete the can be one to long. Press [g_ or [] to store the list name in the current colunm of the stat list editor. The list name becomes item Removing a List from the Stat List Editor on the [_[ST NAMES menu (Chapter an 11). To remove a list from the stat list editor, move the cursor onto the list name and then press [DTn. The list is not deleted from memory; it is only removed from the stat list editor. Note: To delete a list name from memory, use the MEMORY DELETE:List selection screen (Chapter 18). Removing Lists and All Restoring L1 through L6 Clearing All Elements from a List You Use SetUpEdRor • Reset all user-created all memotT • • • lists list names L1 through of two ways. with no arguments (Chapter You can clear all elements • Statistics remove • • 12-12 can editor and restore through 6 in either from the stat list L6 to colunms (page 1 12-21). 18). from a list in any- of five ways. Use ClrList to clear specified lists (page 12-20). In the stat list editor, press [] to move the cursor onto a list name, and then press @ [ggg_. In the stat list editor, move the cursor onto each element, and then press [g_ one by one. On the home screen or in the program editor, enter O->dim(listname) to set the dimension of listname to 0 (Chapter 11). Use ClrAIILists to cleat' all lists in memory (Chapter 18). Editing a List Element To edit a list element, follow 1. Move the rectangular to edit. 2. Press [_ to move these cursor steps. onto the cursor the element to the entry you want line. Note: If you want to replace the current value, you can enter a new value without first pressing _. When you enter the first character, the current value is cleared automatically. 3, Edit tile element in tile entity- line, • Press one or lnore keys to enter the new you enter the ill,st character, the current cleared automatically. • Press [] to move the cta'sor to the character before which you want to insert, D_ess [_ [_NS], and then enter one or more charactegs, • Press [] to move the cta'sor to a chm'acter you want delete, and then press [ff_] to delete the character. To cancel any editing and restore the rectangular cursor, press @ ABe Lt L2 the value. value original [_. When is element to at t _co)=25-1000| Note: You can enter expressions and variables for elements. 4. Press [gNYE_, [], or [] to update the list. If you entered all expression, it is evaluated. If you entered only a variable, the stored value is displayed as a list element. L1 ttl_C L_: 1 :LO _C(_)=20 When updated you edit a list element in nlenloFy ill the stat list editor, the list is inunediately. Statistics 12-13 Attaching Formulas Attaching a Formula to a List Name in Stat List Editor to List Names You can attach a fornmla to a list name in the stat list editor, and then display- and edit the calculated list elements. VCl_enexecuted, the attached fommla nmst resolve to a list. Chapter 11 describes in detail the concept of attaching fornmlas to list names. To attach a fonnula to a list name that is stored in the stat list editor, follow these steps. 1. Press [Kf_T]_ to display the stat list editor. 2. Press [] to move the cursor to the top line. 3. Press [] or [_, if necessm% to move the cm_sor onto the list name to which you want to attach the fornmla. Note: If a formula in quotation marks is displayed on the entry line, then a formula is already attached to the list name. To edit the formula, press_, 4. Press @ andthen edit the formula. [,,], enter the fornmla, and press @ [,,]. Note: If you do not use quotationmarks,the T1-83calculatesand displays the same initiallist of answers,but does not attach the formula forfuture calculations. I i:i_¢ "II] tO L;_ ;; .... L20__ul_5__. LFIEIC+IO"11 Note: Any user-created list name referenced preceded by an L symbol (Chapter 11 ). in a formula must be 5. Press IENTERI. The TI-S3 calculates each list element and stores it to the list name to which the fornmla is attached. A lock symbol is displayed in the stat list editor, next to the list name to which the fornmla is attached. lock symboI / I=I_C Lt tO ;;_:O00 u_1_=15 12-14 Statistics $ j L> _:0 _O::!.0 _: Using the Stat List Editor When Formula- When Generated (Chapter Lists Are Displayed you edit attached element ABC I(, 2_:000 Z$ an element of a list referenced in an fommla, the TI-83 updates the co_Tesponding in the list to which the fornmla is attached 11). LI $ t5 _:0 _:_:0i0 ._0 ._: 1 ItI_C 2_:000 LI $ .2 1 >0 ;:_:0i0 _c_z_ = 1e When a list with a formula attached is displayed in the stat list editor and you edit or enter elements of another displayed list, then the TI-83 takes slightly- longer to accept each edit or ent_3; than attached are in view. when no lists with formulas Tip: To speed editing time, scroll horizontally until no lists with formulas are displayed, or rearrange the stat list editor so that no lists with formulas are displayed. Handling Errors Resulting from Attached Formulas On the home screen, you can attach to a list a formula that t_ferences another list with dimension 0 (Chapter 11). However, you cannot display the fornmla-generated list in the star list editor or on the home screen until you enter at least one element to the list that the formula references. All elements of a list t_ferenced by an attached fornmla nmst be valid for the attached fornmla, For example, if Real number mode is set and the attached formula is log(l_1), then each element of 1.1 nmst be greater since the logarithm of a negative number returns complex result, than a O, Tip: If an error menu is returned when you attempt to display a formula-generated list in the stat list editor, you can select 2:Goto, write down the formula that is attached to the list, and then press _ to detach (clear) the formula. You then can use the stat list editor to find the source of the error. After making the appropriate changes, you can reattach the formula to a list. If you do not want to clear the formula, you can select 1:Quit, display the referenced list on the home screen, and find and edit the source of the error. To edit an element of a list on the home screen, store the new value to list'name(element#) (Chapter 11). Statistics 12-15 Detaching Detaching a Formula from a List Name Formulas You can detach four ways, • • • • List Names (clear) a formula fronl a list name in any of In the stat list editor, nlove the cursor onto the name of the list to which a fornmla is attached. Press [gflT_ @ [Ni_. All list elements remain, but the fommla is detached and the lock symbol disappeat\s. In the stat list editor, nlove the cursor onto an element of the list to which a fornmla is attached. Press [gflT_, edit the element, and then press [ggT_. The element changes, the fornmla is detached, and the lock symbol disappears. All other list elements remain. Use CIrList (page 12-20). All elements of one or more specified lists are cleared, each formula is detached, and each lock symbol disappears. All list names remain. Use ClrAIILists (Chapter 18). All elements of 'all lists in nlenlory are cleared, M1 fornml_ts m'e detached from 'all list names, and all lock symbols disappear. All list nanles Editing an Element of a FormulaGenerated List from renlain. As described above, one way to detach a fornmla fronl a list name is to edit an element of the list to which the formula is attached. The TI-83 protects against inadvertently detaching the fornmla from the list name by editing an element of the fornmla-generated list. Because of the protection feature, you lnust press [gflT_ before you can edit an element of a formula-generated list. The protection feature does not allow you to delete an element of a list to which a formula is attached. To delete an element of a list to which a formula is attached, you nmst first detach the fornmla in any- of the ways described above. 12-16 Statistics Switching Stat List Editor Contexts The Stat List Editor Contexts stat list editor • View-elements • View-nanles has four context context contexts, • Edit-elements • Enter-name context context The star list editor is first displayed in view-elements context. To switch through the four contexts, select from the STAT EDIT menu and follow these steps, Lt _ L_ 1 1, Press [] to move the cursor onto a list name. You are now in view-names context, Press [] and [] to xqew list names stored in other stat list editor columns, 2. Press [_, You are now in edit-elements context, You may edit any element in a list, All elements of the cmTent list are displayed in braces ( { } )in the enhzyline, Press [] and [] to view more list elements. 3. Press [gNY_ again. You are now in view-elements context. Press [], [_, [], and [] to view other list elements. The current element's full value is displayed in the entt3z line. 4. Press fNY_ again. You are now in edit-elements context. You may edit the current element in the entl3z line, 5, Press [] until the cursor is on a list name, then press [_ [INs]. You are now in enter-name context, 20 2,55? 30 35 Z,SE7 2_ Z5 1:Edit _c ={5, 10,25000... LI 5 $ L2 i _5 i ...... I_5._ii_5, _5 i 35 Asc :|5_10,25000... _5C 2_5E? _ _5 LI $ L& i 3_ i 35 LIc3)=25000010 AI_5 5 LI $ L2 i _,5 ...... 2_5E7 25 i 35 LI(3)=|5000010 5 :i._ 2,557 20 25 fist _5 20 2.557 3_ 35 _'1 5 i 15 2.5E7 _ 25 _.5£? i 30 i 35 _ L2 2 6, Press 2. 7, Press [], You are now back in _dew-elements ...... @, You are now in view-naines context. Li =" LR_C+10" _5C 5 :L_ 2.5E7 2_ 25 LI im i 20 i 2,557 i 30 i 35 $ L2 context. ...... LI(I)=15 Statistics 12-17 Stat List Editor Contexts View-Elements Context In view-elements context, the enttT line displays the list name, the cmTent element's place in that list, and the full value of the current element, up to 12 chm'acters at a time. An ellipsis (...) indicates that the element continues beyond 12 characte_\s. hBC Lt 5 t5 2._:E7 ;'0 _0 $ ._ 2 tu_)=25000010 To page down the list six elements, press @ []. To page up six elements, press @ []. To delete a list element, press [DT0.Remaining elements shift up one row. To insert a new element, press [g_ [INS]. 0 is the default value for a new element. Edit-Elements Context In edit-elements context, the data displayed line depends on the previous context. When you switch elements context, is displayed. You then press [] and R_(: LI in the enttT to edit-elements context from xqewthe full value of the cmTent element can edit the value of this element, and [] to edit other list elements. $ L_: ABe LI $ 2g010 _0 _g _0 3E: 2g _co)=25000 25 A_co_=|5000 When you switch to edit-elements context fronl viewnames context, the full vMues of 'all elements in the list are displayed. An ellipsis indicates that list elements continue beyond the screen. You can press [] and [] to edit any element in the list. g t0 _000 IA_c:£5, L1 1_; $ k:;" -, Z0 Zg0t0 10, 25000._ L1 1 I0 Z_:000 _c $ .2 1 ZO 7_010 =I5, 10, 25000... Note: In edit-elements context, you can attach a formula to a list name only if you switched to it from view-names context. 12-18 Statistics View-Names Context In view-names context, and the list elements, LI 5 10 15 _O 25 25 _O _5 € .2 the entry line displays the list name I ,Pc =15,10,25000_. To remove Remaining deleted To insert Remaining Enter-Name Context a list from the stat list editor, press [3_], lists shift to the left one colunm. The list is not from memow. a name in the eutTent colunm, press [_ eolunms shift to the right one colunm, In enter-name context, the Name= prompt the entw line, and alpha-lock is on. [_NS], is displayed in At the Name= prompt, you can create a new list name, Dkste a list nalne fronl L1 to L6 fronl tile keyboard, or paste an existing list nalne froln the LIST NAMES menu (Chapter 11). The • s3qnbol is not required at the Name= prompt. _BC r. 10 _OOO _O .1 ') i 1_r _0 -_SOiO 30 Name=_ To leave enter-name context without entering a list name, press @. The stat list editor switches to xqew-names context. Statistics 12-19 STAT EDIT Menu STAT EDIT Menu To display the STAT EDIT menu, press [_, EDIT CALC TESTS i: Edit.., Displays the stat list editor. 2: SortA( Sorts a list in ascending order. 3: SortD( Sorts a list in descending order. 4: ClrList Deletes all elements of a list. 5: SetUpEditor Stores lists in the stat list editor. Note: Chapter 13: Inferential Statistics describes the STAT TESTS menu items. SortA(, SortD( SortA( (sort ascending) sorts list elements fl'om low to high values, SortD( (sort descending) sorts list elements fl'om high to low values, Complex lists are sorted based on magnitude (modulus). SortA( and SortD( each can sort in either of two ways. With one listname, SortA( and SortD( sort the elements in listname and update the list in memory. With two or more lists, SortA( and SortD( sort keylistname, and then sort each dependlist by placing its elements in the same order as the corresponding elements in keylistname, This lets you sort two-variable data on X and keep the data pairs together, All lists nmst have the same dimension. The sorted lists are updated in nlen]ot_yL SortA(listname) SortD(listname) SortA(k¢ylistname,depe_MJistl[,depezwllist2,...,depezMlist SortD(k_ylistname,depe_Mlistl[,depe_wllist2,...,depe_Mlist {5 4 3}I ,{1,2,3}+L4 {5, 4,33 +L {i _ 2 3} I I _ortR (L_, L4 >Done n]) n]) {3 4 5} {3 2 _ L_ I} Note: SortA( and SortD( are the same as SortA( and SortD( on the LIST OPS menu. CIrList ClrList clears (deletes) from memotT the elements of one or more listnames. Clrkist also detaches any fornmla attached to a listname. ClrList listname l ,listname2,...,listname n Note: To clear from memory al! elements of all list names, use OIrAIILists (Chapter 18). 12-20 Statistics SetUpEditor With SetUpEditor you can set up the stat list editor display- one or more listnames in the order that specify-. You can specify zero to 20 listnames. to you SetUpEditor [listnamel,listname2,...,listname n] SetUpEditor names fron] with one to 20 listnames removes the stat list editor and then stores all list listnames the stat list editor colunms in the specified in order, beginningincoluinnl. SetUPEditor RESI D,L_,L_,TIME,LOH G,RI23 _E_ID .00692 Done L_ ._ _ t 2 12 ".001_ h .OOBh _ ",OOIB 6 ",0106 t_ I_ 16 RESZD<V= -. 0013125_. TIME Lgn6 _123 120 30 s6 B2 ?h Is It0 I1_ ...... _6 98 I_ 130 h TIHE(!) =_ If you enter a listname that is not stored in lnelnory already, then listname is created and stored in memory; becoines an item on the LIST NAMES menu, Restoring L1 through L6 to the Stat List Editor SetUpEditor with no listnames removes all list names the stat list editor and restores list names kl through the stat list editor columns 1 through 6. it fronl ks in SetUPEditor Done | Lt 11 13.2 1_; 1B 2_.1 :*h,h L1(I:_=6,5 L2 ._1 ,6B ,7_ ,79 .BB ,99 1,01 ._ 1 _" t Lh L5 [L6 $ h 1LI h 5 6 [i6 Lh(1)= Statistics 12-21 Regression Model Features Regression Model Features STAT CALC menu items 3 through C are regression models (page 12-24). The automatic residual list and automatic _gression equation features apply to all regression models, Diagnostics display mode applies to some regression models. Automatic Residual List Vclmn you execute a regression model, the automatic residual list feature computes and stores the residuals the list name RESID. RESID becomes an item on the LIST NAMES menu OPS The TI-83 elements. (Chapter 11). MRTH uses the fommla The next section RESID = Ylistname Automatic Regression Equation to below to compute RESID list describes the variable RegEQ. - RegEQ(Xlistname) Each regression nlodel has an optional argulnent, regequ, which you can specify- a Y= variable such as Y1. Upon for execution, the regression the specified Y= variable to 2, -5_÷t_l equation is stored automatically and the Y= function is selected. -2 LinReg(ax+b) Lz,Y_I I Lir_Re9 b= I.333333333 Regardless of whether the regression equation variable RegEQ, which secondmT XY E L_ [ nou _ ,,,1= B -2X+l. 13333333 you specify- a Y= variable no_ 333333 I for regequ, always is stored to the TI-83 is item 1 on the VARS Statistics EQ menu. TEST PTS 3-'b Note: For the regression equation, you can use the fixed-decimal mode setting to control the number of digits stored after the decimal point (Chapter I ). However, limiting the number of digits to a small number could affect the accuracy of the fit. 12-22 Statistics Diagnostics Display Mode When you execute computes coefficient) sonle t_gression nlodels, the TI-83 and stores diagnostics values for r (correlation and r2 (coefficient of determination) or for N2 (coefficient of determination). r and r2 are computed models. and stored LinReg(ax+b) LinReg(a+bx) LnReg ExpReg R2 is computed and stored QuadReg for these regression PwrReg for these t_gression CubicReg models. QuartReg The r and r2 that are computed for LnReg, ExpReg, and PwrReg are based on the linearly transformed data. For example, for ExpReg (y=ab^x), r and r2 are computed on In y=ln a+x(ln b). By- default, these values are not displayed with the results of a regression model when you execute it. However, you can set the diagnostics display mode by executing the DiagnosticOn or DiagnosticOff instruction. Each instruction is in the CATALOG (Chapter 15). det( DiagnostioO_ vDiagnostioOn CATALOG diM( Note: To set DiagnosticOn or DiagnosticOff from the home screen, press _ [CATALOG], and then select the instruction for the mode you want. The instruction is pasted to the home screen. Press to set the mode. When DiagnosticOn the results when is set, di_nostics you execute OiagnostioOnoone L_Reg(a×+b) m'e displayed a regression LinReg _=_x+b L,, a=-2 b=1.333333333 ni=.9230769231 n=-.9607689228 When DiagnosticOff is set, di_nostics are not with the results when you execute a regression Diagno_tioO¢_one L_Reg(ax+b) with model. displayed model. LinReg _=ax+b LI, a=-2 b=1.333333333 Statistics 12-23 STAT CALC STAT CALC Menu Menu To display EDIT the CALC 1:1 Var Stats 2:2 Var Stats 3:Med STAT CALC menu, press [KY_] [_. TESTS Calculates 1-vmiable statistics, Calculates 2-vmiable statistics. Calculates a lnedian-lnedian line, Fits a linear model to data. Med 4: LinReg(ax+b) 5:QuadReg 6: CubicReg 7: QuartReg 8: LinReg(a+bx) 9: LnReg O: ExpReg A: PwrReg B: Logistic C: SinReg Fits Fits a quadratic model to data, a cubic model to data. Fits Fits a quartic model to data, a linear model to data. Fits Fits Fits Fits Fits a logarithmic model to data, an exponential model to data, a power model to data, a logistic model to data, a sinusoidal model to data, For each STAT CALC menu item, if neither Xlistname nor Ylistname is specified, then the default list names m'e kl and k2. If you do not specifyfreqlist, then the default is 1 occurrence of each list element. Frequency of Occurrence for Data Points For most STAT CALC nlenu itenls, data occurrences, or frequencies you can specify (freqlist). Each element infreqlist indicates corresponding data point or data you are analyzing. how many pair occurs a list of times the in the data set For example, if 1_1={15,12,9,14} and LFRlaQ={1,4,1,3}, then the TI-83 interprets the instruction 1-Vat Stats 1.1, LFREO to mean that 16 occurs once, 12 occurs four times, 9 occurs once, and 14 occurs three times. Each element element nmst infreqlist be > 0. nmst be _>0, and at least one Nonintegerfreqlist elements m'e valid. This is useful when entering frequencies expressed as percentages or parts that add up to 1. However, iffreqlist contains noninteger frequencies, Sx and Sy are undefined; wdues m'e not displayed for Sx and $y in the statistical results, 12-24 Statistics 1-Var Stats 1-Var Stats (one-variable statistics) analyzes data with one measm'ed variable. Each element infreqlist is the frequency of occurrence for each corresponding data point in Xlistname. freqlist elements nmst be real numbers > 0. 1-Var Stats [Xlistnamefreqlist] _iVaP 2-Var Stats Stats LI,L 2-Var Stats (two-variable statistics) analyzes paired data. Xlistname is the independent variable. Ylistname is the dependent variable. Each element infreqlist is the frequency of occutTence for each data pair (Xlistname, Ylistname), 2-Var Stats [Xlistname,_Tistnome_freqlist] Med-Med Med-Med (nmdian-n]edian) (ax+b) to the data using the median-nmdim_ line (resistmlt line) technique, calculating the sunul]aYy points xl, yl, x2, y2, x3, and y3. Med-Med displays values for a (slope) and b (y-intercept). fits the model equation y=ax+b Med-Med[Xlis_ame,_is_ame_v_ist,regequ] _=ax+b _ed-Med LinReg (ax+b) L_,L_,Yz a=.875 Med-Med b=1.541666667 I LinReg(ax+b) (linear regression) fits the model equation y=ax+b to the data using a least-squares fit. It displays values for a (slope) and b (y-intercept); when DiagnosticOn is set, it also displays values for r2and r, LinReg(ax+b) [Xlistname,Ylistname_freqlist,regequ] QuadReg (axZ+bx+c) QuadReg (quadratic regression) fits the second-degree polynomial y=ax2+bx+c to the data. It displays values for a, b, and c; when DiagnosticOn is set, it also displays a value for R2. For three data points, the equation is a polynomial fit; for four or more, it is a polynomial regression. At least three data points are required. QuadReg [Xlistname,Ylistname_freqlist,regequ] Statistics 12-25 CubicReg (ax3+bx2+cx+d) CubicReg (cubic regression) fits the third-degree polynomial y=ax:_+bx2+ex+d to the data. It displays wdues for a, b, c, and d; when DiagnosticOn is set, it also displays a wdue for R2. For four points, the equation is a polynomial fit; for five or more, it is a polynomial four points are requil_d. CubicReg Qua_Reg (ax4+bx3+cx2+ dx+e) [Xlistname,_istnamedCreqlist,regequ At least ] QuartReg (quartic regression) fits tile fourth-degree polynomial y=ax4+bx:%cx2+dx+e to the data. It displays values for a, b, c, d, and e; when DiagnosticOn is set, it also displays a wdue for R 2. For five points, the equation is a polynomial fit; for six or more, it is a polynomial regression. At least five points are required. OuartReg LinReg (a+bx) regression. [Xlistname,YlistnamedCreqlist,regequ] LinReg(a+bx) (linear regression) ills the model equation y=a+bx to the data using a least-squalls fit. It displays values for a (y-intercept) and b (slope); when DiagnosticOn is set, it also displays values for r2 and r. LinReg(a+bx) LnReg (a+b In(x)) [Xlistname,_istnamedCreqlist,regequ LnReg (logarithmic regression) y=a+b ln(x) to the data using ] fits the model equation a least-squares fit and transformed values ln(x) and y. It displays b; when DiagnosticOn is set, it also displays and r. values for a and values for r2 LnReg [Xlistname,YlistnamedCreqlist,regequ] ExpReg (ab x) ExpReg (exponential regression) fits the model equation y=ab _ to the data using a least-squares fit and transformed values x and ln(y). It displays values for a and b; when DiagnosticOn is set, it also displays values for r2 and r. ExpReg 12-26 Statistics [Xlistname,YlistnamedCreqlist,regequ] PwrReg (power l_gression) fits the model equation y=ax b to the data using a least-squares fit and transformed values ln(x) and ln(y). It displays wdues for a and b; when DiagnosticOn is set, it 'also displays values for r2 and r. PwrReg (axb) PwrReg [Xlistname,Ylistname_freqlist,regequ] Logistic c/(l+a*e -bx) Logistic fits the model equation y=c/(l+a*e -bx) to tile data using an iterative least-squares fit. It displays values for a, b, and c. Logistic SinReg a sin(bx+c)+d [Xlistname,Ylistname_reqlist,regequ] SinReg (sinusoidal regression) fits the model equation y=a sin(bx+e)+d to the data using an iterative least-squares fit. It displays values for a, b, c, and d. At least fore" data points m'e required. At least two data points per cycle m'e required in order to avoid aliased frequency estimates. SinReg [iterations,Xlistname,I_istname,period,regequ] iterations will iterate is the nlaxinlonl number of times the algorithm to find a solution. The value for iterations can be an integer The algorithm _>1 and _<16; if not specified, nlay find a solution before the default is 3. iterations is l_a('hed. Typically, lm'ger values for iterations result in longer execution times and better accuracy for SinReg, and vice versa. A period guess is optional. If you do not specify-period, the difference between time values in Xlistname must be equal and the time values nmst be ordered in ascending sequential order. If you specify-period, the algorithm nlay find a solution nlore quickly, or it nlay find a solution when it would not have found one if you had omitted a value for period. If you specify period, the differences between time values in Xlistname can be unequal. Note: The output of SinReg is always in radians, regardless of the Radian/Degree mode setting. A SinReg example is shown on tile next page. Statistics 12-27 SinReg Example: Daylight Hours in Alaska for One Year Compute the regression daylight in Alaska durin se_(X, X, 1,361,30 )+LI : {5.5,8, ii, 1 3.5, 16.5, 19, 19.5 ,17, 14.5, 12.5,8. 5_6.5,5.5}+Lz {5.5 8 Ii 13.5 model for the number [liar of Notz _lotx orr IT_Pe:_I.. _ _ -_ li<,listiE 16Jlist:Lz Mark: SinReg of hours one year. ° [] . LI,Li,VI1 SinReg _=a*sin(bx+c)+d a=6.770292445 b=.8162697853 o=-1.215498579 d=12.18138372 With noisy data, you will achieve better convergence results when you specify- an accurate estimate for period. You can obtain aperiod guess in either of two ways. • • Plot the data and trace to determine the x-distance between the beginning and end of one complete period, or cycle. The illustration above and to the right graphically depicts a complete period, or cycle. Plot the data and trace to determine the x-distance between the beginning and end of N complete periods, or cycles. Then divide the total distance by N. M'ter your fit_t attempt to use SinReg and the default value for iterations to fit the data, you may find the fit to be approximately correct, but not optimal. For an optimal fit, execute SinReg 16,Xlistname,I_istfzame,2_ I b where b is the value obtained froln the prexqous SinReg execution. 12-28 Statistics Statistical Variables The statistical variables are calculated and stored as indicated below, To access these variables ff)r use in expressions, press _, and select 5:Statistics. Then select the VARS menu shown in the colunm below under VARS menu. If you edit a list or change vm'iables m'e clem'ed. Variables the type of analysis, 1-Var Stats 2-Var Stats all statistical Other VARS menu mean of x values _ _ XY SUnl of x values Ex Ex E sunl of X2values Yx2 Yx2 E Sx Sx XY _x Gx XY n n XY _ XY 2y 1; sample standard population nulnber deviation standard of x deviation of x of data points mean of y values sunl of y values sunl of y2 values sample standard population dexqation of y standard deviation of y sunl of X * y 'Fy2 y Sy XY _y XY Zxy Z lninimuln of x values minX minX XY lnaxilnuln of x values maxX max)( XY lninimuln of y values minY XY lnaxilnum of y values maxY 1st quartile median 3rd quartile regression/fit polynomial, coefficients coefficients Logistic, and SinReg correlation coefficient coefficient of determination regression equation sulnl:laI T points (Med-Med only) Q1 and Q3 XY Q1 PTS Med PTS Q3 PTS a, b EQ a, b, c, d, e EQ r EQ r2, R2 EQ RegEQ EQ xl, yl, x2, y2, x3, y3 PTS The first quartile (Q1) is the median of points between minX and Meal (median). The third quartile (Q3) is the median of points between Med and maxX. Statistics 12-29 Statistical Entering Stat Data Analysis in a Program You can enter statisticM data, calculate statistical results, and fit models to data from a program. You can enter statistical data into lists directly within the program (Chapter 11), : {1,2,3}÷LI PROGRRM: : {-I, -2, STRTS -5}÷Lz Statistical Calculations To perform these steps, a statistical 1, On a blank calculation ] calculatkm from a program, line in the progrmn editor, select from the $TAT CALC menu. follow the type of 2, Enter the names of the lists to use in the calculation. Separate the list names with a conlnla, 3, Enter a conulla and then the name of a Y= variable, if you want to store the regression equation to a Y= variable. PROGRRM:STRT5 :{1,2,3}÷LI :{-I,-2,-5}÷L1 :LinReg(ax+b) 12-30 Statistics LI Statistical Plotting Steps for Plotting Statistical Data in Lists You call plot types of plots modified box plot. You can statistical data that is stored in lists. The six available m'e scatter plot, xyLine, histogram, plot, regulm" box plot, and normal probability define up to three plots. To plot statistical data in lists, follow these steps. 1, Store the stat data in one or more lists. 2, Select or deselect ¥= functions as appropriate. 3, Define the stat plot. 4. Turn on the plots you want to display. 5, Define the v_ewing window. 6, Display and explore (Scatter) the graph. Scatter plots plot the data coordinate pairs, showing ( + ), or dot ( • ). Xlist and You can use the same list points fronl Xlist and Ylist as each point as a box ( o ), cross Ylist nmst be the sanle length. for Xlist and Ylist, "t]';i'Off ÷ T'_Pe:_m_,._ Xlist.;_t-Vli__L:Lz ÷ +÷ :+_ Mark: [] [] (xyLine) ÷ k____ ÷ ......... xyLine is a scatter plot in which the data points are plotted and connected in order of appearance in Xlist and Ylist. You nlay want to use SortA( or SortD( to sort the lists beffwe you plot them (page 12-20). _Pe: -L_ _ J_ Y,IisL:LI_ Vlist:Lz Mark: [] * . Statistics 12-31 Histogram plots (Histogram) one-variable data. The Xscl window variable value determines the width of each bar, beginning at Xmin. ZoomStat adjusts Xmin, Xmax, Ymin, and Ymax to include all values, and 'also adjusts Xscl. The inequality (Xmax - Xmin) / Xscl _<47 must be true. A value that occurs on the edge of a bar is counted in the bar to the right. m 0f'€ i ; X list,;"Ct Fr.e_: (ModBoxplot) Ip_in=_B.4Bt30B I ModBoxplot (modified box plot) like the regular box plot, except Interquartile Range beyond the Range is defined _s the difference quartile Q3 and the first quartile plotted individually beyond the (5 or + or ,) you select. You can are called outliers. The prompt ff)r outlier points is the maximunl point (maxX) (minX). When outliers exist, display x=. When no outliers prompts for the end of each and Q3 define the box (page plots one-variable data, points that are 1.5 * quartiles. (The Interquartile between the third Q1.) These points are whisker, using the Mark trace these points, which is x=, except when the outlier or the minimunl point the end of each whisker will exist, minX and maxX are the whisker. O1, Med (median), 12-29). Box plots are plotted with respect to Xmin and Xmax, but ignore Ymin and Ymax. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle. When three a_ plotted, the first one plots at the top, the second in the middle, and the third at the bottonL Lt 1 + 2: Plot2...On ,'D,-L2 1 3: P 1 ot3...O_f L1 LZ 4.&P lotsO_ 12-32 Statistics + Boxplot (Boxplot) (regular box plot) plots one-variable data. The whiskers on the plot extend fronl tile nlininlunl data point in the set (minX) to the first quartile (Q1) and from the third quartile (Q3) to the nlaxinmln point (maxX). The box is defined by Q1, Med (median), and Q3 (page 12-29). Box plots are plotted with respect to Xmin and Xmax, but ignore Ymin and Ymax. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle. When three ale plotted, the first one plots at tile top, tile second in tile middle, and the third at the bottonl. L,t li q 2: P lot2...0n le 3: Plot3...Of'f" 44,P 1otsOtPt" (NormProbPIot) ,a .... NormProbPIot (normal probability plot) plots each observation X in Data List vel\sus the corresponding quantile z of the standard nonnM distribution, If the plotted points lie close to a straight line, then the plot indicates that the data are normal. Enter a valid list nalne in the Data List field. Select X or Y for the Data Axis setting. • If you select the z-values X, tile TI-83 plots on the y-axis. tile data on tile x-axis and • If you select the z-values Y, the TI-83 plots on the x-axis. the data on the y-axis and [PandHorp_(35, )÷L_ 2,90 7 36 Plot1 p1OI:;_ m 0f'f" T_Pe: Data Data Mar'k: P 3:Lh -L_ b-_ 31_ _.- a]b I Crst.--: L _ Axis:@ Y = * II N=')E.E:1321E ?=.?hEIBB19 Statistics 12-33 Defining the Plots To define a plot, 1, Press [_ displayed follow these steps. [STAT PLOT]. The STAT PLOTS menu with the current plot definitions, 2, Select the plot you want to use, The stat displayed for the plot you selected, 3, Press _ statistical Select options Statistics is you select On or Off, the type of plot. checked Each type prompts for the in this table. Plot Type XList YList Mark Freq Data List Data Axis _L_ Scatter _ _i _ rl [] [] xyLine _ 121 _ [] [] [] Zn_ Histogram _ [] [] _ [] [] o,. _ [] _ _ [] [] _:_> Boxplot _ [] [] _ [] [] [__ [] [] _ [] _ lTI ModBoxplot NormProbPIot Enter 12-34 editor to select On if you want to plot the data imnlediately. The definition is stored whether 4, plot is list names or select options for the plot • Xlist (list name containing independent • Ylist (list name containing dependent • Mark (aor • Freq (frequency • Data List (list nanle for NormProbPIot) • Data Axis (axis type, data) data) + or.) list for Xlist elements; on which to plot default Data List) is 1") Displaying Other Stat Plot Editors Each stat plot has a unique stat plot editor. The name of the current stat plot (Plot1, Plot2, or Plot3) is highlighted in the top line of the stat plot editor. To display the stat plot editor for a different plot, press [], [], and [] to lnove the cursor onto the name in the top line, and then press [_. The stat plot editor for the selected plot is displayed, and the selected name remains highlighted. _" _ Xlist:L1 Vlist:Lz Mark: [] * Turning On and Turning Off Stat Plots L_ PlotsOn and PlotsOff allow you to turn on or turn off stat plots from the home screen or a program. With no plot number, PlotsOn turns on M1plots and PlotsOff turns off 'all plots. With one or more plot numbers (1, 2, and 3), PlotsOn turns on specified plots, and PlotsOff turns off specified plots. PlotsOff [1,2,3] PlotsOn [1,2,3] PlotsOf'f" Note: You also can turn on and turn off stat plots in the top line of the Y= editor (Chapter 3). Statistics 12-35 Defining the Viewing Window Stat plots are displayed on the current graph. To define the xqewing window, press _ and enter values for the window variables. ZoomStat redefines the xqewing window to display all statistical data points. Tracing a Stat Plot When you trace a scatter plot or xyLine, tracing begins at the first element in the lists. VClmnyou trace a histogram, the cursor nloves fronl the top center of one colunm to tile top center of tile next, starting at the first colunm. When you trace a box plot, tracing begins at Med (the median). Press [] to trace to Ol and minX. Press [] to trace to O3 and maxX. When you press [] or [] to move to another plot or to another Y= function, tracing moves to the current or beginning point on that plot (not the nearest pixel). The ExprOn/ExprOff format setting applies to stat plots (Chapter 3).When ExprOn is selected, the plot number and plotted data lists are displayed in the top-left corner. 12-36 Statistics Statistical Plotting Defining a Stat Plot in a Program in a Program To display a stat plot fronl a program, then display the graph. define the plot, and To define a star plot from a program, begin on a blank line in the program editor and enter data into one or more lists; then, follow these steps. 1. Press [g_ [STATPLOT]to displw tile STAT PLOTS menu. T"tPE MARK i3:Plot3( i4.PlotsOgg 5:Plot.sOn Select the plot to define, which pastes Plot3( to the cursor location. Plot1(, Plot2(, or PROGRAM:PLOT :{I,2,3,4}+LI :{5,6,7,8}+Lz :Plot2(I Press[_[STATPLOT][_todisplaytheSTATTYPE nlenu, PLOTS _ ._Soatter z: x_Line MARK 5:Bo>,'g Iot S:HorMProbPlot Select plot the type of plot, type to the cm'sor which pastes the name of the location. PROGRAM:PLOT :{1,2,3,4}+LI :{5,6,7,8}+Lz :Plot2(SoatterI Statistics 12-37 5_ Press []. Enter the list names, separated by eonunas. 6, Press [] [_ [STAT PLOT] [] to display the STAT PLOT MARK menu. (This step is not necessaqyyou selected 3:Histogram or 6:Boxplot in step 4.) Select the type of nlark (D or + or °) for each data The selected mm'k symbol is pasted to the cursor location. Press [] _ to complete : {I02,3,4}÷LI : {5, 6, 7,8}÷Lz : Plot2(Soattet-, PROGRAM: PLOT Displaying a Stat Plot from a Program To displayinstruction (Chapter line, L 3), :: DisParaF-h Statistics point. a plot from a program, use the DispGraph (Chapter 16) or any of the ZOOM instructions PROGRR_I: PLOT : {1,2,3,4}÷LI : ,.5,6, _, 8}+Lz : Plot2(ScatteP, I,Lz,=) 12-38 the command if L PROGRRM:PLOT :{1,2,3,4}÷Lt :_506,7,8}÷Lz :Plot2(ScatteP,L I,Lz,.) ::_°°MStat 3 Contents and Distributions InferentialStatistics Getting Started: Mean Height of a Population Inferential Star Editors ................................... STAT TESTS Menu ...................................... Inferential Statistics Input I)eseriptions ............ .................. 13-2 13-6 13-9 13-26 Test and Interval Output Variables ....................... Distribution Functions ................................... 13-28 13-29 Distribution 13-35 '_ Shading TEXAS ..................................... T1=83 iNSTRUMENTS z=.ee:l. I_=._?e:_ J STATPLOT TBLSET FORMAT Inferential CALC Statistics TABLE and Distributions 13-1 Getting Getting Started: Started Mean Height of a Population is a fast-paced introduction. Read the chapter for details. Suppose you want to estimate the mean height of a population of women given tile random sample below. Because heights among a biological population tend to be normally distributed, a t distribution confidence interval can be used when estimating the mean. The l0 height wdues below are the first l0 of 90 wdues, randonfly generated from a normally distributed population with an assumed mean of 165.1 cm. and a standard dexqation of 6.35 cm. (randNorm(165.1,6.36,90) with a seed of 789). Height 169.43 168.33 159.55 (in cm.) 169.97 of Each 159.79 of 10 Women 181.42 Press [gTKg][gNT_ to display the stat list editor. Press [] to nlove the cursor onto L1, and then press [_] [,NS]. The Name= prompt is displayed on the bottom line. The [] cursor indicates that alpha-lock is on. The existing list name eolunms shift to the 171.17 162.64 1 167.15 159.53 .I L_ I .1 L;' 1 L_ 3 HaMe== right. Note: Your stat editor may not look like the one pictured here, depending on the lists you have already stored. Enter [H] [G] [H] [T] at the Name= prompt, and then press [gNT_. The list to which you will store the women's height data is created. Press [] to move the cursor onto the first row of the list. HGHT(1)=is displayed on the bottom line. Press 169 [] 43 to enter the first height value. As you enter it, it is displayed on the bottom line. Press [gNT_. The value is displayed in the first row, and the rectangular cursor nloves to the next row. Enter the other nine height values the sanle way, 13-2 hfferential Statistics and Distributions HGHT mmm H6HT(1) = HGHT 1_9.7B 171.17 16Y.tg H6HT(11)= .1 4. Press [gY_ [] to display the STAT TESTS menu, and then press [] until 8:Tlnterval is highlighted. EDIT CRLCIII_ 2ST-Test,, 3:2-SamPZTest 4:2-Sar4eTTest_ 7:ZIntervM,.,"[_tlTInterval... 5. Press _ to select 8:Tlnterval. The inferential stat editor for Tlnterval is displayed. If Data is not selected for Inpt:, press [] [ggY_ to select Data. TlntervM InPt:_ Stats List:HGHT Fre_:1 C-Level:.99 Calculate Press [] and [H] [G] [a] [T] at the List: prompt (alpha-lock is on). Press [] [] [] [email protected] enter a 99 percent confidence level at the C-Level: prompt. 6. Press [] to move the cursor onto Calculate, and then press IgOr. The confidence intet¢TM is calculated, and the Tlnterval results are displayed on the home screen. Interpret Tlnterval (159.74,173.94) R=166.838 Sx=6.907879237 n=lO the results. The first line, (159.74,173.94), shows that the 99 percent confidence inte_xal for the population mean is between about 159.74 cm. and 173.94 cm. This is about a 14.2 cm. spread. The .99 confidence level indicates that in a vet3z lm'ge number of samples, we expect 99 percent of the intervals calculated to contain the population mean. The actual mean of the population sampled is 165.1 cm. (introduction; page 13-2), which is in the calculated interval. The second line gives the mean height of the sample N used to compute this intet_'al. The third line gives the sample standard deviation Sx. The bottom line gives the sample size n. Inferential Statistics and Distributions 13-3 To obtain a more precise bound on the population mean _tof women's heights, increase the sample size to 96. Use a sample mean ._ of 163.8 and sample standard deviation Sx of 7.1 calculated from the larger random sample (introduction; page 13-2). This time, use the Stats (sunullal_y statistics) input option. Press [g_g] [] 8 to display" the inferential star editor for Tlnterval. Press [] [g_N to select Inpt:Stats. The editor changes so that you can enter sunullal_ statistics as input. 8. Press [] 163 [] 8 [N?_ to store Press 7 [] 1 [ggY_ Press 90 [NTgN to store to store 163.8 to _. 7.1 to Sx. 96 to n. Press [] to move the cursor onto Calculate, and then press [g_N to calculate the new 99 percent confidence interval. The results are displayed on the home screen. TInterual InPt:Data I¢_ 5:166.838 Sx:G.90787923Z_ n:10 C-Leuel:.99 Calculate TInterual InPt:Data _ R:IG3.8 Sx:7.1 n:90 C-Leuel:.99 Calculate TInterual (161.83,165.77) R=163.8 Sx=7.1 n=90 If the height distribution among a population of women is normally distributed with a nlean [J of 165.1 cm. and a standard deviation _ of 6.35 cm., what height is exceeded by only 5 percent of the women (the 95th percentile)? 10. Press @ to clear the home Press [2_] [DISTR] to display (distributions) menu. 13-4 hfferential Statistics screen. the DISTR and Distributions DRAW normalcd?( 3:invNorm( 4:tPd?( 5:tod¢( 6:XZpd?( 74XZod¢( 11.Press 3 to invHorr_(. 1_ 6.35) invNorm( to the home paste screen. Press_ 95_ .95 is the area, lS5_ 1_ 6_ 35_ 1G5.1 is p, and 6.35 is o. The result is displayed women are taller than on the home 175.5 cm. I screen; Now graph and shade the top 5 percent it shows Ymin=-.02 Ymax=.08 Yscl=0 13. Press [_ [DISTR] DRAW menu. that five percent Xres=l STR Llli'_l_ ShadeNoPm 3: ShadeX 4: ShadeF 14. Press home Press _ to paste screen. [_ [ANS] [] ShadeNorm( 1 _ [EE l 99_ of the gINDOg XMin=145 Xmax=185 Xsol=5 YMin=-.82 YMax=.88 Yscl=O XPes=1 to display the DISTR [] 175.5448285 of the population. 12. Press [_ and set the window variables to these values. Xmin=145 Xmax=185 Xscl=5 95,165. to the 165[_ 1 D6[]asD. ( z( ( invHor.M(. 95,165. 1,6.35) 175. 5448285 ShadeNoPFKRns, 1E 99, 165. 1,6.35)I Ans (175.5448205 from step 11) is the lower bound. 1E99 is the upper bound. The normal curve is defined by a mean p of 165.1 and a standm'd deviation o of 6.35. 15. Press [gfff_ to plot and shade the normal eui%re. Area is the area above low is the lower bound. bound, the 95th percentile. up is the upper firca=.OB low='l Inferential Statistics and 7_:._:LI_: up,=:LEBB Distributions 13-5 Inferential Displaying the Inferential Stat Editors Stat Editors When you select a hypothesis test or confidence intetsTal instruction from the home screen, the appropriate inferential statistics editor is displayed. The editors yaw according to each test or interval's input requirements. Below is the inferential stat editor for T-Test. T-Test InPt:_ Stats List:L1 Fne_:l _:_ <_ Calculate >_n Orau Note: When you select the ANOVA( instruction, it is pasted to the home screen. ANOVA( does not have an editor screen. Using an Inferential Stat Editor To use an inferential stat editor, follow these steps. 1. Select a hypothesis test (Jr confidence intet_'al from the STAT TESTS menu. The appropriate editor is displayed. 2. Select Data or Stats input, if the selection The appropriate editor is displayed. is available. 3. Enter real numbers, list names, (Jr expressions argument in the editor. for each 4. Select the alternative hypothesis (€, <, or >) against which to test, if the selection is available. 5. Select No or Yes for the Pooled option, if the selection available. 6. Select Calculate (Jr Draw (when Draw is available) execute the instruction. • When you select Calculate, the results on the honle screen. • When you select Draw, the t_sults graph. is to are displayed are displayed in a This chapter describes the selections in the above steps for each hypothesis test and confidence intetwal instruction. 13-6 hfferential Statistics and Distributions Select Data or Stats input Stats Sete_ an alternative hypothesis Enter values for arguments Calculate Selecting Stats Data or Select Calculate or Draw output Omau Most inferential stat editors prompt you to select one of two types of input. (1-PropZlnt and 2-PropZTest, 1-PropZlnt and 2-PropZlnt, x2-Test, and LinRegTTest do not,) • Select Data to enter the data • Select Stats to enter and n, as input. sunmm_ lists _s input. statistics, To select Data or Stats, move the cursor Stats, and then press [ggY_. Entering the Values for Arguments such as 2, Sx, to either Data or Inferential stat editors require a value for ever7 argument. If you do not know what a pm'ticulm" argument symbol represents, see the tables on pages 13-26 and 13-27. When you enter values in any inferential stat editor, the TI-83 stores them in nlenlory so that you can run many tests or intetnT'als without having to reenter evet3z vMue. Selecting an Alternative Hypothesis (_ < >) Most of the inferential prompt you to select stat editors one of three • The first is a _ Mternative the Z-Test. • The second is a < alternative for tile 2-SampTTest. • The third is a > alternative the 2-PropZTest. To select an alternative appropriate alternative, Inferential for the hypothesis tests alternative hypotheses. hypothesis, such hypothesis, hypothesis, as p¢p0 for such such as pl<_t2 as pl>p2 hypothesis, nlove the cursor and then press [ggY_. Statistics and Distributions for to the 13-7 Selecting the Pooled Option Pooled (2-SampTTest whether the vmiances or Draw for a Hypothesis Test m'e to be pooled only) Select No if you do not want the vmiances Population vm'iances can be unequal. • Select Yes if you want wu'iances m'e assumed the wu'iances to be equal. option, move specifies for the • To select the Pooled then press [_T_]. Selecting Calculate and 2-SampTInt calculation, pooled. pooled. the cursor Population to Yes, and Alter you have entered all arguments in an inferential star editor for a hypothesis test, you nmst select whether you want to see the calculated results on the home screen (Calculate) or on the graph screen (Draw). • • Calculate c_dculates the test results and displays the outputs on the home screen. Draw draws a graph of the test results and displays the test statistic and p-value with the graph. The window variables m'e adjusted automatically to fit the graph. To select Calculate or Draw, nlove the cursor to either Calculate or Draw, and then press IgOr. The instruction inunediately executed. Selecting Calculate for a Confidence Interval is Alter you have entered all arguments in an inferential star editor for a confidence inte_'al, select Calculate to display the results. The Draw option is not available. When you press [g_EN, Calculate calculates the confidence inte_w'M results and displays the outputs on the home screen. Bypassing Inferential Editors the Stat To paste a 1wpothesis test or confidence inte_-'al instruction to the home screen without displaying the corresponding inferential stat editor, select the instruction you want from the CATALOG menu. Appendix A describes the input syntm, c for each hypothesis test and confidence inte_nTal instruction. 12-Sar,_PZTest ( I Note:You can pastea hypothesis testorconfidenceinterval instruction to a command line in a program. From within the program editor, select the instruction from either the CATALOG (Chapter I5) or the STAT TESTS menu. 13-8 hfferential Statistics and Distributions STAT TESTS Menu STAT TESTS Menu To display the STAT TESTS menu, press [gT_] [_. When you select an inferential statistics instruction, the appropriate inferential stat editor is displayed. Most STAT TESTS instructions store some output varial_les to memory. Most of these output variables are in the TEST secondmT menu (VARS menu; 5:Statistics). For a list of these varial)les, see page 13-28. EDIT CALC TESTS 1:Z Test,.. Test for 1 p, known 2:T Test,., Test for i p, unknown 3:2 SampZTest... Test compming 2 #'s, known _'s 4:2 SampTTest,.. Test compming 2 #'s, unknown _'s 5:1 PropZTest... Test for 1 proportion 6:2 PropZTest,.. Test compming 2 proportions 7:Zlnterval,., Confidence intmwal for 1 #, known 8:Tlnterval,., Confidence intmwal for 1 #, unknown 9:2 Conf. int. for diff. of 2 p's, known o's Conf. int. for diff. of 2 #'s, unknown o's Confidence int. for 1 proportion Confidence int. for diff. of 2 props Chi-squm'e test for 2-way tables Test compming 2 o's t test for regression slope and p One-way analysis of variance SampZlnt.,. 0:2 SampTlnt.,. A:I PropZlnt.,. B:2 PropZlnt.,. C:X2 Test,,. D:2 SampFTest... E: LinRegTTest,.. F: ANOVA( Note: When a new test or interval is computed, all previous output variables are invalidated. Inferential Stat Editors for the STAT TESTS Instructions In this chapter, the description of each STAT TESTS instruction shows the unique inferential stat editor for that instruction with example arguments. • • Descriptions of instructions that offer the Data/Stats input choice show both types of input screens. Descriptions of instructions that do not ofl_r the Data/Stats input choice show only one input screen. The description that instruction • • then shows the unique output with the example results. screen for Descriptions of instructions that offer the Calculate/Draw output choice show both types of screens: calculated and graphic results. Descriptions of instructions that offer only the Calculate output choice show the calculated results on the home screen. Inferential Statistics and Distributions 13-9 Z-Test Z-Test (one-sample z test; item 1) performs a hypothesis test for a single unknown population mean _ when the population standard deviation cris known. It tests the null hypothesis H0: g= P0 against one of the alternatives below. • • • H_,:_!¢P0 (vt:_to) H_,:_<_00a:<_to) H_,:_>_0 (_t:>_to) In tile example: L1={299,4 297.7 301 298.9 300.2 297} Data Z-Test Inet:_ Input: Calculated results: Stats 0.:3 List:L1 Fre_:l _:#_ _ Calculate >_o Draw Stats Z-Test InPt:Oata v.n : 300 0:3 _: 299. 0333 n:6 v.:#v.n_ >_n Calculate Draw Z-Test v.<300. 0000 z= -. 7893 P=. 2150 _=299. 0333 mx= 1. 5029 Z-Test u<300.0000 z=-.7893 e=.2150 R=299.0333 ir,=6. I n=6.0000 0000 [email protected] [email protected] Drawn results: :=-.7B9_ _=._I_ Note: All examples on pages13-10 through t3-25 assume a fixed- decimal mode setting of 4 (Chapter 1 ). If you set the decimal mode to Float or a different fixed-decimal setting, your output may differ from the output 13-10 Inferential Statistics in the examples. and Distributions T-Test T-Test (one-sample t test; item 2) performs a hypothesis test for a single unknown population mean p when the population standard deviation _ is unknown. It tests the null hypothesis H0:P=P0 against one of the alternatives below. • • H_,:PCPo (p:¢po) H_,:P<Po (p:<po) • H_,:P>Po (,u:>_.to) In the example: TEST={91.9 97.8 111.4 122.3 105.4 95} Input: Data T-Test InPt:_ _n:105 List:TEST FPe_:l _:_ <_n Calculate Stats >_n DPau Stats T-Test InPt:Oata p0:105 7,:103. 9667 Sx: 11.4669 n:6 Calculate T-Test _#105.0000 t=-.2207 P=.8340 R=103.9667 Sx=II.4669 T-Test ,,lo5.00oo t=-.,_20_ Calculated results: P=. 8340 2= 100 • 9667 Sx= 1 I. 4669 in=6. OPau in=6.0000 0000 Drawn results: t= -,i:_:07 _=,g3h Inferential Statistics and Distributions 13-11 2-SampZTest 2-SampZTest (two-sample z test; item 3) tests the equality of the means of two populations (Pl and #2) based on independent samples when both population standard deviations (_1 and a_,) are known. The null hypothesis H0:#1=p2 is tested against one of the alternatives below. • H_,: _[l<_t2 (pl:<p2) • H_,: #1>P2 (pl:>p2) In the example: LISTA={154 LISTB={108 109 137 116 140} 115 126 92 146} Data Input: 2-SamPZTest InPt =I_ ¢I: 15.5 ¢2:13.5 ListI:LISTR List2:LISTB FPe_l:l _Fre_2:l _I:#_2 Calculate <_2 Stats results: 2-SaMPZTest P:. 695 z= I. 4795 P=. 0695 _1=131.0000 RI=131. 0000 Rz=117.4000 l.n i =5. 0000 2z=I17.4000 I i 1_Sx,=18.6145 r,z=5.0000 S×z=20.1941 ni=5.0000 i inz=5.0000 // Drawn resutts: z=l.h795 13-12 Inferential =-LI:#p.2 <p.2 I_ Calculate Dr-a,,J _ Drau 2-SaMmZTest Calculated Stats 2-SaMPZTest InPt:Data ¢I: 15.5 ¢2:13.5 RI: 131 hi:5 R2:117.4 _n2:5 Statistics _=.Ofigg and Distributions 2-SampTTest (two-sample t test; item 4) tests the equality of the lneans of two populations (_l 1 and g2) based on independent samples when neither population standard deviation ((_1or (_2)is known, The null hypothesis n0:_11=_12 is tested against one of the alternatives below. 2-SampTTest • H_,: _11<_l2 (_1:<_2) • H_,: _11>_12 (_1:>_2) In the example: 8AMPl={12.207 16.869 25,05 22,429 8,456 10,589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.642} Input: Data 2-SamPTTest InPt:liI_11_Stats ListI:SRMPI List2:SRMP2 Fre_l:l Fre_2:l SPooled:l_ 9es I Calc.ulate Draw Calculated results: Stats 2-SaMPTTesL Inet: Data !i_rul_lEl 1 : 15. 9333 SxI :6. 7014 nl:6 _2:9.4998 Sx2: I. 9501 i.n2:6 I _LI:_ <_2 >_2 PooI_:[_ Yes Calculate Draw 2-SamPTTest 2-SamPTTest t=2.2579 P=.0659 d_=5.8408 RI=15.9333 $_z=9.4998 t=2.2579 P=.0659 d€=5.8408 RI=15.9333 _2z=9.4998 Sxz=1.9501 ni=6.0000 I nz=6.0000 SXI=6"7014 m =6. 00e I r,z=6. 0000 Drawn resutts: Inferential Statistics and Distributions 13-13 1-PropZTest (one-proportion z test; item B) computes a test for an unknown proportion of successes (prop). It takes as input the count of successes in the sample x and the count of observations in the sample n. 1-PropZTest tests the null hypothesis H0:prop=p0 against one of the alternatives below. 1-PropZTest • • • H_,:prop€p0 (prop:¢p0) H_,:prop<p0 (prop:<po) H_,:prop>p0 (prop:>po) I 1-ProPZTest pill Input: I .5 x: 2848 I n: 4848 I eroI=Ei1"_,'1 <ell >Pal Caloulate Draw l-ProeZTest ProP#. Calculated results: 5000 z=. 8810 P=. o783 _=. 5069 in=4e4e. 0088 Drawn results: 13-14 Inferential Statistics and Distributions 2-PropZTest (two-proportion z test; item 6) computes a test to compare the proportion of successes (Pl and P2) fronl two populations. It takes _ksinput the count of successes in each sample (x 1and x2) and the count of observations in each sample (nl and n2). 2-PropZTest tests the null hypothesis H0:pl=p2 (using the pooled sample proportion _) against one of the alternatives below. 2-PropZTest • • • Input: Calculated results: H_,:pl;eP2 (pl:_p2) H_,:pl<P2 (pl:<p2) H_,:pl>P2 (pl:>p2) 2-PPoeZTest xi:45 hi:61 x2:38 n2:62 el:I <e2 >e2 Calculate Draw B2-ProeZTest e1#ez z=1.4773 P=.1396 @i=.7377 @z=.6129 4#=.6748 | nI=61.0000 nl=62.0000 -I Drawn results: Inferential Statistics and Distributions 13-15 Zlnterval (one-sample z confidence intetsTal; item 7) computes a confidence interval for an unknown population mean p when the population standard deflation cris known. The computed confidence intet_-'al depends on the user-specified confidence level, Zlnterval In the example: L1={299.4 297.7 301 298.9 300.2 297} Data ZInterval In_t:l_ellI_Stats Input: Calculated results: List:L1 Fre_:l C-Level:.9 Calculate -BZInterval (297.02,301.85) R=299.0333 Sx=1.5029 |n=6.0000 13-16 Inferential Statistics and Stats ZInterval Inet:Data _:3 R: 299. 0333 n:6 C-Legel :. 9 Calculate Zlnterval (297.02,301.05) I Distributions Tlnterval Tlnterval (one-sample t confidence inte_nTal; item 8) computes a confidence interval for an unknown population mean p when the population standard deviation _ is unknown. The computed confidence inte_wTal depends on the user-specified confidence level. In the L6={1.6 Input: example: 1.7 1.8 1.9} Data Tlnterval InPt:llL_u1_Stats List:L_ Fre_:l C-Level:.95 Calculate Stats T Interva I InF.t:Data _: 1.75 Sx:. 1291 n:4 C-Level: .95 Caloulate -B- Calculated results: TInterval (1.5446,1.9554) R=1.7500 Sx=.1291 TInterval (1.5446, i.9554) R=1.7500 Sx=.1291 |n=4.0000 |n=4.0000 Inferential Statistics and Distributions 13-17 2-SampZInt (two-sample z confidence inte_wTal;item 9) c()mputes a confidence inte[wTal for the difference between two population means ({11-_12) when both population standard deviations (or1 and a_) are known. The computed confidence inte_'al depends on the user-specified confidence level. 2-SampZlnt In the example: LISTC={154 LISTD={108 Input: 109 137 116 140} 115 126 92 146} Data 2-SamPZlnt InPt:[._Z Stats _i:15.5 _2:13.5 ListI:LISTC List2:LISTD Fre_l:l SFre_2:l C-Level:.99 Calculate 2-SamPZInt (-10.08,37.278) 21=131.0000 2z=117.4000 Calculated results: Sxi=18.6145 Sxz=20.1941 $ni=5.0000 n2=5.0000 | Inferential Statistics and C-Level:.99 Calculate 2-SamPZlnt (-10.08,37.278) 21=131.0000 2_=117.4000 m=5.0000 inz=5.0000 | 13-18 Stats 2-SamPZ I nt InPt:Data _I: 15.5 ¢2:13.5 21:131 ni:5 22:117.4 _n2:5 Distributions 2-SampTInt 2-SampTInt (two-sample t confidence inte[wTal; item O) c()mputes a confidence inte[wTal for the difference between two population means (Pl-P2) when both population standard deviations (a 1 and _) are unknown. The computed confidence interval depends on the userspecified confidence level. In the example: SAMP1={12.207 SAMP2={11.074 16.869 25.05 22,429 8.456 10.589} 9.686 12.064 9.351 8,182 6.642} Stats 2-SaP/PT I r=t Data Input: 2-SamPTlnt InPt:_ ListI:SRMPI List2:SRMP2 Fne_l:1 Fne_2:l C-Level:.95 $Pooled:l:_ Stats Sxl :6. 7014 nl:6 R2:9.4998 Sx2:1.9581 _n2:6 Yes C-Level :. 95 Pooled:l:_ Yes Calculate Calculate Calculated results: 2-SamPTlnt (%5848,13.452) d¢=5.8408 Ri=15.9333 Rz=9.4998 SxI=6.7014 $Sxz=1.9501 | 2-SamPT Int ( -.5849, 13. 452) df=5.8408 _i =15. 9333 R1=9.4998 SxI=6. 7014 _Sx1=1.9501 | i ni=6.0000 nz=6.0000 ni=6.8000 nz=6.0000 | Inferential Statistics and Distributions 13-19 1-PropZInt (one-proportion z confidence inte_'al; item A) computes a confidence interval for an unknown proportion of successes. It takes as input the count of successes in the sample x and the count of obse_'ations in the sample n. The computed confidence intetnTal depends on the userspecified confidence level. 1-PropZlnt input: 1-PPoeZlnt x: 2848 n: 4848 C-Leve I :.99 Caicuiate -Bl-ProeZlnt (.4867,.5272) A=.5069 Calculated results: |n=4040.0000 13-20 Inferential Statistics and Distributions 2-PropZInt 2-PropZlnt (two-proportion z confidence inte_'al; item B) computes a confidence intet_'al for the difference between the proportion of successes in two populations (Pl-P2)- It takes a_n input the count of successes in each sample (Xl and x2) and the count of observations in eaeh sample (n 1 and n2), The computed confidence intetnTal depends on the user-specified confidence level. 2-Pt-oPZ Int xi:49 nl:61 x2:38 Input: n2: 62 C-Leve I :.95 Calculate -I Calculated results: 2-PPoeZInt (.0334,.3474) #I=.8033 #z=.6129 ni=61.0000 |nz=62.0000 Inferential Statistics and Distributions 13-21 z2-Test (chi-squm'e test; item C) computes a chi-squm'e test for association on the two-way table of counts in the specified Observed lnatrix. The null hypothesis H 0 for a two-way table is: no association exists between row variables and colunm variables. The Mternative hypothesis is: the vm'iables are related. z2-Test Before computing a zZ-Test, enter the obsetnTed counts in a matrix. Enter that matrix variable name at the Observed: prompt in the z2-Test editor; default=[A]. At the Expected: prompt, enter the matrix variable name to which you want the computed expected counts to be stored; default=[B]. [ 5.0000 19.000 MATRIX[R] J.3.000 3 x2 ] Note: Press _ select 1 :[A] from EDIT menu. [] [] 1 to the MATRX Matrix editor: [ i0. o000 t,.000 Xi-Test Observed:[R] Exeected:[B] Calculate Draw Input: Note: Press_ display [B] [[8.0000 XZ-Test XZ=3.3750 P=.1850 d€=2.0000 Calculated results: Inferential Statistics and [B] _ [B]. 16.000. [ :888816.000...i Drawn results: 13-22 matrix Distributions to 2-SampFTest 2-SampVTest (two-sample V-test; item D) computes an V-test to compare two normal population standard deviations ((31 and (32). The population means and standard deflations are all unknown. 2-$ampFTest, which uses the ratio of sample variances Sxl_/Sx2 _, tests the null hypothesis H0:(31=(32 against one of the alternatives below. • H_,: (315(32 (G1:_(52) • H_,:(31<(32 H_,:(31>(32 • In the Calculated results: ((51 :>(52) example: SAMP4={ SAMPS={ Input: ((51 :<(52) 7 -4 18 -1 12 -1 17 -3 -3 3 -5 -5 1 10 11-2} 5 2-11 -1-3} Data 2-SamPFTest InPt:_ SLats ListI:SRMP4 List2:SRMP5 FPe_l:l FPe_2:l _i:_ <z2 >z2 Caloulate OPaw Stats 2-Sar/PFTest InPt: Data_ Sx i :8. 7433 hi: 10 Sx2: 5. 9007 n2: II zl:_ <_2 >z2 Calculate Dra_,J 2-SaMPFTest zl #zz 2-SameFTest zl#zz F=2. 1956 P=. 2364 S× _=8. 7433 Sxz=5. 9007 _nl =10. 0000 F=2. 1955 P=. 2365 Sxl =8. 7433 Sx z =5. 9007 _i =5. 0000 z= -.2727 n_=lO. 0000 nz=l I.0000 2 in _ = 1 I. 0000 Drawn results: Inferential Statistics and Distributions 13-23 LinRegTTest LinRegTTest (linear regressk)n t test; item E) computes a linear regression on the given data and a t test on the value of slope _ and the correlation coefficient p for the equation y=(x +_x. It tests the null hypothesis H0:_=0 (equivalently, p=O) against one of the alternatives below. • Hr,: _€0 and pC0 ([3 & p:_0) • H_,: _<0 and p<0 (9 & p:<0) • H_,: _>0 and p>0 (9 & P:>0) The regression equation is automatically stored to (MARS Statistics EQ secondary menu). If you enter variable name at the RegEO: prompt, the eMeulated regression equation is automatically stored to the Y= equation. In the example below, the regression is stored to Y1, which is then selected (turned on). In the specified equation example: L3={38 56 59 L4={41 63 70 Input: RegEQ a Y= 64 74} 72 84} LinRegTTest Xlist:L_ 91ist:L4 Fre_:l B & P:_ <0 RegEQ:_ Calculate >0 lJ- Calculated results: LinRegTTest _=a+bx B_O and p_O t=15.9405 P=5.3684E-4 ",371B-3. 6596+i. 69X xYz= d€=3.8888 4a=-3.6596 xY4= PloLt xVs= xY_= PloI:Z PloL3 19 $b=i.1969 s_1.9820 P_=.9883 P=,9941 When LinRegTTest is executed, the list of residuals is created and stored to the list name RESID automatically. RESID is placed on the LIST NAMES menu. Note: For the regression equation, you can use the fix-decimal mode setting to control the number of digits stored after the decimal point (Chapter I). However, limiting the number of digits to a small number could affect the accuracy of the fit. 13-24 Inferential Statistics and Distributions ANOVA( ANOVA( (one-way analysis of variance; item F) computes a one-way analysis of variance for COlnparing the means of two to 20 populations. The ANOVA procedure for COlnparing these means involves analysis of the variation in the sample data. The null hypothesis H0:#1=#2 ..... #k is tested against the alternative H_,: not all p 1---#l_are equal. ANOVA(listl,list2[,...,list20]) In the example: L1={7 4 6 6 5} L2={6 5 5 8 7} L3={4 7 6 7 6} RNOVR(LI,Lz,L_)I Input: ll- Calculated results: One-_au RNOVR F=.olll P=.7384 Factor d_=2.0000 SS=.9333 _MS=.4667 Error d_=12.0000 SS=18.0000 MS=1.5000 I_xP=1.2247 Note: SS is sum of squares Inferential and MS is mean square. Statistics and Distributions 13-25 Inferential Statistics Input Descriptions The tables in this section describe the inferential statistics inputs discussed this chapter. You enter values for these inputs in the inferentiM stat editors. The tables present the inputs in the same order that they appear in this chapter. in Input Description _0 Hypothesized testing. G The known population number > 0. List The name of the list containing Freq The name of the list containing the frequency values for the data in List. Default=l. All elements must be integers ->0. Calculate/Draw Determines the type of output to generate for tests and intervals. Calculate displays the output on the home screen. In tests, Draw draws a graph of the results. _, Sx, n Sumlnary statistics (mean, standard deviation, size) for the one-sample tests and intervals. _1 The known population standard deviation fronl the first population for the two-sample tests and intervals. Must be a real number > 0. _2 The known population standard deviation fronl the second population for the two-sample tests and intervals. Must be a real number > 0. List1, List2 The names of the lists containing the data you are testing for the two-salnple tests and intervals. Defaults are L1 and L2,respectively. Freql, Freq2 The names of the lists containing the frequencies for the data in List1 and List2 for the two-salnple tests and intervals. Defaufis=l. All elements must be integers _>0. _1, Sxl, nl, _2, Sx2, n2 Sununary Pooled Specifies whether variances are to be pooled for 2-SampTTest and 2-SampTInt. No instructs the TI-83 not to pool the variances. Yes instructs the TI-83 to pool the variances. 13-26 Inferential value of the population standard mean that you are deviation; must be a real the data you are testing. and sample statistics (mean, standard deviation, and sample size) for sample one and sample two in the two-salnple tests and intervals. Statistics and Distributions Input Description P0 The real The and x expected sample proportion for 1-PropZTest. Must be a nmnber, such that 0 < I90 < 1. count of successes in the sample for the 1-PropZTest 1-PropZlnt. Must be an integer _>0. n Tile count of observations in the sample for the 1-PropZTest and 1-PropZlnt. Must be an integer > O. xl The count of successes fronl sample one for the 2-PropZTest and 2-PropZlnt. Must be an integer _>0. x2 The count of successes froln sample two for the 2-PropZTest and 2-PropZlnt. Must be an integer _>0. nl The count of observations in sample one for the 2-PropZTest and 2-PropZlnt. Must be an integer > 0. n2 The count of observations in sample two for the 2-PropZTest and 2-PropZlnt. Must be an integer > 0. The confidence level for the inteP_-al instructions. Must be >_0 and <100. If it is _>1, it is assumed to be given as a percent and is divided by 100. Default=0.95. C-Level Observed (Matrix) The matrix name that represents the colunms and rows for the obseP_'ed values of a two-way table of counts for the z2-Test. Observed nmst contain 'all integers _>0. Matrix dimensions nmst be at least 2x 2. Expected (Matrix) The matrix name that specifies where the expected values should be stored. Expected is created upon successful completion of the z_Test. Xlist, Ylist The names of the lists containing the data for LinRegTTest. Defaults are L1 and L2, respectively. The dimensions of Xlist and Ylist nmst be the same. RegE(:l The prolnpt for the name of the Y= variable where the cMculated regression equation is to be stored. If a Y= variable is specified, that equation is automatically selected (turned on). The default is to store the regression equation to the RegEQ variable only. Inferential Statistics and Distributions 13-27 Test and Interval Output Variables The inferential variables statistics are calculated as indicated below. variables for use in expressions, press [_, 5 (5:Statistics), the VARS menu listed in the last column below. these select Variables Tests Intervals To access and then LinRegTTest, ANOVA VARS Menu p-value p p TEST test z, t, Z2_ F t, F TEST df TEST statistics degrees of freedom df df sample sample mean of x values 1 and sample 2 21,22 21, 22 TEST sample standard deviation of x for sample 1 and sample 2 Sxl, Sx2 Sxl, Sx2 TEST nulnber of data points 1 and sample 2 nl, n2 nl, n2 TEST SxP SxP /3 /3 TEST pooled standm'd for for sample deviation SxP TEST estimated sample proportion estimated population sample 1 proportion for /31 /31 TEST estimated population sample 2 proportion for /32 /32 TEST lower, upper TEST 2 _ XY Sx Sx XY n n confidence mean interval pair of x values sample standm'd nulnber of data standard error deviation of x points about the line XY s TEST a, b EQ correlation coefficient r EQ coefficient of determination r2 EQ regression equation RegEQ EQ regression/fit 13-28 coefficients Inferential Statistics and Distributions Distribution DISTR menu Functions To display DISTR the DISTR menu, press [_ [DiSTR], DRAW Normal Normal Inverse i: normalpdf( 2: normalcdf( 3:invNorm( probability distribution cunmlative densityprobability normal distribution Student-t probability density Student-t distribution probability Chi-square probability densityChi-square distribution probability F probability densityF distribution probability Binomial probability Binomial cunmlative densityPoisson probability Poisson cunmlative density Geometric probability Geometric cunmlative density- 4:tpdf( 5:tcdf( 6: z2pdf( 7: x2cdf 8: Fpdf( 9: Fcdf( O: binompdf( A: binomcdf( B: poissonpdf( C: poissoncdf( D: geometpdf( E: geometcdf( Note: -1E99 and IE99 specify infinity. If you want to view the area left of upp¢rbound, for example, specify lowerbound_1E99. normalpdf( norwmalpdf( computes the probability density function (pdf) for the normal distribution at a specified x value, The defaults are mean p=O and standard deviation cr=l. To plot the normal distribution, p_k_te normalpdf( to the Y= editor. The probability density function (pdf) is: 1 - (x-")= f(x)=_e 2_ ,_>0 4"z_c_ normalpdf(x[,p,o]) Pl,:,tl P10L2 Plot3 ",V1 Bnor.r_alPdf" (X, 35,2> Note: Xmin Xmax Ymin Ymax For this example, = 28 = 42 =0 = .25 Tip: For plotting the normal distribution, you can set window variables Xmin and Xmax so that the mean p falls between them, and then select 0:ZoomFit from the ZOOM menu. Inferential Statistics and Distributions 13-29 normalcdf( normalcdf( computes between lowerbound nlean u and standard and 6= 1. the normal distribution probability and upperbound for the specified deviation or. The defaults are u =0 normalcdf(_werbound,upperbound[,p,_]) noPmalod_(-iE99, 36,35,2) .6914624678 invNorm( invNorm( computes the inverse cumulative normal distribution function for a given area under the normal distribution cut_'e specified by mean p and standard de_iation cr. It calculates the x value associated with an area to the left of the x value. 0 _<area _<1 must be true. The defaults are p =0 and or=1. invNorm(area[,p,_]) invNorr_(. 6914624 678,35, 2) 36. ee0000e4 tpdf( tpdf( computes the probability density- function (pdf) %r the Student-t distribution at a specified x value, df (degrees of freedom) must be >0. To plot the Student-t distribution, paste tpdf( to the Y= editor, function (pdf) is: F [(df + 1)/2] f(x) probability (1 + x2/df) - (if + 1)/2 x/_f dJ) Pl_{:[ P1¢_: Plo{. _ ",YI BtPd{'(X, 2) I Note: For this example, Xmin = -4.5 Xmax = 4.5 Ymin = 0 Ymax = .4 13-30 Inferential density- = F(df /2) tpdf(x, The Statistics and Distributions tcdf( tcdf( computes the Student-t distribution probability between lowo'bound and uppe_"bound for the specified (degrees of freedom), which nmst be > O. df tcdf(lowerbound,uppe'rbou.rwl,d]_ tc.d_" ( •9657465644 -2, 3, 18) x2pdf( z2pdf( computes the probability density function (pdf) ff)r the X2 (chi-square) distribution at a specified x value, df (degrees of freedoln) nmst be an integer > 0, To plot the X 2 distribution, paste x2pdf( to the Y= editor, The probability density function (pdf) is: f(x) 1 = r(df (1/2)df/2 x/f/:) - 1e - x/:), x _>0 /2) :2pdf(x,dj) P1,;,tl PloLZ Plot_ \YI B:KZPdf'(X, 9) ",VZ I_I;_ Z Pdla (X _F) Note: Xmin Xmax Ymin Ymax xYs= \Y_= \Y_= xY_= \Y_= x2cdf( For this example, =0 = 30 = -.02 = .132 x2cdf( computes the Z z (chi-square) distribution probability between lowerbound and upperbound for the specified df (degrees of freedom), which nmst be an integer > O. z2cdf(lowe'rbound,upperbound,dj) _Zc.d_(O, 19. 023,9 .9750019601 Inferential Statistics and Distributions 13-31 Fpdf( Fpdf( computes the probability density- function (pdf) for the F distribution at a specified x value, numerator df (degrees of freedonl) and denominator dfnmst be integers > O. To plot the F distribution, paste Fpdf( to the Y= editor. The probability density function (pdf) is: f(X) F[(n+d)/2] = F(n/2)F(d/2) where (d)n/2xn/2 n = numerator d = denominator F pdf(x,numero tor dr, denominator Plot:l, plot:i: Plo_,3 _._1BFPdf Fcdf( l(l+,_a_./d)(n+d)/2,X> (X, 24, dJ_ Note: For this example, 19 Xmin Xmax Ymin Ymax == 05 =0 = 1 Fcdf( computes the F distribution probability between lowerbound and uppe'rbound for the specified nume_-ator df (degrees of freedon0 and denominator dr. numerator dfand denominator df nmst be integers >0. F cdf(lowerbound,upperbound,numerator denominator dJ) Fodf'(O, 2. 4523,24 ,19) -, • 9_ 49989576 13-32 degrees of freedom degrees of fi'eedom Inferential Statistics and Distributions dr, 0 binompdf( binompdf( computes a probability at x ffw the discrete binomial distribution with the specified numtrials and probability of success (1)) on each trial, x can be an integer or a list of integers. O_<p_<lnmst be true. numtrials nmst be an integer > O. If you do not specify x, a list of probabilities from 0 to numtrials is returned. The probability density function (pdf) is: f( X ( _7/, )=/xiP x n-x (l-p) where , X =O,1,...,n n = numtrials binompdf(numtrials,p[,x ]) binomPd¢(5,. 6, {3 ,4,5}) {. 3456 .2592 .0... binomcdf( binomcdf( computes a cunmlative probability at x ff)r the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial, x can be a real nmnber or a list of real nmnbers. O_<p_< 1 nmst be true. numtrials nmst be an integer > O. If you do not specify- x, a list of cunmlative probabilities is returned. binomcdf(numtrials,p[,x ]) binomcd¢(5,. 6, {3 ,4,5}) {,66304 .92224 ... poissonpdf( poissonpdf( computes a probability at x ff)r the discrete Poisson distribution with the specified mean {l, which nmst be a real nmnber > O. x can be an integer or a list of integers. The probability density function (pdf) is: f(x) = e - _ ,uX/x!, x = 0,1,2,... poissonpdf(p,x) PoissonPd¢(6,10) .0413030934 Inferential Statistics and Distributions 13-33 poissoncdf( poissoncdf( computes a eunmlative discrete Poisson distribution which nmst be a real number probability at x for the with the specified mean _l, > O. x can be a real number or a list of real numbers. poissoncdf(p,x) eoissonod¢(.126, {0,1,2,3}) {.8816148468 .9... geometpdf( geometpdf( computes a probability at x, the number of tlle trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. 0_<p_<l nmst be true. x can be an integer or a list of integers. The probability density function (pdf) is: f(x) = p(1 - p)X - 1, x = 1,2,... geometpdf_,x) geo_eted?(.4,6) .031104 geometcdf( geometcdf( computes a cunmlative probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. O_<p_< 1 must be true. x can be a real number or a list of real numbers. geometcdf_,x) geo_etod¢(.5,{l, 2,3J) {.5 13-34 Inferential Statistics .75 and .875} Distributions Distribution DISTR DRAW Menu Shading To display the DISTR DRAW menu, p_ss _ [DISTR] []. DISTR DRAW instructions draw vmious types of density functions, shade the area specified by lower'bound and uppc'rbound, and display- the computed area vMue. To clem" the drawings, menu (Chapter 8). select l:CIrDraw from the DRAW Note: Before you execute a DISTR DRAW instruction, you must set the window variables so that the desired distribution fits the screen. DISTR i: DRAW ShadeNorm( 2:Shade t( 3:Shadez2( 4:ShadeF( Shades normal Shades Student-t distribution. Shades Shades )_ distribution. F distribution, distribution, Note: -1E99 and IE99 specify infinity. If you want to view the area left of upperbowad, for example, specify lowe'rbownd_1E99. ShadeNorm( ShadeNorm( draws the normal density function specified by mean u and standard deviation a and shades the m'ea between lowc'rbound and upperbound. The defaults are u=0 and a= 1. ShadeNorm(lowerboural,uppc'rbound[,g,c_]) Note: For this example, Xmin = 55 Xmax = 72 Ymin = -,05 Ymax = ,2 Inferential Statistics and Distributions 13-35 Shade_t( Shade_t( draws the density function distribution specified by df (degrees shades the area between lowe_rbound for the Student-t of freedom) and and upperbound. Shade_t(lowerbound,upperbound,dJ_ Note: For this example, Xmin = -3 4)IShade-t(-l'IE99' Xmax = 3 Ymin = -,lS Ymax = .S Shadex2( Shadex2( draws the density function for the Z 2 (chi-square) distribution specified by df (degrees of freedom) and shades the area between lowerbou_l and uppe_rbound. Shadex2(lowerbound,uppe_'bound,dj) IShadeXZ (0, 4, 10)I I Note: Xmin Xmax Ymin For this example. =0 = 35 = -.025 Ymax = .1 ShadeF( ShadeF( draws the density function for the F distribution specified by numerator df (degrees of freedom) and denominator dfand shades the area between lowed'bound and upperbour_l. ShadeF (lowe'rbound,upperbound,numerator denominator ShadeF()i 1,2, dr, d_ 10, 15 Note: Xmin Xmax Ymin For this example, =0 = S = -.25 Ymax = .9 13-36 Inferential Statistics and Distributions 14 Contents Financial Functions Getting Started: Einaneing a Car. ........................ Getting Started: Computing Compound Interest .......... Using the TVM Solver .................................... Using the Financial Functions ........................... Calculating Time Value of Money (TVM) ................. Calculating Cash Flows .................................. Calculating Amortization ................................ Calculating Interest Conversion .......................... Finding Days between Date_)efil_N Paynlent Method ..... Using tile TVM Variables ................................. TEXAS I4-2 14-3 14-4 14-5 14-6 14-8 14-9 I4-I2 14-13 14-14 T1=83 INSTRUMENTS N=360.00 I_=IB.00 PV=100000.00 -PMT=-I507.09 FV=0.00 P/V=12.00 C/Y=12.00 PMT:L_ BEGIN STAT PLOT TBLSET FORMAT CALC TABLE Financial Functions 14-1 Getting Getting Started: Started Financing a Car is a ftkst-paced introduction. Read the chapter for details. You have found a cat" you would like to buy-. The car costs 9,1)00. You can afford payments of 250 per month for four years. What annual percentage rate (APR) will make it possible for you to afford the car? Press[_[][][][][_to setthe fixed-deeimalmode seging to 2. The TI-83 will display all numbers with two decimal places. Sci Ehg _I_3456789 Degree Pol Se_ Dog Horiz 2. Press [_ [FINANCE]to display" the FINANCE CALC menu. G-T VRRS Solver... gum_I% gvm_PV tvm_N tvm_FV ,nev( 3. Press [_ to select I:TVM Solver. The TVM Solver is displayed. Press 48 [_ to store 48 months to N. Press [] 9000 [gNT_ to store 9,000 to PV. Press [] 2S0 [gNT_ to store -250 to PMT. (Negation indicates cash outflow.) Press 0 [ggg_ to store 0 to FV. Press 12 F_tggl to store 12 payments per year to P/Y and 12 compounding periods per year to O/Y. Setting PlY to 12 will compute an annual percentage rate (compounded monthly) for I%.Press [] [gNT_ to select PMT:END, which indicates that payments are due at the end of each period. 4. 14-2 Press [] [] [] [] [] [] to move the cursor to the I%prompt. Press @ [SOLVE] to solve for I%.What APR should you look for? Financial Functions N=0.00 I%=0.00 PV=0.00 PMT=0.00 FV=0.00 P/Y=l.O0 C/V=l.00 PMT:L_ BEGIN N=48.00 I%=0.00 PV=9000.00 PMT=-250.00 FV=0.00 P/Y=12.00 C/Y=12.00 PMT:[__[LL_ BEGIN N=48.00 "1%=14.90 PV=9000.00 PMT=-250.00 FV=0.00 P/Y=12.00 C/Y=12.00 PMT:L:[II_BEGIN Getting At what 2,000 Started: annual interest Computing rate, Compound compounded monthly, will Interest 1,250 accumulate to in 7 years? Note: Because there are no payments when you solve compound interest problems, PMT must be set to 0 and PlY must be set to 1. Z.._tvVRR5 M Solver _,_PMt 3: tw,_l% 4: tvM_PV 5: tur,,_N 6: tvr.__FV 74nPv( Press [_ [FINANCE] to display- the FINANCE CALC menu. Press [_ to select I:TVM Solver. Press 7 to enter the number of periods in years, Press [] [] [] 12S0 to enter the present value as a cash outflow (investment). Press [] 0 to specify- no payments. Press [] 2000 to enter the future value as a cash inflow (return), Press [] 1 to enter payment periods per year, Press [] 12 to set compounding periods per yea[" to 12. N=7 1%=0 PV=-1250 PMT=O FV=2000 P/9=I C/Y=12 PMT:L_IiE BEGIN Press [] [] [] [] [] to place the cursor the 1%prompt. N=7 1%=| PV=-1250 PMT=O FV=2000 P/Y=1 C/Y=I2 PMT:I=_I_ BEGIN Press @ [SOLVE] to solve for I%, the annual interest ['ate. on .N=7.O0 1%=6.73 PV=-1250.00 PMT=0.00 FV=2000.00 P/Y=l.00 C/Y=12.00 PMT:_ BEGIN Financial Functions 14-3 Using the TVM Solver Using the TVM Solver The TVM Solver displays the time-value-of-money (TVM) variables. Given four variable wdues, tile TVM Solver solves for the fifth variable. The FINANCE VARS menu section (page 14-14) describes the five TVM variables (N, I%, PV, PMT, and FV) and PlY and C/Y, PMT: END BEGIN in the TVM Solver corresponds to the FINANCE CALC menu items Pmt_End (pa3qnent at the end of each period) and Pmt_Bgn (payment at the beginning of each period). To solve for an unknown TVM vm'iable, follow these steps. 1, Press [2ffa][FINANCE] _ to display the TVM Solver. The screen below shows the default values with the fixeddecimal mode set to two decimal places, N=0.00 Ia=0.00 PV=0.00 PMT=O,00 FV=0.00 P/V=I.00 C/V=I.O0 PMT:[__II_ BEGIN 2. Enter the known vMues for four TVM variables. Note: Enter cash inflows as positive numbers and cash outflows as negative numbers. Enter same C/Y. 4. Select a value for P/Y, which automatically enters the wdue for C/Y; if PW € CIY, enter a unique value for END or BEGIN to specify- 5. Place the cursor want to solve. on the the pa3qnent TVM vm'iable method. for which you Press @ [SOLVE].The answer is computed, displayed in tile TVM Solver, and stored to the appropriate TVM variable, An indicator square in the left colunm designates the solution variable. N=360.00 I%=1B.00 PV=100000.00 PMT=-I507.09 FV=0.00 P/Y=I2.00 CXY=12.00 PMT:I:IIIIBEGIN 14-4 Financial Functions Using the Financial Functions Entering Cash Inflows and Cash Outflows When FINANCE CALC Menu To display using the TI-83 financial functions, CALC the enter FINANCE CALC menu, press [_ [FINANCE]. VARS i : TVM Sol ver.,. 2 : tvm Pmt 3: tvm I% 4:tvm PV 5:tvm N 6:tvm FV 7:npv( 8:irr( 9: bal( O:EPrn( A:EInt( B:_Nom( C:_Eff( D:dbd( E: Pmt End F: Pmt Bgn Displays Conlputes Conlputes Computes Colnputes Computes Computes Computes Computes Computes Computes Computes Computes tile TVM Solver. the amount of each payment. the interest rate per year, the present value. the nulnber of paylnent periods, the future value, the net present value, the internal rate of l_tum. the amortization sched, balance, the amort, sched, principal sum, the amort, sched, interest sum. the nominal interest rate, the effective interest rate. Calculates the days between two dates, Selects ordinary annuity (end of period). Selects annuity- due (beginning of period), [ _se these functions to set up and perform calculations on the home screen, TVM Solver you lnust cash inflows (cash received) as positive numbers and cash outflows (cash paid) as negative numbel\_. The TI-S3 follows this convention when computing and displaying answers. TVM Solver displays tile TVM Solver (page Financial financial 14-4). Functions 14-5 Calculating Calculating Time Value of Money Time Value of Money I _se tilne-value-of-lnoney (TVM) (TVM) functions (menu through 6) to analyze financial instruments such annuities, loans, mortgages, leases, and sa_ings. items 2 as Each TVM function takes zero to six arguments, which must be real numbers. The wdues that you specify as arguments for these functions m'e not stored to the TVM variables (page 14-14). Note: To store a value to a TVM variable, use the TVM Solver (page 14-4) or use _ and any TVM variable on the FINANCE VARS menu (page 14-14). If you enter less than six arguments, the TI-83 substitutes previously stored TVM vm'iable value for each unspecified argument. tvm_Pmt If you enter place the argmnent any argunlents with a TVM function, or arguments tvm_Pmt computes the amount tvm_Pmt [(N,I %,PV,FV, P_, In the example nlust in parentheses, of each payment. C/Y) ] N=360 I%=8.5 Pg=IO0000 PMT=O FV=O P/?=I2 C/V=12 PMT:I_I[ BEGIN Note: you a above, the values tvm_Pmt -768 91 tvm_Pr_t (360, 9: 5) I I -840.85 are stored to the TVM variables in the TVM Solver. Then the payment (tyro_Pint) is computed on the home screen using the values in the TVM Solver. Next, the interest rate is changed to 9.5 to illustrate the effect on the payment amount. 14-6 Financial Functions tvm_]% tvm_I% computes the annual inte[_st rate. tvm_1%[(N,PV,PMT, FV, P/Y, C/Y) ] 10000, I tvm_l%(48, -250,0, tvm_PV 12) 9 24 Rns÷l% 9124 tvm_PV computes the present tvm_PV[(_I%,PMT, FV, P/Y,C/Y)] vMue. 360÷N:II÷I%:-100 ÷PMT:O÷FV:12÷P/ tvm_PV I tvm_N 12.00 1o5oo6.351 tvm_N computes the number tvm_N[(I%_V_MT, of paylnent periods. FV, P/Y,C/Y)] 6÷I%:9000÷PV:-351 O÷PMT:O+FV:3÷P/V tvm_N tvm_FV l 3.00 36.47 tvm_FVcomputesthe _turevMue. tvm_FV[(_I%,PV, PMT_X,C/Y)] 6÷N:8÷I%:-5500÷P V:0÷PMT:l÷P/_.00 tvm_FV 8727.81 Financial Functions 14-7 Calculating Calculating a Cash Flow Cash Flows Use the cash flow functions (menu items 7 and 8) to analyze the value of money over equal time periods. You can enter unequal cash flows, which can be cash inflows outflows. The syntax descriptions for npv( and irr( use these arguments. • interest rate is the rate by which to discount flows (the cost of money) over one period. the • CFO is the initial nunlber. be a real • CFList is a list of cash c_sh flow CFO. • CFFreq is a list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList. The default is 1; if you enter values, they nmst be positive integers < 10,000. For example, 2000 cash express 2000 ; I flow flow at time 0; it nmst alnounts this uneven cash 2000 T after flow cash the initial in lists. 4000 1 or I 4000 I - 3000 CFO = 2000 CFList CFFreq npv(, irr( = {2000,-3000,4000} = {2,1,2} npv( (net present value) is the sunl of the present values for the cash inflows and outflows. A positive result for npv indicates a profitable investment. npv(interest rate,CFO,CFList[,CFFreq]) irr( (internal rate of return) is the interest rate at which the net present value of the cash flows is equal to zero, irr(CFO,CFList[,CFFreq]) 1000 0 1 2000 1 -2500 {1000,-2500,0,501 00,3000_+L1 I <1000.00 14-8 Financial Functions 5000 -2500 .... nPv(6,-2000,Lt) 2920.65 irP(-2000,L1) 27.88 3000 Calculating Amortization Calculating an Amortization Schedule Use the amortization functions (menu bal( bal( computes tile balance ff)r an amortization schedule using stored wdues ff)r I%, PV, and PMT. npmt is the number of the payment at which you want to calculate a balance. It nmst be a positive integer < 10,000. roundvalue specifies the internal precision the calculator uses to calculate the balance; if you do not specify roundvalue, then the TI-83 uses the cmTent Float/Fix decimal-mode calculate balance, sum of principal, an amortization schedule. items and sum 9, 0, and A) to of interest for setting. bal(npmt[,roundvalue]) IO0000÷PV: EPrn(, Elnt( 8.5÷I% bal (12) I_.O0 99244.07 EPrn( computes the sunl of the principal during a specified period for an amortization schedule using stored values for I%, PV, and PMT. pmtl is the starting paylnent, pmt2 is the ending payment in the range, pmtl and pmt2 nmst be positive integers < 10,000. roufwlvalue specifies the internal precision the calculator uses to calculate the principal; if you do not specify- _vu.rwlvalue, the TI-83 uses the current Float/Fix deeinml-mode setting. Note: You must enter values for 1%, PV, PMT, and before computing the principal. EPrn(pmtl,pmt2[,rou_wlvalue]) Elnt( computes the stun of the interest period for an amortization schedule I%, PV, and PMT. pmtl is the starting ending payment in the range, pmtl during a specified using stored values for paylnent, pmt2 is the and pmt2 nmst be positive integers < 10,000. roundvalue specifies the internal precision the calculator uses to calculate the interest; if you do not specify- roundvalue, the TI-83 uses the emTent Float/Fix deeinml-mode setting. Elnt(pmt l ,pmt2[ ,roundvalue 360÷N: 100000÷PV: 8.5÷1%: -768.91÷P MT:I2÷P/V 12.00 I ]) EF'Po (I, 12)755._ 93 EInt(l,12)_8470.99 Financial Functions 14-9 Amortization You want Example: Calculating an Outstanding Loan Balance percent APR. Monthly payments are 800, Calculate the outstanding loan balance after each payment and displaythe results in a graph and in the table, to buy a home with a 30-year mortgage at S 1, Press [_]. Press [] [] [] [] _ to set the fixed-decimal mode setting to 2, Press [] [] [] _ select Par graphing mode, Sci to I Eng II_34567891 Degree _Pol I Se_ Dot I SiMi hi, I e^8' Horiz G-T 2, Press [_ [FINANCE] _ I to display the TVM Solver. 3. Press 360 to enter number of payments. Press [] 8 to enter the interest rate. Press [] [] [] 800 to enter the paynmnt amount. Press [] 0 to enter the future value of tile mortgage. Press [] 12 to enter the payments per year, which also sets the compounding periods per year to 12. Press [] [] _ to select PMT:END, N=360.00 I%=8.00 PV=0.00 PMT=-800.00 FV=0.00 P/Y=12.00 C/Y=12.00 PMT:[_:IIL_ BEGIN 4. Press Press [] [] [] [] [] to place the cul_or on tile PV prompt. @ [SOLVE] to solve for the present value. N=360.00 I%=8.00 PV=109026.80 PMT=-800.00 FV=0.00 PIV=I2.00 C/Y=12.00 PMT:I:I_I_BEGIN 5, Press [] to display stat plots. Press _ [FINANCE] 9 _[_ pI,:,I:I pl,:,l:._ \X1 "r_T YIT_baI(T) 14-10 Financial Functions plol:_ tile parametric Y= editor. Turn off all to define X1T as T. Press [] [g_ to define Y1T as bal(T). 6. Press _ to display- the window tile values below. Tmin=0 Xmin=0 Tmax=360 Xmax=360 Tstep=12 Xscl=50 variables. Enter Ymin=0 Ymax=125000 Yscl=10000 7, Press _ to draw the graph and activate the trace cursor. Press [] and [] to explore the graph of the outstanding bahmce over time. Press a number and then press [gNY_ to xqew the balance at a specific time T. 1T=T Y1T=b_I(T) S, Press [g_ TblStart=0 ATbI=12 [TBLSET] and enter the vMues below. 9, Press [g_ [TABLE] to display the table of outstanding balances (Y1T). Tim O,00 tZ.00 ,"4 t -,a" IaL0O 10907::7 YtT 10Bl11_ tlIEII00 E0.O0 31L00 rIB.00 I;0,00 lO60E:I, 1Oh9O_: 1031_g2 T-?_2{_00 72.00 10_:29g 10.Press [g0_ [] [] [] [] [] [] [] [] [] [V_Y_ to select G-T split-screen mode, in which the graph and table are displayed sinmltaneously. Press _ the table. to display- XIT (time) and YIT (balance) _0.00 72,00 1.0Eg 1,0E5 96.00 t0B,0 .._.Eh.00 99_h 97510 t.OEg T=132 X=132 ?=93621.91 in _ Financial Functions 14-11 Calculating Calculating Interest Conversion an ,Nom( Interest Conversion Use the interest conversion functions Onenu items B and C) to convert interest rates from an annual effective rate to a nominal rate (_Nom() or from a nominal rate to an annual effective rate (_Eff(). _Nom( computes the nominal interest rate. effective and compounding periods nmst be real numbers. compounding periods nmst be >0. _Nom(effective rate,compounding _Nor_( 15.87, ,Eft( 14-12 Financial periods) 4)15.00 )Elf( computes compounding compounding the effective periods must periods must _Eff(nominal rate,compounding _E€€(8,12) Functions rate 8.30 interest be real be >0. rate. nominal nulnbers. periods) rate and Finding Days between Dates/Defining dbd( Use the date Payment Method dbd( (menu function item D) to calculate the number of days between two dates using the actual-daycount method, datel and date2 can be numbers or lists of numbers calendar. within the range of the dates on the standard Note: Dates must be between the years I950 through 2049. dbd(date l ,date2) You can enter • • datel and date2 in either of two formats. MM.DDYY (United States) DDMM.YY (Europe) The decimal placement differentiates the date formats, dbd( 12. 3190, 12.3 192) 731.00 Defining the Payment Method Pmt_End and Pmt_Bgn (menu items E and F) specify- a transaction _k_an ordinmy7 annuity or an annuity due. VC]mn you execute either conunand, the TVM Solver is updated. Pint_End Pmt_End (payment end) specifies an ordinmTy- annuity-, where payments occur at the end of eaeh payment period. Most loans are in this catego[% Pint_End is the default. Pmt_End On the TVM Solver's PMT:END PMT to ordinmTy- annuity. Pmt_Bgn BEGIN line, select Pmt_Bgn (payment beginning) specifies where payments occur at the beginning period. Most leases are in this catego_7. END to set an annuity due, of each payment Pmt_Bgn On the TVM Solver's PMT:END set PMT to annuity due. BEGIN line, select Financial Functions BEGIN to 14-13 Using the TVM Variables FINANCE VARS Menu To display the FINANCE VARS menu, press _ [_. You can use TVM variables in TVM functions values to them on the home screen, CALC VARS 1: N Total number of payment 2:1% Annual interest rate 3: PV Present value 4: 5: 6: 7: PMT FV P/Y C/Y [FINANCE] and store periods Payment amount Future value Number Number of payment periods per year of compounding periods/year N, [%, PV, PMT, FV N, I%, PV, PMT, and FV are the five TVM wu'iables. They t_present the elements of eonunon financial transactions, as described in the table above. I%is an annual interest rate that is converted to a per-period rate based on the values of P/Y and C/Y. PlY and C/Y PW is the number of payment financial transaction. C/Y is the number salne transaction. periods of compounding per year in a periods per year in the When you store a value to P/Y, the value for C/Y automatically changes to the same value. To store a unique value to g/Y, you nmst store the value to C/Y after you have stored a value to PlY. 14-14 Financial Functions 5 Contents CATALOG,Strings, HyperbolicFunctions Browsing tile TI-83 CATALOG ........................... Entering and Using Strings ............................... Storing Strings to String Variables ....................... String Functions and Instructions in the CATALOG Hyperbolic Functions in tile CATALOG .................. ...... 15-2 15-3 15-4 15-6 15-10 T1=83 TEXAS INSTRUMENTS m CATALOG _abs( and angle( QNOUA( Ans augnenL( AxesO_¢ J STAT PLOT TBLSET FORMAT CATALOG, Strings, BALe TABLE Hyperbolic Functions 15-1 Browsing the TI-83 CATALOG What Is the CATALOG? The CATALOG is an alphabetical list of all functions and instructions on the TI-83. You also can access each CATALOG item fronl a menu or the keyboard, except: • • • • The six string functions (page 15-6) The six hyperbolic functions (page 15-10) The solve( instruction without the equation solver editor (Chapter 2) The inferential stat functions without the inferential stat editors (Chapter 13) Note:The only CATALOG programming commandsyou can execute from the home screen are GetCalc(, Get(, and Send(. Selecting an Item from the CATALOG To select a CATALOG item, follow these steps. 1. Press F_a] [CATALOG] to display the CATALOG. i*abs( and angle( RNOVR( Rn_ iCRTRLOG augment( Axes0€€ The _ in the first colunm is the selection cursor. 2. Press [] or [] to scroll the CATALOG until the selection cursor points to the item you want. • • • To jump to the first item beginning with a particular letter, press that letter; alpha-lock is on. Items that begin with a number are in alphabetical order according to the first letter 'after the number. For example, 2-PropZTest( is among the itenls that begin with the letter P. Functions that appear as symbols, such as +, -1, <, and g(, follow the last item that begins with Z. To jump to the first s3qnbol, !, press [@ 3. Press [ggY_ to paste the item to the current Iabs(1 screen. I Tip: From the top of the CATALOG menu, press [] to move to the bottom. From the bottom, press [] to move to the top. 15-2 CATALOG, Strings, Hyperbolic Functions Entering What and Using Strings Is a String? A string is a sequence On the TI-83, • It defines text to be displayed • It accepts input Characters Entering a String of characters quotation marks, applications. from Count • Count each instruction cos(, as one character; instruction or function number, letter, and space to form as one character, a string follow on a blank line on the home these steps. 1, Press @ [,] to indicate 2, Enter the characters that the beginning comprise Use any combination names, or instruction • To enter • To enter several alpha characters [A-LOCK] to activate alpha-lock. @ space, [-] to indicate screen or in a of the string. the string. • 3, Press a string. or function name, such as sin( or the TI-83 interprets each name as one character. To enter program, ablank within primaFy" in a program, that you combine • enclose has two in a p_x)gram. the keyboard are the units each that you a string of numbers, letters, function names to create the string. press @ [_], in a row, press [_ the end of the string. "string" 4. Press [ENY_. On the home screen, the string is displayed on the next line without quotations. An ellipsis (...) indicates that the string continues beyond the screen, To scroll the entire string, press [] and EO"RBC,D, 1234 EFGH 5678 RBCD 1234 EFGH ... Note: Quotation marks do not count as string characters. CATALOG, Strings, Hyperbolic Functions 15-3 Storing Strings String Variables to String Variables The TI-83 has 10 variables You can use string instructions. to which variables with you can string store functions strings. and To display the VARS STRING menu, follow these steps. 1, Press _ to display- the VARS menu, Move the cursor to 7:String. _ Y-VRRS ndo_z.. 2: Zoom. 3: GDB... 4: Picture... 5: Statistics_. 6: Table... WString... 2, Press_ to displaytheSTRING secondarymenu, 5:Str3 Str4 Str5 Str6 ,Str7 15-4 CATALOG, Strings, Hyperbolic Functions Storing a String to a String Variable a string to a string 1. Press @ [,], enter 2. Press _. To store 3. Press _ 4. Select which variable, the string, 7 to display the string you want follow these and press steps. @ [-]. the VARS STRING menu. variable to store (from $trl the string. to $tr9, or $tr0) to 4:Str.4 5:StP5 6:_tr6 74Str-7 The string variable is D_sted to the current location, next to the store symbol (-)). cursor Press _ to store the string to the string variable. On the home screen, the stored string is displayed on the next line without quotation marks. "HELL0"eStP2 HELLO Displaying the Contents of a String Variable To display the contents of a string variable on the home screen, select the string variable from the VARS STRING menu, and then press [gNT_. The string is displayed. I St.r2 HELLO CATALOG, Strings, Hyperbolic Functions 15-5 String Functions Displaying String Functions and Instructions in the CATALOG and Instructions String functions in the CATALOG and instructions m'e available only fronl the CATALOG. The table below lists the string functions and instructions in the order in which they appem" among the other CATALOG menu items. The ellipses in the table indicate the presence of additional CATALOG items. CATALOG + (Concatenation) Equ)String( expr( Converts Converts inString( Returns a chm'acter's length( Returns a string's String)Equ( sub( Converts Returns a string to an equation, a string subset as a string, To concatenate two or more 1, Enter stringl, 2, Press [], 3, Enter string2, necessmT, stringl 4, Press 15-6 CATALOG, number. chm'acter length. follow name. which can be a string or string name, press [] and enter to display- Hyperbolic steps, or string string3, If and so on, , , the strings as a single string. : 5tr To select a string function or instruction current screen, follow the steps on page Strings, these can be a string +string2+string3, [_ strings, place which 1 +"LMHOP" "HIJK "+StPl HIJK LMNOP Selecting a String Function from the CATALOG an equation to a string, a string to an expression. Functions and paste 15-2. it to the Equ*String( Equ*String( converts to a string an equation that is stored to any- VARS ¥-VARS variable. Yn contains the equation. Strn (from Strl to Strg, or Str0) is the string variable to which you want the equation to be stored as a string. Equ*Stdng(Yn,Strn) expr( "3X"÷Y1 E_u*String(gt, Done St rl) Done expr( converts an expression the chm'acter and executes string contained in string to it. string can be a string or a stringvariable. expr(string) ,,l+2+XZ,,) l_X:"5X"+Strl x_r(Strl)÷R inString( 10 I0 7 exPr( inString( returns the chm'acter position in string of the first character of substring, string can be a string or a string variable, start is an optional character position at which to start the search; the default is 1. inString(string,subst,ring[ inStr ,start]) ing ( "PQRSTU V", "STU" ) 4 inStr ing ( "RBCRBC , Note: RBC ,4) 4 If st:_ing does not contain snbst:Hng, or start is greater than the lengthof string, inString( returns O. CATALOG, Strings, Hyperbolic Functions 15-7 length( length( returns can be a string the number or string of chara('ters in st'ring, string variable. Note: An instruction or function name, such as sin( or cos(, counts as one character. length(string) WXYz"WXYZ"eStrl length(Strl) String*Equ( 4 String*Equ( converts st'ring into an equation and stores equation to Yn. st'ring can be a string or string vmiable, String*Equ( is tlle inverse of Equ*String(. String*Equ(st'ring,Yn) I String*E_u(Str2, '.?z) Plot1 Done Plot;" Plot3 ,,yl= ",YzB2X 15-8 CATALOG, Strings, Hyperbolic I I Functions tlle sub( returns sub( a string that is a subset of an existing st'ring. string can be a string or a string variable, begin is the position number of the first character of the subset, length is the number of characters in the subset. sub(st_ng,b_in,length) I sub(StP5,4,2) ABCDEFG"RBCDEFG"÷SLP5 DE Entering Function a to Graph during Program Execution Inapmgram, youcanentera programexecutionusin Nnctiontographdunng theseconunands. PROGRRM:INPUT :InPut "ENTRY ='' , StP3 :String*E_u(Str3 ,Y_) :DisPGraPh PPYmINPUT ENTRY=3XI / / / Note: When you execute this program, enter a function to store to Y3 at the ENTRY= prompt. CATALOG, Strings, Hyperbolic Functions 15-9 Hyperbolic Functions Hyperbolic Functions The hyperbolic in the CATALOG functions are available only from the CATALOG, The table below lists the hyperbolic functions in the order in which they appear among the other CATALOG menu items. The ellipses in the table indicate the presence of additional CATALOG items. CATALOG sinh(, cosh(, tanh( c0 s h ( c 0 s h-1 ( Hyperbolic Hyperbolic cosine arccosine s i nh ( si nh-1 ( Hyperbolic Hyperbolic sine arcsine t a nh ( t a nh- 1( Hyperbolic Hyperbolic tangent arctangent sinh(, cosh(, and tanh( are the hyperbolic functions. valid for real numbers, expressions, and lists. Each sinh(value) cosh(value) tanh(value) sinh(.5) .5210953055 cosh( {.25,. 5, I} ) {1.8314131 sinhd(, cosh-l(, tanh-l( 1.12 sinh-l( is the hyperbolic arcsine function, cosh-l( is the hyperbolic arccosine function, tanh-l( is the hyperbolic m'ctangent function. Each is valid for real nulnbers, expressions, and lists. sinh- l(value) cosh- 1(value) sinh -1(value) sinh-1({O,l}) I {0 .881373587}I tanh-1(-.5) -.5493061443 15-10 CATALOG, Strings, Hyperbolic Functions is 6 Contents Programming Getting Started: Volume of a Cylinder .................... Creating and Deleting Programs ......................... Entering Colnmand Lines and Executing Programs Editing Programs ........................................ Copying and Renaming Programs ........................ PRGM CTL (Control) Instructions ....................... PRGM I/O (Input/Output) Instructions ................... ('ailing Other Programs as Subroutines .................. '_ TEXAS ...... 16-2 16-4 16-5 16-6 16-7 16-8 16-16 16-22 T1=83 INSTRUMENTS PROGRRM: CYL INDER :PromPt R, H :_R zH÷V :O ise "VOLUME IS .,.j :I J STATPLOT TBLSET FORMAT CALC TABLE Programming 16-1 Getting Getting Started: Started Volume is a fast-paced of a Cylinder introduction. Read the chapter for details. A program is a set of connnands that the TI-83 executes sequentially, as if you had entered them fl'om the keyboard. Create a program that prompts for the radius R and the height H of a cylinder and then computes its volume. Press [E_ [] [] to display the PRGM NEW menu. EXEC EDIT [{L_ BBCreate Press [_ to select 1:Create New. The Name= prompt is displayed, and alpha-lock is on. Press [c] [Y] [L][I] [N] [D] [E] [R], and then press [g_-gm to name the prograin CYLINDER. Flew PIROGRRM:CYLINDER You are now in the program editor. The colon ( : ) in the first colunm of the second line indicates the beginning of a command line. Press [E_ [] 2 to select 2:Prompt from the PRGM I/O menu. Prompt is copied to the command line. Press @ [R] [] @ [H] to enter the variable names for radius and height. Press [_. Press [g_ Ix] @ [R] [] @ [H] [g?_ @ [v] [_ to enter the expression _R2H and store it to the variable V. 16-2 Programming PROGRRM: CYL INDER Press J_ [] 3 to select 3:Disp fronl the PRGM I/O menu. Disp is p_ksted to the conunand line. Press J_ [A-LOCK]["] [V] [O] [L] [U] [M] [E][_] [I] [S] ["]@1_ @ [V] _ to set up the program to display" the text VOLUME IS on one line and the calculated value of V on the next. 6. Press J_ screen. PROGRAM:CYLINBER l:ProMPt R,H I :=RZH+V _DisP "VOLUME IS :i v [QUIT]to display tile home 7. Press [gff_ to display- the PRGM EXEC menu. The items on this menu are the names of stored programs. _EOIT NEW LINOER Press [g_ to paste prgmCYLINBER to the cmTent cursor location. (If CYLINDER is not item 1 on your PRGM EXEC menu, move the cursor to CYLINDERbefore you press [ggT_. ) Prg_CYLINOER| Press [ggT_ to execute the prograln. Enter 1.8 if)r the radius, and then press [g_. Enter a for the height, and then press [g_. The text VOLUME iS, the value of V, and Done are displayed. PPgMCYLINDER R=?1.5 H=?3 VOLUME IS 21.20575041 I Bone Repeat steps 7 through 9 and enter different values for R and H. Programming 16-3 Creating and Deleting Programs What Is a Program.'? A prograln Creating a New Program To create a new program, is a set of one or more connnand lines. Each line contains one or more instructions. When you execute a prograln, the TI-83 perk)tins each instruction on each connnand line in the salne order in which you entered them. The number and size of programs that the TI-83 can store is limited only by available lnelnolT. 1. Press _ k)llow these steps. [] to display tile PRGM NEW menu. EXEC EDIT IIL=I_ HBCreate New 2. Press _ is displayed, to select 1:Create New. The Name= proInpt and alpha-lock is on. 3. Press a letter fi'oln A to Z or 0 to enter tile first character of tile new program nalne. Note: A program name can be one to eight characterslong. The first character must be a letter from A to Z or e. The second through eighth characters can be letters, numbers, or e. 4. Enter zero to seven letters, numbers, the new prograln nalne. 5, Press ITNYERI, Tile prograin 6. Enter one or more prograln editor is displayed. commands 7. Press [_ [QUIT]to leave the progranl to the holne screen. Managing Memory and Deleting a Program or 0 to conlplete (page 16-5). editor and return To check whether adequate nlenlol_y- is available for a prograln you want to enter, press [_ [MEM], and then select 1:Check RAM froln the MEMORY menu (Chapter 18). To increase available nlenlolTy- , press [_ [MEM], and then select 2:Delete froln the MEMORY menu (Chapter 18). To delete a specific prograln, press [_ [MEM], select 2:Delete froln the MEMORY menu, and then select 7:Prgm froln the DELETE FROM seeondalT menu (Chapter 18). 16-4 Progranuning Entering Command Entering a Program Command Line Lines and Executing Programs You emn enter on a eonulland lille any instruction or expression that you could execute from the home screen. In the program editor, each new eonunand line begins with a colon. To enter more than one instruction or expression on a single eonunand line, separate each with a colon. Note: A command line can be longer than the screen is wide; Iong command lines wrap to the next screen line. While ill the program editor, you call display and select fronl menus. You can return to the prograln editor fronl a menu in either of two ways. • Select a menu item, which pastes the item to the cmTent conunand line. • Press @. When you complete CUrSOr nloves a eolnmand tile next to line, press [NY_. The eonulland lille, Progralns can access variables, lists, lnatrices, and strings saved in nlenlol_yL If a prograln stores a new wdue to a variable, list, lnatrix, or string, the prograln changes the value in nlenlory during execution. You e an call another and page 16-22). Executing a Program prograln as a subroutine (page 16-15 To execute a program, begin on a blank line on the home screen and follow these steps. 1. Press [_ to display- the PRGM EXEC menu. 2. Select a pmgraln nalne froln the PRGM EXEC lnenu (page 16-7). prgmname is pasted to the home screen (for example, prgmCYUNDER). 3. Press [_ to execute the program. While the program is executing, the busy indicator is on. L_Bt Answer (Ans) is updated during prograln execution. Last EntlT is not updated as each eonulland is executed (Chapter 1). The TI-83 checks for errors during prograln execution. does not check for errors msyou enter a progranL Breaking a Program To stop nlenu prograln execution, press [_. The It ERR:BREAK is displayed. • To return • To go where to the honle screen, the interruption 1:Quit. select occurred, select Programming 2:Goto. 16-5 Editing Programs Editing a Program To edit a stored 1. Press [V_ program, ff)llow [] to display- these the PRGM steps. EDIT menu. 2. Select a program name froln the PRGM EDIT menu (page 16-7), Up to the first seven lines of the program are displayed. Note: The program editor does not display a ¢ to indicate that a program continues beyond the screen. 3, Edit the program conlnland lines. • Move tile cursor to the appropriate then delete, ove_wvrite, or insert. • Press @ to clear all program eomnmnd line (the lending colon enter a new progrmn eonmmnd. location, eominands remains), and on the and then Tip: To move the cursor to the beginning of a command line, press [_; to move to the end, press _ lB. To scroll the cursor down seven command lines, press @ [_. To scroll the cursor up seven command lines, press @ [_. Inserting and Deleting Command Lines To insert a new eonnnand line anywhere in the progranl, place the cursor where you want the new line, press [_ [tNs], and then press [_T_. A colon indicates a new line. To delete a conlnland line, place the cursor on the line, press @ to clear all instructions and expressions on the line, and then press [ff_ to delete the eonlnland line, including the colon. 16-6 Programming Copying and Renaming Copying and Renaming a Program Programs To copy all conunand program, Program follow steps 1 through 5 for Creating a New (page 16-4), and then follow these steps. lines fronl one progranl into a new 1. Press [_ [RCL]. Rcl is displayed on the bottom line of the prograln editor in the new program (Chapter 1). 2. Press _ [] to display- the PRGM 3. Select a nalne fronl the menu. tile bottom line of the program EXEC menu. prgmname editor. is pasted to 4. Press [ENt_. All colnnland lines fl'om the selected program are copied into the new program. Copying programs applications. h_s at least • You can create a template that you use Kequently. • You can rename a new program. a program two convenient for groups by copying of instl_ctions its contents into Note: You also can copy all the command lines from one existing program to another existing program using RCU Scrolling the PRGM EXEC and PRGM EDIT Menus The TI-S3 sorts PRGM EXEC and PRGM EDIT menu automatically into alphanumerical order. Each labels the first 10 itenls using 1 through 9, then items menu 0. only To jump to the first prograln name that begins with a particular alpha character or O, press @ [letter from A to Z or 0]. Tip: From the top of either the PRGM EXEC or PRGM EDIT menu, press [] to move to the bottom. From the bottom, press [] to move to the top. To scroll the cursor down the menu seven items, press @ []. To scroll the cursor up the menu seven items, press @ []. Programming 16-7 PRGM CTL (Control) PRGM CTL Menu Instructions To display the PRGM CTL (program control) [_ from the prograln editor only. CTL I/0 i: If 2: Then 3: Else EXEC 4: For( 5: While 6: 7: 8: 9: O: A: B: C: menu, press Repeat End Pause Lbl Geto IS>( DS<( Menu( D: prgm E: Return F: Stop G: DelVar H: GraphStyle( Creates a conditional test. Executes conlnlands when If is true, Executes eonnnands when If is false, Creates an incrementing loop. Creates a conditional loop. Creates a conditional loop. Signifies the end of a block. Pauses program execution, Defnes a label. Goes to a label. Increments and skips if greater than. Decrements and skips if less than. Defines menu items and branches. Executes a program as a subroutine. Returns from a subroutine. Stops execution. Deletes a wuiable from within program. Designates the graph style to be drawn. These menu items direct the flow of an executing program. They make it eaksy to repeat or skip a group of commands during program execution. When you select an item from the menu, the name is pasted to the cursor location on a conlnland line in the program. To return to the program press @. Controlling Program Flow OF If N=I and M:l:Goto Programming selecting an item, Program control instructions tell the TI-83 which command to execute next in a program, If, While, and Repeat check a defined condition to determine which command to execute next, Conditions frequently use relational or Boolean tests (Chapter 2), as in: If A<7:A+I->A 16-8 editor without Z [ _se If for testing and branching. If condition then the command inunediately following condition is true (nonzero), then the next executed. If instructions can be nested. is false (zero), If is skipped. If command is :If condition :command :command (if true) Program PROGRAM: : O÷R _ :Lbl COUNT output PrgmCOUNT IR IS ::OisP A+l÷A._ M T_-,, i_ _,,, : If' R_2 I: Stop 1:Goto If-Then R IS Z Then following an If executes condition is true (nonzero). group of commands. a group of commands if End identifies the end of the :If condition :Then :command :command :End (if true) (if true) :co_and Program PROGRRM:TEST :I÷X:IO÷Y :I_ X<IO :Then :2X+3÷X :2Y-3÷Y l:End I:OisP X,Y output PPgmTEST Programming O0_! 16-9 If-Then-Else Else following If-Then executes condition is false (zero). group of commands. a group End identifies of commands if the end of the :If condition :Then :command :command :Else (if true) (if true) :command :command :End :command (if false) (if false) Pro_lram PROGRRM" TESTELSE :InPut "X=",X : Ii_ X<B : Then : Xz÷y : Else : X÷Y : End : OisP For( output _:_TESTELSE {5 5} X=-5 Done {-5 25} Done {X,Y} For( loops and inc[_ments. It increments begin to e_d by increme_t, increment is 1) and can be negative (end<begin). or lnininmnl value not to be exceeded. end of the loop. For( loops variable fron] is optional (default end is a nlmKinlunl End identifies the can be nested. :For(variable,begin,end[,increme_t]) :command (while end not exceeded) :command (while e_d not exceeded) :End :command Pro_lram PROGRRM: SQURRE : For(R, 0, 8, 2) output ::EDi, Ip RZ PPgf_SQURRE 16-10 Programming Oon40e643616 While While performs a group of commands while condition is true. condition is frequently a relational test (Chapter 2). condition is tested when While is encountered. If condition is true (nonzero), the program executes a group of commands, End signifies the end of the group, When condition is false (zero), the p_)gram executes each command following End. While instructions can be nested. :While condition :command (while condition :command (while condition :End :command Program PROGRAM: : O÷l :While : J+l÷J : I+l÷I : End I:DisP Repeat is true) is true) Output LOOP _,.,_ ,_9mLOOP J= Done6 ,J Repeat repeats a group of commands until condition is true (nonzero). It is similar to While, but condition is tested when End is encountered; therefore, the group of commands is always executed at least once. Repeat instructions can be nested. :Repeat condition :command (until :command (until :End :command condition condition Program PROGRRM: RLOOP I:0÷I :O÷J > :Repeat I_6 :J+l÷J : I+l÷I :End F DisP .J= , J is true) is true) Output ,_r-cJrqRLOOP Programming Done6 16-11 End End identifies the end of a group of commands. You nmst include an End instruction at the end of each For(, While, or Repeat k)op. Also, you nmst paste an End instruction at the end of each If-Then group and each If-Then-Else group. Pause Pause suspends execution of the program so that you can see answers or graphs, During the pause, the pause indicator is on in the top-right corner. Press _ to resume execution. Pause without a value temporarily If the DispGraph or Disp instruction the appropriate screen is displayed. pauses the pr()gram. has been executed, Pause with value displays value on the current screen, value can be scrolled. home Pause [value] Program PROGRRM: PRUSE : 10+X : "XZ+2"÷y1 :DisP "X=", X : Pause : DisPGraF-h I: Pause l:OisP 16-12 Programming output PPgF_PRUSE X= 10 Lbl, Goto Lbl (label) and Goto (go to) are used together for branching. Lbl specifies the label for a conlnland, two characters (A through Z, 0 through label can be one or 99, or 0). Lbl label Goto causes encountered. the program to branch to label when Goto is Goto label output Pro_lram PROGRRM: CUBE : Lbl 99 : Input R : If' R._100 : Stop :Dise R -_ IPegmCUBE ?31105 I:Pause I:Goto IS>( Done 27 8 99 IS>( (inc_ment and skip) adds 1 to variable. If the answer ]s > value (which can be an expression), the next command is skipped; if the answer is _<value, the next command is executed, variable cannot be a system variable, :lS>(variable,value) :command (if answer :command (if answer _<value) > value) Program Output I IPROGRRM::::: DispDi-_pT÷RIs>(R;'6)NOT> ISKIP6 > 6" _r_mISKIP Done Note: IS>( is not a looping instruction. Programming 16-13 DS<( (decrement DS<( and skip) subtracts 1 fronl variable. If the answer is < value (which can be an expression), the next command is skipped; if the answer is _>value, the next command is executed, variable cannot be a system variable, :DS<(variable,wdue) :command (if answer :command (if answer _>value) < value) Pro_lram :DS\ (A, 6> :DisP "> DSKIP 6" PROGRRM:: I+R :DisP 'NOT > 6 I Note: DS<( is not a looping instruction. Menu( sets Menu( up branching within If Menu( is a program. encountered during prograln execution, the menu screen displayed with the specified menu items, the pause indicator is on, and execution pauses until you select a menu item. is The lnenu title is enclosed in quotation lnarks ( " ). Up to seven pairs of menu items follow. Each pair conlprises a text item (also enclosed in quotation marks) to be displayed as a menu selection, and a label item to which to branch if you select the corresponding menu selection. Menu("title","te:ct l",label l ,"te:ct2",label2 .... ) Program :Menu( TOSS DICE ","FRIR OICE",R, PROGRR_,!: TOSSDICE ;WEIGHTED DICE , The progranl above pauses until you select select 2, for example, the menu disappears program continues execution at Lbl B. 16-14 Programming DICE i 1 or 2. If you and the prgm [ _se prgm to execute other programs as subroutines (page 16-22). When you select prgm, it is pasted to the cut, or location. Enter characters to spell a program name. Using prgm is equivalent to selecting existing programs fronl the PRGM EXEC menu; however, it allows you to enter the name of a program that you have not yet created. prgmname Note: You cannot directly enter the subroutine name when using RCL. You must paste the name from the PRGM EXEC menu (page I6-7). Return Return quits the subroutine and returns execution to the calling program (page 16-22), even if encountered within nested loops. Any loops are ended. An implied Return exists at the end of any- program that is called as a subroutine. Within the main program, Return stops execution and retut_ls to the honle screen. Stop Stop stops execution of a program and returns to the home screen. Stop is optional at the end of a program. DelVar DelVar deletes fronl nlenlory the contents of variable. DelVar variable PROGRRH: DELMRTR : DelUar. [R]I GraphStyle( I GraphStyle( designates the style of the graph to be drawn. fanction# is the number of the Y= function name in the current graphing mode. graphstyle is a number from 1 to 7 that corresponds to the graph style, as shown below. 1 2 3 4 = = = = ". "i ![ [k (line) (thick) (shade (shade above) below) 5 = '_.)(path) 6 = .'.'.'(animate) 7 = ". (dot) GraphStyle{fanction#,graphstyle) For example, GraphStyle(1,5) in Func mode sets the graph style for Y1 to '_.)(path; 5). Not all graph styles are available in all graphing modes. For a detailed description of each graph style, see the Graph Styles table in Chapter 3, Programming 16-15 PRGM I/0 (Input/Output) PRGM I/0 Menu To display press _ CTL I10 i: the [] Instructions PRGM I/0 (progranl fronl within menu, editor only. EXEC Enters Input a value or uses Prompts 3: Disp Displays text, value, or the home screen. Displays the current graph. Displays the current table. Displays text at a specified position. Cheeks the keyboard for a keystroke. Clears the display. Clears the current table. Gets a wtriable froln another TI-83. Gets a varialfle from CBL 2/CBL or CBR. Sends a variable to CBL 2JCBL or CBR. 5: DispTable 6:Output( 7: getKey 8:C1 rHome 9: ClrTable O: GetCalc( A: Get( B: Send( for enhT the cursor. 2: Prompt 4: DispGraph These instructions control program during execution. and displayTo return press Displaying a Graph with Input input/output) tile prograln answers input They during to the program values. to and output fronl a allow you to enter values program editor of variable execution. without selecting an item, @. Input without a variable displays the current graph. You can move the free-moving cursor, which updates X and Y (and R and 0 for PolarGC format). The pause indicator is on. Press [gNYgmto resulne prograln execution. Input Program PROGRRM: GIHPUT : FnOff :ZOeoimal I:Input : Dise Output Pr, gmG IHPUTI X, V I1=_:,6 [. ?=:!..5 PrgmG IHPUT 2.6 1.5 Done 16-16 Programming Storing Variable with a Value Input Input with variable displays a ? (question nlark) prompt dm'ing execution, variable may be a real number, complex number, list, matrix, string, or Y= function. Dm'ing program execution, enter a wdue, which can be an expression, and then press [_T_]. The value is evaluated and stored to variable, and the program resumes execution. Input [variable] You can display- text or the contents of Strn (a string variable) of up to 16 ehm'acters as a prompt. During program execution, enter a value after the prompt and then press [_T_]. The value is stored to variable, and the progranl resunlos execution. Input ["text",variable] Input [Strn,variable] Program PROGRRM: HINPUT output Pr.gFiH INPUT ?2 -'InPut "YI=",YI ?{1,2,3} -'InPut DRTR :OisP :OisP "DRTR=", Vt ="2X+2" VI(R) YI(LI) -"Oi_P '_t (LORTR) DRTR={4, 5, 6} 6 {4 6 8} {10 12 14} Oone Note: When a program prompts for input of lists and Yn functions during execution, you must include the braces ( { } ) around the list elements and quotation marks ( " ) around the expressions. Programming 16-17 During Prompt program execution, Prompt displays each variable, one at a time, followed by =?. At each prompt, enter a value or expression for each variable, and then pl_ss [ggT_. The values are stored, and the prograln resulnes execution. Prompt variableA [,variableB,...,variable n] Program PROGRAM:WINDOW :PronPt XMin :Pror_Pt XMax :ProMPt Ymin output :PromPt V_ax=?3 XMin=?-le X_ax=?lO _Min=?-3 PrgMWINOOW YMax Done Note: Y= functions are not valid with Prompt. Displaying the Home Screen Disp (display) without a value displays the home screen. To _ew the home screen during program execution, follow the Disp instruction with a Pause instruction. Disp Displaying Values and Messages Disp with one or more values displays Disp [valueA,valueB,valueC,...,value is a variable, the value of each. n] • If value • If value is an expression, it is evaluated displayed on tile right side of the next • If value is text within quotation marks, it is displayed the left side of the current display- line. -) is not valid text. Program :OisP "THE PROGRRM:R R IS ,x/2 RNSWE If Pause is encountered temporarily so you can execution, press [_T_]. the current value is displayed. and the result line. is on as Output PPgNA THE ANSWER IS 1.578796327 Done after Disp, the program halts examine the screen, To resume Note: If a matrix or list is too large to display in its entirety, ellipses (...) are displayed in the last column, but the matrix or list cannot be scrolled. To scroll, use Pause w/ue (page I6-I2). 16-18 Programming DispGraph DispGraph (display- graph) displays the current graph. Pause is encountered after DispGraph, the program temporarily so you can examine the screen. Press resume execution, If halts _ to DispTable DispTable (display table) displays program halts temporarily so you Press _ to resume execution, Output( Output( displays text or value on the current home screen beginning at row (1 through 8) and column (1 through 16), ove_vriting any existing characters. Tip: tile current table, The can examine the screen. You may want to precede Output( with ClrHome (page 16-20). Expressions are evaluated and values are displayed according to the current mode settings. Matrices are displayed in entw format and wrap to the next line. -> is not valid as text. Output(fvw,column,"text") Output(row,column,v_ue) Program • I PROGRRM.OJTPUT :3+5+B :CIrHoMe :OutPut(5,4,"RHS WER:" :Out.eut.(5,12,B) For Output( on a Horiz split screen, the nlaxinlunl row is 4. value for Programming 16-19 getKey returns a number corresponding to the last key pressed, according to the key code diagraln below. If no key- has been pressed, getKey t_turns O. Use getKey inside loops to transfer control, for example, when creating video getKey gaines. Program PROGRRM:GETKEV :While 1 :getKeu+K :While K=O :getKe_eK :End :OisP K :I¢ K=105 Output PPg_GETKEV Note: _, [_, [_, and were pressed during program execution. :Stop :End Note: You can press [_ program (page 16-5). TI-83 Key Code Diagram at any time during execution to break the C15D12_22! IZD C_ IZ] Ei_ --E521- ClrHome (clear home screen) during program execution. ClrHome, CIrTable 1 Done clears the home screen ClrTable (clear table) clears the values in the table during program execution. 16-20 Programming GetCalc( GetCalc( gets the contents of variable on another TI-83 and stores it to variable on the receiving TI-83. variable can be a real or complex number, list element, list name, matrix element, matrix name, string, Y= variable, graph database, or picture. GetCalc(variable) Note: GetCalc( Get(, Send( does not work between TI-82s and TF83s. Get( gets data fronl the Calculator-Based Laboratory TM (CBL 2 TM, CBL TM) System or Calculator-Based Ranger TM (CBR TM) and stores it to variable on the receiving TI-83. variable can be a real number, list element, list name, nmtrix element, nmtrix name, string, Y= variable, graph database, or picture. Get(variable) Note: If you transfer a program that references the Get( command to the TF83 from a TI-82, the TF83 will interpret it as the Get( described above. Use GetCalc( to get data from another TI-83. Send( sends the contents of variable to the CBL 2/CBL or CBR. You cannot use it to send to another TI-83. variable can be a real nmnber, list element, list name, matrix element, matrix name, string, Y= variable, graph or picture, variable can be a list of elements. database, Send(variable) PROGRRM:GETSOUND :Send({3,.000_5, 99,1,0,0,0,0,1}) :Get(L1) :Get(Lz) Note: This program and time in seconds CBL 2/CBL. gets sound data from Note: You can access Get(, Send(, and GetCalc( from the CATALOG to execute them from the home screen (Chapter 15). Programming 16-21 Calling Other Programs Calling a Program from Another Program as Subroutines On the TI-83, any stored program can be called fronl another program as a subroutine, Enter the name of the program to use as a subroutine on a line by itself, You can enter a program name on a conunand line in either of two ways, • Press NggM][] to display the PRGM EXEC menu and select the name of the program (page 16-7). prgmname is pasted to the cm_'ent cm_sor location on a conullalld line. • Select prgm from the PRGM CTL menu, and then enter the program name (page 16-15), prgmnome When prgmname is encountered during execution, the next command that the program executes is the first command in the second program. It returns to the subsequent conunand in the first program when it encounters either Return or the implied Return at the end of the second program. Pro_lram PROGRAM: VOLCYL :Input "D=",D : InPut. "H=",H :PPgrIRRERCIR :RmH÷V :DisP V Subroutine Output H=5 62. 83185307 Done I t PROGRRM:RRERCIR:Return:n.RZ÷A:D/2÷R I Notes Calling about Programs Variables are global. label used with Goto and kbl is local to the program where it is located, label in one program is not recognized by another program. You cannot use 6oto to branch to a label in another program. Return exits a subroutine and returns to the calling program, even if it is encountered within nested loops. 16-22 Programming 7 Contents Applications Comparing Test Results Using Box Plots ................ Graphing Pieeewise Functions ........................... Graphing Inequalities .................................... Sohdng a System of Nonlinear Equations ................ Using a Program to Create the Sierpinski Triangle ....... Graphing Cobweb Attractors ............................ Using a Program to Guess the Coefficients ............... Graphing the Unit Circle and Trigonometric (;ma_es ...... Finding the Area between Curves ........................ Using Parametric Equations: Ferris Wheel Problem ...... Demonstrating the Fundamental Theorem of ('aleulus... ('omputing Areas of Regular N-Sided Polygons .......... Computing and Graphing Mortgage Payments ........... TEXAS 17-2 17-4 17-5 17-6 17-7 17-8 17-9 17-10 17-11 17-12 17-14 17-16 17-18 TI-83 INSTRUMENTS J STATPLOT TBLSET FORMAT CALC TABLE Applications 17-1 Comparing Problem Test Results An experiment Using Box Plots found a significant difference between boys and gifts pertaining to their ability to identify objects held in their left hands, which are controlled by the right side of their brains, versus their right hands, which are controlled by the left side of their brains, The TI Graphics team conducted a similm" test for adult men and women. The test involved 30 slnall objects, which pm'ticipants were not allowed to see. First, they held 15 of the objects one by one in their left hands and guessed what they were. Then they held the other 15 objects one by one in their right hands and guessed what they were. Use box plots to compare _isually the eotTect-guess data from this table. Correct Women Le_ Women 8 9 12 11 10 8 12 7 9 11 Procedure Guesses Men Men Right Left Right 4 1 8 12 11 !1 13 !2 !1 12 7 8 7 5 7 8 11 4 !0 14 13 5 12 6 12 12 7 11 12 8 12 11 9 9 1, Press _ 5 to select 5:SetUpEditor, Enter list names WLEFT, WRGHT, MLEFT, and MRGHT, separated by conlnlas, Press [_. The stat list editor now contains only these four lists. 2. Press [_Y] 1 to select 1:Edit. 3. ]_nter into WLEFT the number of correct guesses each woman made using her left hand (Women Left). Press [] to move to WRGHT and enter the number of correct guesses Right). each woman made using her right hand 4. Likewise, enter each lnan's correct guesses (Men Left) and MRGHT (Men Right). (Women in MLEFT 5. Press [_ [STAT PLOT], Select 1:Plot1. Turn on plot 1; define it as a modified box plot 4>- that uses WLEFT. Move the eta'sot to the top line and select Plot2. Turn on plot 2; define it as a modified box plot that uses WRGHT, 17-2 Applications 6.Press @.Turnoffallfunctions, 7.Press _. SetXscl=landYscl=0. Press _ 9to select 9:ZoomStat. Thisadjusts theviewing windowand displays theboxplotsforthewomen's results. 8. Press _. kd=9.5 Use [] and [] to exalnine minX, Ol, Med, O3, right hand? With which hand accurate guessers, according maxX and for each plot. Notice the outlier to the women's hand data. What is the median ff)r the left hand? were the women to the box plots? rightFor the more 9. Examine the men's results. Redefine plot 1 to use MLEFT, redefine plot 2 to use MRGHT. Press _. _" d=7.5 Men's right-hand data " " Press [] and [] to examine minX, Q1, Med, Q3, and maxX for each plot. What difference do you see between the plots? 10.Compare the left-hand results. Redefine plot 1 to use WLEFT, redefine plot 2 to use MLEFT, and then press to examine minX, Q1, Med, Q3, and maxX for each plot. Who were the better left-hand guesse_\% men or women? 11. Company the right-hand results. Define plot 1 t_) use WRGHT, define plot 2 to use MRGHT, zu_d then press to examine minX, OI, Med, O3, and maxX for each plot. Who were the better right-herod guesse_? In the original experiment boys did not guess as well with right hands, while girls guessed equally well with either hand. This is not what our box plots show for adults. Do you think that this is because adults have learned to adapt or because our sample was not large enough? Applications 17-3 Graphing Piecewise Problem The Functions fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50; plus 5 for each kph from 46 to 55 kph; plus 10 for each kph froln 56 to 65 kph; plus 20 for each kph from 66 kph and above. Graph the piecewise function that describes the cost of the ticket. The Procedure fine (Y) as a function of kilometers per horn" (X) is: Y=0 0<X_<45 Y= 50 + 5 (X- 45) Y= 50 + 5 *10 +10 (X - 55) Y= 50 + 5. 10 + 10. 10 + 20 (X- 45 < X_< 55 55<X_<65 65 < X 1, Press Noel. Select 65) Func and the default settings. 2. Press @. Tm'n off all functions and stat plots. Enter Y= function to describe the fine. Use the TEST menu operations to define the pieeewise graph style for Y1 to ". (dot). PloLt F'lol:2 function. the Set the PI<,I:_: '..Y1 B(50+5(X-45) ) (45<X) (X_<55)+(10 0+10(X-55) ) (5.J< X )(X_<65)+(200+20( X-65) ,,yz= ,,V_= ) (65< X)I Press _ and set Xmin=-2, Xscl=10, Ymin=-5, and Yscl=10. Ignore Xmax and Ymax; they are set by AX and AY in step 4. Press [_ [QUIT] to return to the holne screen. Store 1 to AX, and then store 5 to AY, AX and AY m'e on the VARS Window X/Y secondary menu. AX and AY specify the horizontal and vertical distance between the centers of adjacent nice values Press _ the ticket 17-4 Applications pixels, Integer for tracing, values to plot the function. exceed 250? for AX and AY produce At what speed does Graphing Problem Inequalities Graph the inequality 0.4X;_ - 3X + 5 < 0.2X + 4. Use the TEST menu operations to explore the values of X where the inequMity is true and where it is false, Procedure Press [M0_]. Select Dot, Simul, and the default settings. Setting Dot mode changes 'all graph style icons to '. (dot) in the Y= editor. Press @. Turn off all functions and stat plots. Enter the left side of the inequality as Y4 and the right side as Y5. '..9 _B. 4X^3-3X+5 I"-Y _B. 2X+411 ...Yti= [..Y?= Enter the statement of the inequality as Y6. This function evaluates to 1 if true or 0 if false. '..Y_B. 4X"3-3X+5 '..Y_B; 2X+4 '-.Y_B_<Y_II .5??= 4. Press _ window. 6 to graph the inequality in the standard 5, Press _ [] [] to move to Y6, Then press [] and [] to trace the inequality, observing the value of Y, --' ;' = [ 11=.ti_8;;9;_87 I?=i. Press @. Turn off Y4,Y5,and Y6.Enter equations to graph only the inequality. '..'.?_=, 4X"3-3X+5 ".Y_=. _.X+4 '..9_=_,_<9_ ..YnBYt*9_ Press _. Notice that the values of Y7 and Y8 are zero where the inequality- is false. ?ll=¥fi_?_; ll:':t._Bg._6;_ !Y:0 :I=':L4Bg._fi,_ t=0 Applications 17-5 Solving a System of Nonlinear Problem a graph, Using solve Equations the equation X :_- 2X = 2cos(X). Stated another way-, solve the system of two equations and two unknowns: Y = X:_-2X and Y = 2cos(X), Use ZOOM factors to control the decimal places displayed on the graph. Procedure Press [_, Select the default lnode Turn off 'all functions and stat plots. settings. Press @. Enter the functions. \V_BX_-2X ",'t oB2cos Press _ that two functions (X) I 4 to select 4:ZDecimal, The display shows solutions may exist (points where the two appear to intersect). r 3, Press _ [] 4 to select 4:SetFactors fi'om the ZOOM MEMORY menu. Set XFact=lO and YFact=lO. 4. Press _ 2 to select 2:Zoom In. Use [_, [], [], and [] to move the free-moving cm_or onto the apparent intersection of the functions on the right side of the display. As you move the cursor, notice that the X and Y values have 5, Press [_ intersection, one decimal the X and Y values 6, Press [_ cursor onto the number place. to ZOOln in. Move the cursor over the As you move the cursor, notice that now have two decimal places. to zoom in again. Move the free-lnoving a point exactly- on the intersection, Notice of decimal places. 7. Press K_ [CALC] 6 to select 6:intersect. Press _ select the first cmwe and [_ to select the second cm_'e. To guess, move the trace cursor near the intersection, Press [_. What are the coordinates the intersection point? 8, Press _ 4 to select original graph, 4:ZDecimal to redisplay the 9. Press _. Select 2:Zoom In and repeat steps 4 through 8 to explore the apparent function intersection on the left side of the display. 17-6 Applications to of Using a Program to Create the Sierpinski Triangle Setting up the Program This program creates a drawing of a falnous ffactal, the Sietpinski Triangle, and stores the drawing to a picture. To begin, press #ggM] [] [] 1. Name the prograln SlERPINS, and then press [gg7_l. The program editor is displayed. Program PROGRAM:SIERPI NS :FnOff :ClrDraw : Pl otsOff :AxesOff ::0->Ymi 0->Xmi nn::l->Ymaxl-> Xmax } Set _qewing window. : rand->X: rand->Y : Fo r ( K, 1,3 00 0 ) : rand->N -1-- Beginning of Fo r group. :Then :. 5X->X ::If.SY->Y N<1/3 :End :If I/3<N :Then If/Then group } and N<2/3 7 :. 5(, 5+X)->X :. 5( I+Y)->Y :End If/Then group. :Then :. 5 ( l+X )->X ::If. 5Y->Y 2/3<N :End : Pt On( X, Y ) : End : StorePi If/Then group, } Draw point. End of For group. c 6 Store picture. After you execute the prograln above, you can recall and display the picture with the instruction RecallPic 6. Applications 17-7 Graphing Cobweb Problem Using Attractors Web format, and repelling Procedure you behavior can identify points in sequence graphing, with Press [MO0_. Select Seq and the default Press _ [FORMAT]. Select Web format fonnat settings, attracting nlode settings. and tile default Press @, Clear all functions and tul_ off all stat plots. Enter the sequence that corresponds to the expression Y = K X(1-X), u(n)=Ku(n- 1)(1 - u(n- 1)) u(nMin)=.01 3, Press store [g_ [QUIT] to return 2.9 to K. 4, Press _, nMin=0 nMax=lO PlotStart=l to tim holne Set the window Xmin=0 Xmax=l Xscl=l screen, and then variables, Ymin=-.26 Ymax=l.1 Yscl=l PlotStep=l Press trace _ to display- the graph, and then press [] to the cobweb. This is a cobweb with one attractor, lu=Hu,:_-:i.XI-u(_-I)) Change K to 3.44 and trace with two attractors. the graph to show a cobweb 7, Change K to 3.54 and trace with four attractors, the graph to show a cobweb 6, U=I_u{_-lXl-uCo-1)) 17-8 Applications ..- I Using a Program to Guess the Coefficients Setting Up the Program This program graphs the function A sin(BX) with random integer coefficients between 1 and 10. Try to guess the coefficients and graph your guess at C sin(DX). The program continues until your guess is correct. Program PROGRAM:GUESS :PlotsOff :Func :FnOff :Radian :ClrHome :"Asin(BX)"_Yl :"Csin(DX)"_Y2 Define :GraphStyle(l,l) :GraphStyle(2,5) :FnOff 2 Set line and path styles. :randlnt(l,lO)_A :randlnt(l,lO)_B :O_C:O_D :-2_Xmin :2_Xmax :_/2_Xscl :-lO_Ymin :lO_Ymax :l_Yscl - :DispGraph :Pause :FnOn 2 :Lbl Z = :Prompt Initialize graph coefficients. I Set viewing window. I I C,D :DispGraph :Pause :If C=A :Text(l,l,"C :If C_A :Text(l,l,"C :If D=B :Text(l,50,"D :If D_B :Text(l,50,"D equations, - Display graph, Prompt for guess, Display graph, Display results, IS OK") IS WRONG") IS OK") IS WRONG") :DispGraph :Pause :If C=A and D=B - :Stop :Goto -- Display graph. Quit if guesses are correct, Z Applications 17-9 Graphing the Unit Circle and Trigonometric Curves [ _sing parametric graphing mode, graph the unit circle and tile sine curve to show the relationship between them. Problem Any function that can be plotted in Func mode can be plotted in Par mode by defining the X component as T and the Y component as F(T). Procedure 1. Press [MffffE]. Select Par, Simul, and the default 2. Press _. Tmin=0 Tmax=2_ Tstep=.1 Set the viewing window. Xmin=-2 Xmax=7.4 Xscl=_/2 settings. Ymin=-3 Ymax=3 Yscl=l 3, Press @, Turn off all functions and stat plots. Enter the expressions to define the unit circle centered on (0,0). Not:J, PI0L2 P10t) ",XIT_cos (T) Y1T lisin(T) \XzT fiT YzT lisin(T) 4. Enter the expressions PlotJ. Plot_ to define the sine curve. PloI:3 ",X1T lic.os(T) YIT lisin(T) "..X zTliT Y.-Tlisin(T) 5. Press _. As the graph is plotting, you may press [ggT_ to pause and [ggT_ again to resulne graphing as you watch the sine function "unwrap" from the unit circle. :{IT=C.,:,;(T) == Y1T=_irff.T) = 2/ Note: You can generalize the unwrapping. Replace sin(T) in Y2Twith anyother trig function to unwrapthatfunction. 17-10 Applications Finding the Area between Problem Find the area of the region bounded fix) g(x) x Procedure Curves 1. Press by = 300x/(x 2 + 625) = 3cos(. ix) = 75 [MffffE].Select 2. Press _. Xmin=0 Xmax=100 Xscl=10 the default Set the viewing Ymin=-5 Ymax=10 Yscl=l Xres=l 3. Press @. Turn off all functions upper and lower functions. Y1=a00x/(x2+625) Y2=3COS(.1X) lnode settings. window. and stat plots. Enter the 4. Press [g_] [CALC]5 to select 5:Intersect. The graph is displayed. Select a first cutwe, second cut,'e, and guess for the intersection toward the left side of the display. The solution is displayed, and the value of X at the intersection, which is the lower limit of the integral, is stored in Ans and X. Press _ [QUIT] to go to the home screen. Press [_ [DRAW]7 and use Shade( to see the area graphically. Shade(Y2,Y1,Ans,75) 6, Press [2_] expression region, to return to tile honle screen. Enter tile to evaluate the integral for the shaded [QUIT] fnlnt(Y1-Y2,X,Ans,75) The area is 325.839962. Applications 17-11 Using Parametric Problem Equations: [ _sing two Ferris Wheel Problem pai_\q of parametric two objects plane. in motion equations, are closest to each determine other when in the Salne A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate (s) of one revolution ever T 12 seconds. The paralnetric equations below describe the location of a fen'is wheel passenger at time T, where (x is the angle of rotation, (0,0) is the bottom center of the fen'is wheel, and (10,10) is the passenger's location at the rightmost point, when T=0. X(T) Y(T) = r cos (x = r + r sin (x where (x = 2xTs and r = d/2 A person standing on the ground throws a ball to the ferds wheel passenger. The thrower's ann is at the sanle height as the bottoln of the ferds wheel, but 25 meters (b) to the right of the fen'is wheel's lowest point (25,0). The person throws the ball with velocity (v0) of 22 meters pet" second at an angle (0) of 66 ° froln the horizontal. The parametric equations below describe the location of the ball at tinle T. X(T) Y(T) 9,_ Procedure = b - Tv0 cos0 = Tv0 sin0 - (g/2) nl/see T_ where g = 2 1, Press [MO0_. Select Simul (sinmltaneous) nlotion over tinle. Press _. Tmin=0 Tmax=12 Par, Simul, and the default settings. mode sinmlates the two objects Set the viewing Xmin=-13 Xmax=34 Tstep=.l Xscl=lO in window. Ymin=0 Ymax=31 Yscl=lO Press @. Turn off all functions and stat plots. Enter tile expressions to define tile path of the ferris wheel and tile )ath of the ball. Set tile graph style for X2T to 4j (path). i PloL:L Plot_: Plot_: ",X1T B1Ocos(xT/6) YITBlO+lOsin(_T t6) *)XzT B25-22Toos(6 5° ) ViT B22Tsin(66 ° ) -(9.8/2)TZ Tip: Try setting the graph styles to ",.'_XlT and 0 X2T, which simulates chair on the ferris wheel and the bal! flying through the air when you press _. 17-12 Applications a 4. Press [_ to graph the equations. they are plotted. Notice that the ball wheel passenger appear to be closest cross in the top-right quadrant of the 5, Press [_. concentrate Tmin=l Tmax=3 Tstep=.03 Watch closely as and the ferris where the paths ferris wheel, Change the _iewing window to on this portion of the graph. Xmin=0 Ymin=10 Xmax=23.5 Ymax=25.5 Xscl=10 Yscl=10 6. Press _. After the graph is plotted, press [] to nlove neat" tile point on the ferris wheel where the paths cross, Notice the values of X, Y, and T, IIT=t0_.O_;(1T_ YtT=IO÷10;;_ 7, Press [] to nlove to the path of the ball. Notice the values of X and Y (T is unchanged). Notice where the cursor is located. This is the position of the ball when the fetTis wheel passenger passes the inter\section. Did the ball or the passenger reach the intersection first? You can use _ to, in effect, take snapshots in tilne and explore the relative behavior of two objects in motion, Applications 17-13 Demonstrating Problem 1 the Fundamental of Calculus Using the functions fnlnt( and nDeriv( fronl the MATH menu to graph functions defined by integrals and derivatives demonstrates graphically that: fx F(x)= Procedure Theorem 1 1 1/tdt=ln(x),x>0 Dx Ifx 1/t dt 1= 1/x 1. Press and that 1 1_. Select 2. Press _. Xmin=.01 Xmax=10 Xscl=l tile default Set the viewing Ymin=-l.5 Ymax=2.5 Yscl=l settings. window. Xres=3 Press @, Turn off 'allfunctions and stat plots. Enter tile numerical integral of 1/T from 1 to X and the function ln(X). Set the graph style for Y1 to "..(line) and Y2 to .4:,(path). Plot:l. Pl¢,t2 ",Yt Bi'n InL( 1,X) _¢2Bln(g) 4. P1ot_ l/T, T, Press _. Press [], [], [], and [] to eolnpare values of Y1 and Y2, the 5. Press @. Turn off Y1 and Y2, and then enter the numerical derivative of the integral of 1/X and the function 1/X. Set the graph style for Y3 to ', (line) and Y4 to _. (thick), Ploti p1,,:,l:2 Plot_: :,Y:, _oior_1_T, T, _Y2'=In(g) _BnOeri_,(Y1 _,YuBI/X , X, Press _. Again, use the cursor keys to compare values of the two graphed functions, Y3 and Y4. 17-14 Applications the Problem 2 Explore the functions X Y:f-2 Procedure 2 defined by X t2dt' f0 X t2dt' and f2 t2dt Press @, Turn off all functions to define these three functions the function in Ys. and stat plots. sinmltaneously. Use a list Store _'_=nDerib=(Yt"°Yz=lr_(x)l'x)Pl°t:L Plol:Z F'loL_. _ _ ,,Y_B?nlnL(T z, '_Y_=I/X i-::,o,2>,x) 2, Press _ $ to select 3, Press _. only shifted Press @, T, ( $:ZStandard. Notice that the functions vertically by a constant. Enter the numerical \Y_=nDeriv(Y1, X) "*Y_=I/X "..Y_B_nIn÷.(TZ, appear derivative identical, of Y5 in Y6, X, T, ( -2,0,2>,X) \YeBnOer iv(Y_, X, x) Press _. Notice that although the three graphs defined by Y5 are different, derivative, they share tile same N="t.9£_Bi!_?i¢).6_,fiBt?9 Applications 17-15 Computing Problem Areas Use of Regular the equation N-Sided solver to store regulm" N-sided polygon, and then given the other variables. Explore case is the area of a circle, _r 2. Polygons a fornmla Consider the fonnula A = NB 2 sin(_/N) m'ea of a regulm' polygon with N sides B distance from the center to a vertex. N = 4 sides Procedure ff)r the m'ea of a solve for each vm'iable, the fact that the limiting cos(_/N) for the of equal length and N = 8 sides N = 12 sides 1, Press [_ 0 to select 0:Solver froln the MATH menu, Either the equation editor or the interactive solver editor is displayed. If the interactive solver editor is displayed, press [] to display the equation editor, 2, Enter the fonnula then press [_. as 0=A-NB2sin(_ The interactive / N)cos(_ / N), and solver editor is displayed. R_NBZsin(_/N).,,=O bound={ 3, Enter -1 E99, 1... N=4 and B=6 to find the area a distance (B) from center to vertex (A) of a square with of 6 centimeters, 4, Press [] [] to nlove the cursor onto A, and then press @ [SOLVE], The solution for A is displayed on the interactive solver editor. :l-NBZsin(_/N)...=el : 2.00o000000 I B=6 bound={ -1 E99, 1... le_t-rt=e 5. Now solve for B for a given area with vm'ious number of sides. Enter A=200 and N=6. To find the distance B, lnove the cursor onto B, and then press @ [SOLVE]. 6, Enter N=8, To find the distance B, nlove the cursor onto B, and then press @ [SOLVE]. Find B for N=9, and then for N=10. 17-16 Applications FindtheareagivenB=6, 10000. Compare with radius your 6), which and N=10, 100, 150, 1000, and results with =62 (the area of a circle is approximately 113.097. 7. Enter B=6. To find the area A, move and then press @ [SOLVE]. Find N=100, then N=160, then N=1000, and Notice that as N gets large, the area the cursor onto A, A for N=10, then finally N=10000. A approaches _B 2. Now graph the equation to see visually how the area changes as the number of sides gets lm'ge. 8, Press NgffE].Select the default lnode settings, 9. Press _. Xmin=O Xmax=200 Xscl=lO Set the viewing window. Ymin=O Ymax=150 YscI=IO Xres=l 10.Press @. Turn off all functions and stat plots. Enter the equation for the m'ea. I Jse X in place of N Set the graph styles as shown. Plot]. F'10t2 F'10t._ xViBXBZsin<_/X)c os(_/X) -W._BnB z ,.'-,as= xY.1= ,,V_:= ,&'6= 11. Press _. After the graph is plotted, press I O0[gNgggl to trace to X=100. Press 150 [ggTgm.Press 188 [ggTg_. Notice that _LsX increases, the value of Y converges to =62, which is approximately 113.097. Y2=_B2 (the area of the circle) is a horizontal asymptote to Y1. The area of an N-sided regular polygon, with r as the distance fl'om the center to a vertex, approaches the area of a circle with radius r (_r 2) as N gets large. ;' 1:1-,'B;a_;ir= r..'n"r' N),2.o _;( Tr_'g :E '¢_::Tr£::: 8:tBB 8:tEE _Y=lt3.0762B, _Y:ti3.0973_ Applications • 17-17 Computing Problem and Graphing You at_ a loan Mortgage officer Payments at a mortgage conlpany, and you recently closed on a 30-yem' holne lnortgage at 8 percent interest with monthly payments of 800, The new home owners want to know how nmch will be applied to the interest and how nmch will be applied to the principal when they make the 240th payment 20 years from now. Procedure 1, Press [_ and set the fixed-decimal lnode to 2 decimal places. Set the other mode settings to the defaults. 2. Press [_ [FINANCE] these values. 1 to display" the TVM Solver. Enter N=360.00 I_=8.00 PV=0.00 PMT=800.00 FV=0.00 P/V=I2.00 C/V=12,00 PMT:[_=[II_ BEGIN Note: Enter a positive number (800) to show PMT as a cash inflow. Payment values will be displayed as positive numbers on the graph. Enter 0 for FV, since the future value of a loan is 0 once it is paid in ful!. Enter PMT: END, since payment is due at the end of a period. 3, Move the cursor onto the PV= prompt, and then press @ [80LYE], The present value, or lnortgage amount, of the house is displayed at the PV= prompt, N=360.00 I%=8.00 PV=-IO9026,B0 PMT=B00.00 FV=0.00 P/V=12.00 C/Y=12.00 PMT:LqIL_ BEGIN 17-18 Applications Nowcompare thegraphoftheamount ofinterest withthe graphoftheamount ofprincipal foreachpayment. 4, Press [NffffE].Set Par and Simul. 5, Press these @, Turn equations off all functions and stat plots. Enter and set the graph styles as shown. Plot1 Plol:_ Plot_: ",XIT BT Vi T BFPr'n(T, T) _XzT BT 'Y'zT B_- Int.< T, T) ".X_T BT V:_T BVIT +VZT Note: ZPrn( and ZInt( are located on the FINANCE 6, Press _. Tmin=l Tmax=360 Tstep=12 Set these window Xmin:0 Xmax=360 Xscl=10 CALC menu, variables. Ymin=0 Ymax=1000 Yscl=100 Tip: To increase the graph speed, change Tstep to 24. 7. Press _. After the graph is drawn, press 240 to move the trace cursor to T=240, which is equivalent to 20 years of payments. IIT=T ?tT='_F'r_rKT__ The graph shows that ff)r the 240th payment (X=240), 358.03 of the 800 pay3nent is applied to principal (Y:368.03). Note: The sum of the payments (Y3T=Y1T+Y2T) is always 800. Applications 17-19 8. Press [] tomovethecursorontothefunction for interest defined byX2T andY2T. Enter240. The graph shows that for the 240th payment (X=240), 441.97 of the 800 payment is interest (Y=441 .gT). 9. Press home _ [QUIT] [_ screen. Check [FINANCE] the figures 9 to paste 9:bal( to the from the graph. _ai(239) -66295.33 _nsm(.08/12) -441,97 At which monthly payment will the principal surp_kss the interest allocation? 17-20 Applications allocation 18 Contents Menrn2gq/ement Checking A_ailable MemolTy ............................. Deleting Items from MemmTy ............................ Clearing Entries and List Elements ...................... Resetting the TI-83 ...................................... TEXAS INSTRUMENTS I8-2 I8-3 18-4 18-5 TF83 RRM_ Delete... 3:Clear Entries 4: CIRRI ILists 5: Reset... J STAT PLOT TBLSET FORMAT CALC TABLE Memory Management 18-1 Checking Available MEMORY Menu Memory To display the MEMORY menu, press [_ [MEM]. MEMORY i: Check RAM... Reports memory availability/usage, Displays DELETE FROM menu, Clem's ENTRY (l_kst-entry storage). 2: Delete... 3: Clear Entries 4: ClrAllLists Clears all lists in memo_T. Displays RESET menu (all/defaults). 5: Reset.., Displaying the Check RAM Screen Check RAM displays the Check RAM screen. The top line t_ports the total amount of available nlenlol_y-. The remaining lines report the amount of lnelnot7 each variable type is using. You can check this screen to see whether you need to delete variables from memo_T to nmke room for new data, such as programs. To check 1. Press RAM usage, follow [2_] [MEM] to display these the steps. MEMORY menu. RRM... _:Clear Entries _:ClrRllLists 5:Reset... 2. Select I :Check RAM to display the Check RAM screen. The TI-S3 expresses memory quantities in bytes. MEM FREE 27285 Real 15 ComPlex 8 List 8 Matrix 8 Y-Vats 248 Prgm 14 4Pio 8 GOB String Note: The J_in the left column of the bottom row indicates that you can scroll or page down to view more variable types. 0 0 Note: Real, List, Y-Vars, and Prgm variable types never reset to zero, even after memory is cleared. To leave the Check RAM screen, press either [_ @. Both options display- the home screen. 18-2 Memmw Management [QUIT] or Deleting Items from Deleting an Item Memory To increase any- variable Y= variable, follow these available nlenlol_ by deleting the contents of (real or colnplex nulnber, list, matrix, prograln, picture, graph database, or string), steps. 1. Press [2_] [MEN]to display the MEMORY lnenu. 2. Select 2:Delete to display- the DELETE FROM secondalTynleno. 3. Select the type of data you want to delete, or select 1:All for a list of all variables of 'all types. A screen is displayed listing each variable of the type you selected and the number of bytes each variable is using. For exalnple, is displayed. if you select 4:List, the DELETE:List screen DELETE: Li_t _LI DATA 63 39 4. Press [] and [] to nlove tile selection cursor (_) next to the item you want to delete, and then press _. The variable is deleted fronl nlenlot_y-. You Call delete individual vm'iables one by one froln this screen. To leave ally DELETE: screen without deleting anything, press [_ [QUIT],which displays the home screen. Note: You cannot delete some system variables, such as the lastanswer variable Ans and the statistical variable RegEQ Memory Management 18-3 Clearing Clear Entries Entries and List Elements Clear Entries clears storage area follow these 1, Press [_ of the ENTRY (last entry) the contents (Chapter steps. 1). To cleat" the [MEM] to display the 2, Select 3:Clear Entries to paste home screen. 3. Press [_ IcleaP to clear the Entt'ie_one area, MEMORY menu. the instruction ENTRY storage to the area. I Clear Entries, press To cancel ENTRY storage @, Note: If you select 3:Clear Entries from within a program, the Clear Entries instruction is pasted to the program editor, and the Entry (last entry) is cteared when the program is executed. CIrAIILists CIrAIILists sets to 0 tile To clear all elements 1, Press [_ _ from all lists, [MEM] to display 2, Select 4:ClrAIIkists screen. 3. Press dimension the to paste of each follow list in lllelllOl_yL these steps, MEMORY menu, the instruction to set to 0 the dimension to the home of each list in nlenlory. IC1rA11Lists To cancel CIrAIILists, lionel press @. CIrAIILists does not delete list nanles fronl nlenlol_y-, fronl the LiST NAMES menu, or froln the stat list editor. Note: If you select 4:CIrAIIkists from within a program, the CIrAIILists instruction is pasted to the program editor. The lists are cleared when the program is executed. 18-4 MemolT Management Resetting the TI-83 RESET Secondary Menu The Resetting All Memory Resetting all nlenloFy Oil the TI-83 restores nlenlory to the factor7 settings, It deletes all nonsystem variables and all programs. It resets all system variables to the default settings. seconda[7 RESET lnenu gives you the option of resetting all memory (including default settings) or _setting the default settings while prese_Mng other data stored in lnelno_T, such as programs and Y= functions. Tip: Before you reset all memory, consider restoring sufficient available memory by deleting only selected data (page I8-3). To reset all nlenlory 1. Press [2_] [MEM] to display 2. Select 5:Reset _... on the TI-83, to display the follow these steps. MEMORY menu. the RESET secondary menu. Mer_or-u... 2:: Defau 3, Select tertimT lts... 1 :All Memory to display the RESET MEMORY nlenu. Resetting memoru erases all data and Programs, 4. Read the message below tile RESET MEMORY menu. • To cancel memoL_- reset and retm'n to tile home screen, select 1:No. • To erase fronl lnelnol T all data and progralns, 2:Reset. All factory defaults are restored. Mere cleared is displayed on the home screen. I Mem select cleared Note:When you clearmemory, thecontrast sometimeschanges.If thescreenisfadedorblank,adjustthecontrast (ChapterI). Memory Management 18-5 Resetting Defaults When you reset restored are not defaults on the TI-83, to the factory changed. settings. Stored These are some examples of TI-83 restored by resetting the defaults. defaults are and programs that are Mode settings such as Normal (notation); Func (graphing); Real (numbers); and Full (screen) • Y= functions • Window variable values such Xscl=l; YscI=I; and Xres=l • Stat plots • Format settings such as eoordOn (graphing on); AxesOn; and ExprOn (expression on) • rand seed off value all TI-83 1. Press [g_] [MEM] to display factory 5:Reset Consider Xmax=lO; coordinates to 0 To reset 4. as Xmin=-lO; off defaults, to display 3. Select 2:Defaults tertimT menu. to display the reset follow these steps. MEMORY menu. the RESET secondary menu. the RESET DEFAULTS of resetting defaults. the consequences • To cancel 1:No. • To restore factory default settings, select 2:Reset. Default settings are restored. Defaults set is displayed on the home screen. Defaults Memmw data • 2. Select 18-6 all defaults Management and return set to the home screen, select 19 Contents ci° municati°n Getting Started: Sending Variables ....................... TI-83 kINK ............................................... 19-2 19-3 Selecting Items to Send .................................. Receiving Items .......................................... Transmitting Items ....................................... Transmitting Lists to a TI-82 ............................. Transmitting from a TI-82 to a TI-8:I ..................... 19-4 19-5 19-6 19-8 19-9 Backing Up MemmTy"..................................... TEXAS INSTRUMENTS 19-10 1"1=83 RECEIVE to TI82... J STAT PLOT TBLSET FORMAT CALC T._,B L E Communication Link 19-1 Getting Getting Started: Started Sending is a fast-paced Variables introduction. Read the chapter for details. Create and store a wu'iable and a matrix, and then transfer then] to another TI-83. On the home screen of the sending unit, press 5 [] 5 [email protected] O. Press [gfff_ to store 5.5 to Q. Press[_[[][_[[l 1[]2[_[11[_[[ ] 3 _ 412_ [1 ] [2_ [1 ] _ [NN_ 1. Press [_ to store the lnatrix to [A]. 3. Connect the calculators with the link cable. Push both ends in firmly. 4. On the receiving unit, press [_ [LINK] [] tO display tile RECEIVE menu. Press 1 to select 1:Receive. The message Waiting... is displayed and the busy indicator is on. SEHD [_ IERec.e ive 5, On the sending unit, press [2_] display the SENDmenu. [LINK] to Z,_AI RECEIVE 6, Press 2 to select 2:All-. The All- SELECT screen is displayed. 3:Prgm... 4:List... 5:List.s to TI82... 6:GOB... 7gPic... Press [] until the selection cursor ( _ ) is next to [A] MATRX.Press [ggTEg]. 8. Press [] until the selection cursor is next to Q REAL. Press [_. A square dot next to [A] and O indicates that each is selected to send. TRRNSMIT k_ LIST .L_ LIST [R] MRTRX Window WINOW RclWindouZSTO TblSet TABLE _Q RERL 9. SELECT 7, On the sending unit, press [] to display the TRANSMIT menu. IdII._IIIiIIi [llTransr_it 10. On the sending unit, press 1 to select 1:Transmit and begin transmission. The receiving unit displays the message Receiving....When the items are transmitted, both units display the name and type of each transmitted variable. 19-2 Conununication Link Receiving,.. [ R] MRTRX 'Q REDRLne TI-83 LINK TI-83 Link Capabilities The TI-83 has a port to connect and conlnlunicate Linking Two TI-83s You can transfer all variables and programs to another TI-83 or backup the entire nlenlol'y of a TI-83. The softwm'e that enables this communication is built into TI-83. To transmit from one TI-83 steps on pages 19-6 and 19-7. Linking a TI-82 and a TI-83 You can transfer programs. L1 through fronl a TI-82 that enables to another, to a TI-83 Also, you cal_ tral_sfer L6. The softwaxe from Two with perform follow all variables a TI-83 and lisL_ is built int_) the t_) a TI-83, follow • The only data type you can transmit from a TI-83 to a TI-82 is list data stored in L1 through L6, Use the kINK SEND menu item 5:Lists to TI82 (page 19-8). 2. Insert the other calculator's end of the cable into from the You cannot TI-83, either backup the • 1. Insert a memory TM TM the to a TI-82 this conunm_ication TI-83. To tral_nlit data from a TI-82 steps on pages 19-6 at_d 19-7. Connecting Calculators the Cable with another TI-83, a TI-82, the Calculator-Based Lal)oratory (CBL 2 TM, CBL TM) System, the Calculator-Ba_ed Ranger (CBWM), or a personal conlputer. The unit4o-unit link cable is included with the TI-83. This chapter describes how to comnmnicate with another calculator. a TI-82 the port very end of the cal>le into to a firmly. the other port. Linking to a CBR or the CBL 2/CBL System CBR and the CBL 2/CBL System are optional that connect to a TI-83 with the unit-to-unit With a CBR or a CBL 2/CBL and a TI-83, and analyze real-world data. you can Linking to a PC or Macintosh TI-GRAPH LINK TM is an optional to enable conmmnication with that links conlputer. accessorya personal Communication accessories link cal fie, collect Link a TI-S3 19-3 Selecting Items to Send LINK SEND Menu To display LINK SEND menu, the press [_ [LINK]. SEND RECEIVE i : A11 +.., 2 : A11 -.., 3 : P rgm... 4: 5: 6: 7: 8: 9: 0: A: B: Displays Displays Displays Li st... Lists to T182... GDB... Pi c... Matrix... Real ... Compl ex.., Y Vars... String.,. C: Back Up.,, M1 items 'all items selected. deseleeted. all progranls names. 'all list names, Displays Displays list names L1 through Displays 'all graph databases. Displays M1 picture data types, Displays 'all matrix data types. M1 real vmiables, Displays Displays 'all complex variables. M1 Y= variables. Displays Displays all string variables. Selects all for backup to TI-83. Ls. When you select an item on the LINK SEND menu, the corresponding SELECT screen is displayed. Note: Each SELECT screen, except All+ SELECT, is displayed initially with no data selected. Selecting Items to Send To select items to send on the sending steps. unit, follow these 1. Press [2_] [LINK]to display" the LINK SEND menu. 2. Select the menu item that describes the data type to send. The corresponding SELECT screen is displayed. 3. Press [] and [] to nlove the selection item you want to select or deselect. 4. Press _ nalnes are to select or deselect with a .. cursor (_) to an the iteln. Selected nlarked _ TRRNSMIT EQU • Y_ EQU Xl T EQU Vi T EQU u EQU FWindow WINDW RclWindowZSTO 5, Repeat steps 3 and 4 to select or deselect additional 19-4 Conununication Link items. Receiving LINK RECEIVE Menu Receiving Unit Items To display LINK RECEIVE menu, the SEND RECEIVE 1 : Re e e i v e Sets unit to receive press data _ [LINK] C_. transmission. VClmnyou select 1:Receive from the LINK RECEIVE menu on the receiving unit, the message Waiting... and the busy indicator are displayed. The receiving unit is ready to t_eeive transmitted items. To exit the receive mode without receiving items, press [0N], and then select 1 :Quit from the Error in Xmit menu. To transmit, follow the steps on page 19-6. When transmission is complete, the unit exits the receive mode. You can select 1 :Receive again to receive mot_ items. The receiving unit then displays a list of items received. Press [_ [QUIT] to exit the receive mode. DuplicateName Menu During transmission, if a variable name is duplicated, the Dup[icateName menu is displayed on the receixqng unit. Dupl i cateName i : Rename 2: Overwrite Prompts to rename Ove_wvrites data in Skips transmission Stops transmission 3: Omit 4: Quit receiving variable. receiving variable. of sending variable. at duplicate variable. When you select 1:Rename,the Name=prompt is displayed, and alpha-lock is on. Enter a new variable name, and then press [_. Transinission resuines. When you select 2:Overwrite, the sending unit's data ovet_vrites the existing data stored on the receiving unit. Transmission resumes. When you select 3:Omit, the sending unit does not data in the duplicated variable name. Transmission resumes with the next item. When you select receiving Insufficient Memory in Receiving Unit unit 4:Quit, transmission exits receive stops, send the and the mode. During transmission, if the receiving unit does not have sufficient lnelnol T to receive an item, the Memory Full lnenu is displayed on the receiving unit. • To skip this item for the current transmission, select 1 :Omit. Transmission resumes with the next item. • To cancel the transmission select 2:Quit. and exit receive mode, Communication Link 19-5 Transmitting Items Transmitting Items To transmit selected items after you have selected items to send on the sending unit (page 19-4) and set the receiving unit to receive (page 19-5), follow these steps. unit to display- the TRANSMIT 1. Press [] on tile sending nlenu, I T%Ts I 2. Confirm that Waiting,.. is displayed on the receiving unit, which indicates it is set to receive (page 19-5). 3. Press [g_-gm to select 1:Transmit. The name and type of each item are displayed line by line on the sending unit as the item is queued for transmission, and then on tile receiving unit as each item is accepted. *'79 9t EQoUoneEQU I *V_ VIRotei_,,i ng... EQ_oneEQU I After all selected items have been transmitted, the lnessage Done is displayed on both calculators. Press [] and [] to scroll through the names. Stopping a Transmission To stop a link transmission, press []_]. The Error in Xmit menu is displayed on both units. To leave the error menu, select 1 :Quit. Error Conditions A transnlission error occurs after one or two seconds • A cable is not attached to the sending • A cable is not attached to the receiving if: unit. unit. Note: If the cane is attached, push it in firmly and try again. • The receiving • You • You attempt a data transfer from a TI-83 to a TI-82 with data other than lists L1 through L6 or without using menu item 5:Lists to TI82. attempt unit is not a backup Although a transmission conditions nlay prevent 19-6 Conununication set to receive between transmission. a TI-82 and a TI-Sa. error does not occur, these two successful transmission. • You ttT to use Get( with a calculator CBL 2/CBL or CBR. • You tit to use GetCalc( with a TI-82 instead Link instead of a of a TI-83, Transmitting Items to an Additional TI-83 After sending transmission sending reselect or receiving to additional data, you can repeat the same TI-83 units--from either the unit or the receiving unit--without data to send. The current items having to remain selected. Note: You cannot repeat transmission if you selected All+ or All-. To transmit to an additional 1, Set the TI-83 TI-83, to receive (page follow these steps. 19-5), 2, Do not select or deselect any new items to send. If you select or deselect an item, all selections or deselections from the previous transmission are cleared. 3, Disconnect the link cable to the additional TI-83, 4. Set the additional TI-83 from one TI-S3 to receive 5, Press [7_ [LINK] on the sending LINK SEND menu. (page TI-83 and connect 19-5), to display the 6, Select the menu item that you used for the l_kst transmission. The data from your last transmission still selected. 7, Press 8, [] to display Confirm (page 9, Press that the LINK TRANSMIT the receiving unit it is menu, is set to receive 19-5). [EfiY_ to select 1 :Transmit and begin Communication translnitting. Link 19-7 Transmitting Lists to a TI-82 Transmitting Lists to a TI-82 The only data is list data To transmit lists type stored you can transmit in L1 through to a TI-82 the list data L1, L2, L3, L4, LS, or L6, follow 1, Set the TI-82 to receive fronl a TI-83 to a TI-82 L6. (page that is stored these steps. to TI-83 19-5). 2, Press [_ [LINK] 5 on the sending TI-83 to select 5:Lists to TI82. The SELECT screen is displayed. 3, Select 4. Press each [] to display 5, Confirm that (page 19-5). 6, Press list to transmit. [_ the LINK TRANSMIT the receiving to select unit menu, is set to receive 1 :Transmit and begin transmitting. Note: If dimension > 99 for a T1-83 list that is selected to send, the receiving TI-82 will truncate the list at the ninety-ninth element during transmission. 19-8 Coinnmnication Link Transmitting from a TI-82 to a TI-83 Resolved Differences between the TI-82 and TI-83 but differences between tile two products may affect some transmitted data, This table shows differences for which GenerMly, you can transmit items to a TI-83 fronl the software built into the TI-83 automatically when a TI-83 receives TI-82 data, TI-82 TI-83 nMin PlotStart nStart Un Vn nMin u v UnStart VnStart TblMin u(nMin) v(nMin) TblStart a TI-82, adjusts For example, if you transmit from a TI-82 to a TI-83 a program that contains nStart on a command line and then display" the p_ogram on the receiving TI-83, you will see that nMin has automatically conlnland line, Unresolved Differences between the TI-82 and TI-83 The s(dtware differences described built into replaced nStart the TI-S3 cannot on the resolve some between the TI-82 and TI-83, which are below. You nmst edit the data on the TI-83 you transmit to account for these will misinterpret the data. differences, The TI-83 reinterprets TI-82 prefix functions ()pen parentheses, which may add extraneous to transmitted expressions. after or the TI-83 to include parentheses For example, if you transmit sin X+5 from a TI-82 to a TI-83, the TI-83 reinteq_rets it as sin(×÷5. Without a closing parenthesis after ×, the TI-83 interprets this as sin(×÷5), not the stun of 5 and sin(X). If a TI-82 instruction that the TI-83 cannot translate is transmitted, the ERR:INVALID menu is displayed when the TI-83 attempts to execute the instruction. For example, on the TI-82, the chm'acter group Un-1 is pasted to the cursor location when you press _ [un- 1]. The TI-83 cannot directly translate Un-1 to the TI-83 syntax u(n-1), so the ERR:INVALID menu is displayed. Note: T1-83 implied multiplication rules differ from those of the T1-82. For example, the TI-83 evaluates 1/2X as (1/2)*X, while the TI-82 evaluates 1/2X as 1/(2"X) (Chapter 2). Communication Link 19-9 Backing Up Memory Memory Backup To copy the exact contents of lnelnol_y- in the sending TI-83 to the lnelnory of the receiving TI-83, put the other unit in t_ceive mode. Then, on the receiving unit, select C:Back Up fronl the LINK SEND menu. Warning: receiving receiving C:Back Up ove_wvrites the lnelnol_y- in the unit; all information in the lnelnory of the unit is lost. Note: If you do not want to do a backup, select 2:Quit to return to the LINK SEND menu. • Select 1:Transmit to begin transmission. BItTt-ansr_ 2: Quit Receiving Unit i t As a safety check to prevent accidental loss of nlenlory, the message WARNING - Backup is displayed when the t_cei_lng unit receives notice of a backup. • • To continue with the backup process, The backup transmission begins. To prevent the backup, select 2:Quit. Note:If a transmissionerroris returnedduring unit is reset. Memory Backup Complete (domnmnication a backup, the receiving When the backup is complete, both the sending calculator and receiving calculator display a confirlnation screen. IMEMOR'? BACKUDPonel 19-10 select 1:Continue. Link A Contents Tablesand Reference Information Table of Functions and Instructions ..................... TI-83 Menu Map ......................................... Variables ................................................ Statistics Formulas ...................................... Financial Formulas ...................................... Tables and Reference A-2 A-39 A-49 A-50 A-54 Information A-1 Table of Functions and Instructions Functions return a value, list, or matrix. You can use functions in an expression. Instructions initiate an action. Some functions and instructions have arguments. Optional arguments and accompanying conunas are enclosed in brackets ( [ ] ). For details about an item, including argument descriptions and restrictions, turn to the page listed on the right side of the table. From the CATALOG, you can paste any function or instruction to the home screen or to a conunand line in the program editor. However, some functions and instructions are not wflid on the home screen. The items in this table appear in the same order as they- appear in the CATALOG. f indicates keystrokes that are valid in the program editor only. Some keystrokes display menus that are available only in the program editor. Others paste mode, fommt, or table-set instructions only- when you are in the program editor. Function or Instruction/ Arguments abs(value) abs(complex 'value) Returns the nmgnitude of a complex nmnber or list. ANOVA(listl,list2 [,list3,...,list20]) Ans and CPX 5:abs( [_ [TEST] LOGIC 1 :and Returns 1 if both valueA and valueB are € 0. valueA and valueB ean be real numbers, expressions, or lists. Returns the polar angle of a [_ complex number or list of CPX complex numbers. 4:angle( Performs a one-way analysis of [gg_] variance for comparing the TESTS means of two to 20 F:ANOVA( populations. Returns the last answer. [_ [ANS] angle{value) Tables Key or Keys/ Menu or Screen/Item Returns the absolute value of a [_ real number, expression, list, NUM or matrix. 1 :abs( valueA and valueB A-2 Result Reference Information 2-13 10-10 2-19 2-26 2-19 13-25 1-18 Function or Instruction/ Arguments Result Key or Keys/ Menu or Screen/Item Retm'ns a mahlx, width is matrixB appended to matrixA as new colunms. MATH 7:augment( 10-14 augment(listA,listB) Returns a list, which is listB concatenated to tile end of listA. _ [LIST] OPS 9:augment( 11-15 AxesOff Turns off the graph axes. ; [2_ AxesOn Turns on tile graph axes. ; [2_ [FORMAT] AxesOn 3-14 a+bl Sets tile mode to reetangular complex number mode (a+bi). i I_ a+bi bal(npmt[,roundvalue]) Computes the balance at npmt for an amortization schedule using stored values for PV, I%, and PMT and rounds the computation to roundvalue. [_ [FINANCE] CALC 9:bal( binomcdf(numtrials,p[,x]) Computes a cumulative probability at x for the discrete binomial distribution ,slth tile specified numtrials and probabilityp of success on each trial. [_ [D}STR] DISTR A:binomcdf( binompdf(numtriols,p[,x]) Computes a probability tile discrete binomial at x for [_ [DtSTR] DISTR distribution _ith tile specified nuratrials and probabilityp of success on each trial. 0:binompdf( Computes tile g 2 distribution probability between lower'bound and upped)ound for the specified degrees of freedom dJ2 _ [DISTR] DISTR 7:x2cdf( augment(matrixA,matrixB) [FORMAT] AxesOff x2cdf(low6_pbound, upperbound,dy') Tables and Reference 3-14 1-12 14-9 13-33 13-33 13-31 Information A-3 Function or Instruction/ Arguments z2pdf(x,dj ") Key or Keys/ Menu or Screen/Item Result Computes the probabi]ity density function (pdf) for tile X2 distribution at a specified x value for the specified degrees of freedom df [_ z2-Test(observedmatrix, expeetedmatrix [,drawflag]) Performs a ehi-square test. drmqflag=l draws results; drmqflag=O calculates results. i [_ TESTS C:x2-Test( Circle(X,Y, radius) Draws a circle with (X,Y) and radius. [_ Clear Entries center Clears the contents of the Last EntKy storage area. ClrAIILists Sets to 0 the dimension lists in memoKy'. ClrDraw Clears all drawn elements a graph or dra_lng. from ClrHome Clears Clrkist listnamel [,listuame2, ..., listname n] Sets to 0 the dimension or more listnames. ClrTable Clears table. conj(value) Returns tile complex of a complex number complex numbers. Connected Sets connected plotting mode; resets all Y= editor graph-style settings to "... A-4 Tables and Reference the home of all all values Information screen, of one from the conjugate or list of [DISTR] DISTR 6:z2pdf( 13-31 13-22 [DRAW] DRAW 9:Circle( 8-11 [_dl [MEM] MEMORY 3:Clear Entries 18-4 [_ [MEM] MEMORY 4:ClrAIIkists 18-4 [_ [DRAW] DRAW 1 :ClrDraw 8-4 i [0ggM] IIO 8:Clrl-tome 16-20 [gg_] EDIT 4:ClrList 12-20 i [gggM] I/O 9:ClrTable 16-20 [_TH] CPX 1 :conj( 2-18 i Connected 1-11 Function or Instruction/ Arguments CoordOff Key or Keys/ Menu or Screen/Item Result TLims oft" cursor coordinate value display. i- _ CoordOn Turns on cursor value display. 1 [2_ cos(value) Returns cosine of a real nunlber, expression, list. [FORMAT] CoordOff coordinate CoordOn or arccosine of areal expression, or list. 2-3 Returns number, cosh(value) Returns hyperbolic cosine of a real number, expression, or list. Kffd] [CATALOG] cosh( cosh-l(value) Returns hyperbolic arccosine of a real number, expression, or list. Kffd] [CATALOG] cosh-l( CubicReg [Xlistname, Ylistname_fr_qlist, regequ] Fits a cubic regression model to Xlistname and Ylistname with frequencyfrvqlist, and stores tile regression equation to vegequ. NTAf] CALC 6:CubicReg cumSum(list) Returns a list of the cumulative stuns of tile elements in list, starting _lth the first element. [_ [LIST] OPS 6:cumSum( cumSum(matrix) Returns a matrix cunmlative sums MATH of tile of matrix Kffd] [cos -1] 2-3 15-10 15-10 12-26 elements. returned Each element inthe nmtrlx is a cunmlative SUnl of a matrix cohlnln fi'om to[) to bottom. 0:cumSum( dbd(datel,date2) Calculates the number of days between date1 ram date2 using the actual-day-count method. Kffa] [F,NANCE] CALC D:dbd( value_Dec Displays a real or complex number, expression, list, or matrix in decimal format. MATH 2:_Dec and 3-14 [g6N] cos-l(volue) Tables 3-14 [FORMAT] Reference 11-12 10-15 Information 14-13 2-5 A-5 Function or Instruction/ Arguments Result Key or Keys/ Menu or Screen/Item Degree Sets degree angle mode. i DelVar variable Deletes from nlemolTy" the contents of .variable. i DependAsk Sets table to ask for dependent-variable values. -1-[_ DependAuto Sets table to generate dependentwariable values automatically. -;- [_ Degree det(matrix) Returns matrix. determinant DiagnosticOn Sets dim(listname) Returns tile dilnenslon listname. of dim(matri:vname) Returns tile dimension matri:_'name as a list. of Depend: Auto 7-3 Assigns anew dimension (length) to a new or existing listname. Assigns new dimensions to a new or existing matri:vname. Disp Displays and Reference 10-12 _ [CATALOG] DiagnosticOff 12-23 mode; r, r2, [_ [CATALOG] and R2 m'e displayed as DiagnosticOn regression model results. Disp [valueA,valueB, valueC,...,value n] 7-3 [TBLSET] diagnostics-on {rows,columns}-> dim(matri:vname) Tables Depend: Ask MATH l:det( Sets dia_lostlcs-offmode; r, r2, and R 2 are not displayed as regression model results. length->dim(listname) 16-15 [TBLSET] of DiagnosticOff A-6 CTL G:DelVar 1-11 Displays the home each value, Information screen. 12-23 [_ [LIST] OPS 3:dim( 11-11 MATH 3:dim( 10-12 _ [LIST] OPS 3:dim( 11-11 MATH 3:dim( 10-13 i IIO 3:Disp 16-18 I/O 3:Disp 16-18 i Function or Instruction/ Arguments Result DispGraph Displays tile graph. DispTable Displays value_DMS Displays Key or Keys/ Menu or Screen/Item ; I_ I/O tile table. value 4:DispGraph 16-19 IIO 5:DispTable 16-19 -;- il1 [)MS fornlat. [_ [ANGLE] ANGLE 4:_DMS Dot Sets (lot plotting mode; resets all.Y= editor graph-style to ... DrawF expression Draws expression X) on the graph. i [_ settings (in terms of Dot [DRAW] DRAW 6:OrawF Draws the immerse of expression by plotting X values on the y-axis and Y values on the x-axis. [_ [DRAW] DRAW 8:Drawlnv :DS<(variable,value) :commandA :commands Decrements variable by 1; skips cornmandA if variable value. i e^(power) Returns e^(list) Returns a list of e raised list of powers. Exponent: valueEexponez_t Returns value exponez_t. Exponent: listEe_onent Retm'ns list elements to the exponent. Exponent: rnatrixEexponecnt Returns matrix elements 10 to the exponea_t. _Eff(nominal rate, compounding periods) Computes rate. 8-9 8-9 < to power. 1-11 [_ Drawlnv expression e raised 2-24 CTL B:DS<( _ [ex] _ [ex] [_ [EE] [_ tEE] [_ tEE] 16-14 2-4 times to a 2-4 10 to the 1-7 the effective times 10 1-7 times 1-7 interest [_ [FINANCE] CALC C:_Eff( 14-12 Else See If:Then:Else Tables and Reference Information A-7 Function or Instruction/ Arguments End Key or Keys/ Menu or Screen/Item Result Identifies end of For(, If-Then-Else, Repeat, or While loop. Eng Sets engineering display -;CTL 7:End mode. Eng Equ)String(Y= va_;Stru) 1-10 Converts tile contents of a Y= vat to a string and stores it in Stru. [_ [CATALOG] Equ)String( expr(string) Com_erts expression [_ ExpReg [Xlistname, }qistuame,flreqlist,regequ] Fits an exponential regression model to Xlistuame and lqistuame with frequency freqlist, and stores the regression equation to regequ. ExprOff Turns off the expression display during TRACE. -;- [_ ExprOn Turns on the expression display during TRACE. -;- [_ Fcdf(lowerbound, upperbound, numerator df, denominator dr) Computes the F distribution probability between lowerbound and upperbound for the specified numerator (degrees of freedom) and denominator djr _M] Fill(value,raatri:_name) Stores value mat.ri:vname. to each Fill(volue,listuame) Stores value listuame. to each Fix # Sets fixed-decimal of decimal places. Float A-8 SD'_ng and Reference Information decimal 15-7 all and executes Sets floating Tables to [CATALOG] expr( it. 15-7 CALC 0:ExpReg 12-26 [FORMAT] ExprOff 3-14 [FORMAT] ExprOn 3-14 [DISTR] DISTR 9:Fcdf( df element element mode for # mode. 16-12 i 13-32 in MATH 4:Fill( 10-13 in _ [LIST] OPS 4:Fill( 11-11 i 0123456789 (select one) 1-10 Float 1-10 i Function or Instruction/ Arguments Key or Keys/ Menu or Screen/Item Result fMax(expression,variable, lower',upper'[,tolerance]) Retm'ns the value of variable where the local maximum of expression occm's, between lower" and upper', with specified toleronee. fMin(expression,variable, lower',upper'[,toleranee]) Returns tile value of variable where the local mininmn] of expression occm's, between lower" trod upper', with specified toleronee. fnlnt(expression,variable, lower',upper'[,tolerance Returns the function integral of [_ expression with respect to MATH variable, between/ower, and 9:fntnt( upper', with specified toleronce. FnOff [function#, function#,...,function FnOn [function#, .function#,..._function D n] Deselects specified all Y= functions Y= functions. n] Selects all Y= fimctions specified Y= functions. MATH 7:fMax( 2-6 MATH 6:fMin( 2-6 Y-VANS On/Off 2:FnOff 3-8 Y-VANS On/Off 1 :FnOn 3-8 or :For(variable,begin,er_d [,incremer_t]) :commands :End :commands Executes commands through End, incrementing variable fi'om begin by increment until variable>end. i [gggM] CTL 4:For( fPart(value) Returns the fractional part or pm'ts of a real or complex number, expression, list, or matrix. [_ NUM 4:fPart( Computes tile g distribution probability between lower'bound and upperbound for tile specified numerator (degrees of freedom) and dermminator df [_ Fpdf(x,numerotardf, denominator dy) 2-7 or 16-10 Tables and 2-14 10-11 [DtSTR] DISTR 8:Fpdf( df Reference 13-32 Information A-9 Function or Instruction/ Arguments Key or Keys/ Menu or Screen/Item Result value_Frac Displays a real o1"eon]plex nmnber, expression, list, or matrix as a fraction simplified to its simplest terms. [_ MATH 1 :_Frac Full Sets full screen i [_ Full Func Sets function mode. graphing mode. 2-5 Func gcd(valueA, valueB) geometcdf_,x) geometpdf(p,x) Get(variable) GetCalc(variable) Returns the greatest common divisor of volueA and valueB, which can be realnmnbers or lists. [_ NUM 9:gcd( (;omputes a emnulative probability at x, the number of the trial on which the first suceess oeeurs, for tile diserete geometric distribution with tile specified probability of success p. [_ Computes a probability at x, the number of the trial on which the [_ [DISTR] DISTR first success occurs, for the discrete geometric distribution wlth the specified probability of success p. D:geometpdf( Gets data from the CBL 2/CBL System or CBR and stores it in variable. -;- Gets contents of variable on another TI-83 and stores it to i variable 1-12 i 1-11 2-15 [DISTR] DISTR E:geometcdf( 13-34 13-34 I/O A:Get( 16-21 I/O on the receix_ N TI-83. 0:GetCalc( 16-21 getKey Returns tile key code for the current keystroke, or 0, if no key is pressed. i [0_ IIO 7:getKey 16-20 Goto label Transfers i control to label. CTL O:Goto A-IO Tables and Reference Information 16-13 Function or Instruction/ Arguments Result Key or Keys/ Menu or Screen/Item GraphStyle(function#, grophstyle#) Sets a grophstyle function#. GridOff Turns off grid format, i- _ GridOn Turns on grid format. -;- _ G-T Sets graph-table vertical split-screen mode. i Horiz Sets horizontal split-sereen mode. for -;CTL H:GraphStyle( 16-15 [FORMAT] 6ridOff Horizontal y identity(dimension) Draws a horizontal line at y. Returns the identity matrix of dimension rows x dimension eolumns. = O (false), skips 3-14 [FORMAT] GridOn 3-14 G-T 1-12 i I_bg] Horiz 1-12 [_ [DRAW] DRAW 3:Horizontal MATH S:identity( :If condition :commandA :commands If condition commandA. i [g_ CTL 1:If :If condition :Then :commands :End :commands Executes commands from Then to End if condition = 1 (true). i [0ggM] CTL 2:Then :If condition :Then :commands :Else :commands :End :commands Executes commands from Then to Else if condition = 1 (true); from Else to End if condition = O (false). i [0ggM] CTL 3:Else imag(value) Returns the imaginmTy (nonreal) part of a complex number or list of complex numbers. 8-6 10-13 16-9 16-9 16-10 Tables and Reference CPX 3:imag( 2-18 hfformation A-11 Function or Instruction/ Arguments IndpntAsk Key or Keys/ Menu or Screen/Item Result Sets table to ask for independent-variable -;-[_ [TBLSET] Indpnt: Ask values. IndpntAuto Sets table to generate independent-variable values automatically. -1-[2_ [TBLSET] Indpnt: Auto Input Displays graph. -1IIO 1:Input Input [.variable] Prompts for value Input variable. ["text",variable] Input [Strn,variable] to store 7-3 to I/0 1:Input 16-17 I/O 1:Input 16-17 -;- inString(s#qng,subs#qng [,start]) Returns tile (-haraeter position in string of tile first eharaeter of substring beginning at start. [_ [CATALOG] inString( int(value) Returns the lm'gest integer real or complex ntmlber, expression, list, or matrkx. [_TH] NUM 5:int( _<a Conlputes tile sum, rounded roundvalue, of the interest amount between pmtl and pint2 for an amortization schedule. invNorm(area[,p,_;]) Computes emnulative to tile inverse normal distribution funetion for a given area under the normal distribution curve specified by/_ and a. iPart(value) A-12 Tables Returns tile integer part of a real or eomplex number, expression, list, or matrix. and Reference Inforination 16-16 i Displays Strn and stores entered value to variable. Elnt(pmtl,pmt2 [,roundvalue]) 7-3 15-7 2-14 10-11 [_ [FINANCE] CALC A:Zlnt( 14-9 _ [DtSTR] DISTR 3:invNorm( 13-30 NUM 3:iPart( 2-14 10-11 Function or Instruction/ Arguments Result Key or Keys/ Menu or Screen/Item irr(OFO,OFList[,OFF_q]) Returns the interest rate at which the net present vahle of file cash flows is equal to zero. [_ [FINANCE] CALC 8:irr( :lS>(variable,value) :commandA :commands Increments variable by 1; skips commandA variable>volue. i Llistname Identifies characters list name. LabelOff Turns off axes 14-8 LabelOn if the next one to five as a user-created labels. CTL A:IS>( 16-13 [_ [UST] OPS B:L 11-16 -1-[_ [FORMAT] LabelOff Turns ol1 axes labels, i- [_ [FORMAT] LabelOn Lbl label 3-14 3-14 Creates a label of one or two characters. i Icm(valueA,valueB) Returns the least conunon inultiple of volueA and valueB, which can be real nulnbers or lists. [_ NUM 8:lcm( length(string) Returns the number chm'aeters in st_ng, [_ [CATALOG] length( Line(X1,Y1Jd2,Y2) [)raws a line from (X2,Y2). (X1,Y1) to [_ [DRAW] D RAW 2:Line( S-5 Line(X1,Y1,X2,Y2,0) Erases a line from (X2,Y2). (X1,Y1) to [_ [DRAW] D RAW 2:Line( 8-5 Tables and of Reference CTL 9:Lbl 16-13 2-15 Information 15-8 A-13 Function or Instruction/ Arguments Key or Keys/ Menu or Screen/Item Result LinReg(a+bx) [Xlistname, Iqistname,freqlist, regequ] Fits a linear regression inodel to Xlistname and Iqistname with frequencyfrvqlist, and stores the regression equation to regequ. kinReg(ax+b) [Xlistname, Iqistname_freqlist, regequ] Fits a linear regression model to Xlistname and Iqistname with frequency.fr_qlist, and stores the regression equation to regequ. [g_g] CALC 4:kinReg(ax+b) LinRegTTest [Xlistname, Iqistname,freqlist, olternative,regequ] Performs a linear regression and a t-test, alternative=-1 is <; alternative=O is €; alternative=l is >. i [g_g] TESTS E:LinRegTTest AList(list) Returns a list containing the differences between consecutive elements in list. _ Fills matrixname colunm by cohmm with the elements from each specified listuame. [_ In(value) Returns the natural logarithm of a real or complex number, expression, or list. @ knReg [Xlistname, Ylistname,fr_qlist, regequ] Fits a logarithmic regression model to Xlistuame and }qistuame with frequency freqlist, and stores the regression equation to regequ. [g_T] CALC 9:LnReg log(value) Returns [[OG] List_ matr(listnamel,..., listname n,matri:_'name) complex logarithm nilnlber, or list. A-14 Tables and Reference Information of a real or expression, CALC 8:LinReg(a+bx) 12-26 12-25 13-24 [LIST] OPS 7:AList( 11-12 [LIST] OPS 0:List _ matr( 10-14 11-15 2-4 12-26 2-4 Function or Instruction/ Arguments Key or Keys/ Menu or Screen/Item Result Logistic [Xlistname, YTist.name,fr_ql.ist, regequ] Fits a logistie regression mode] to Xlistname and YTistname with frequeneyfr_qlist, and stores the regression equation to regequ. [gTAT] CALC B:kogistic Matr_ list(matrix, listnameA,...,listname Fills each listname with elements from eaeh column matrix. [_ [LIST] OPS A:MatO list( n) MatrMist(mat.rix, column#,listname) Fills a listuame from a specified matrix. rnax(valueA,valueB) Returns the larger and valueB. in _lth elements eoluran# in 12-27 [_ 10-14 11-16 [LIST] OPS A:MatO list( 10-14 11-16 of valueA NUM 7:rnax( 2-15 max(list) Returns largest real or complex element in list. [2_] [LIST] MATH 2:max( rnax(listA,listB) Retm'ns a real or eomplex list of the larger of each pair of elements in listA and listB. [2_] [LIST] MATH 2:max( max(value, Retm'ns a real or complex list of the larger of value or each list element. [_ [LIST] MATH 2:max( 11-16 rnean(list[,frvqlist]) Returns the mean frequeney frvqlist. [_ [LIST] MATH 3:mean( 11-16 median(list[,fr_qlist]) Returns the median frequeney frvqlist. [_ [LIST] MATH 4:median( 11-16 Med-Med [Xlistname, Ylistname_fr_qlist, regequ] Fits a median-median model to Xlistname and Ia'ist'name _lth frequeneyfrvqlist, and stores the regression equation to regequ. Menu("title","textl"',labell [,...,"textT',labelT]) Generates a menu of up to seven items during program exeeution. 11-16 11-16 list) Tables and of list with of list with Reference CALC 3:Ned-Ned 12-25 i [_ CTL C:Menu( 16-14 hfformation A-15 Function or Instruction/ Arguments min(valueA,valueB) Key or Keys/ Menu or Screen/Item Result Returns valueB. smaller of valueA and NUM 6:min( min(list) Returns smallest complex element real or in list. _ 2-15 [LIST] MATH l:min( 11-16 min(listA,listB) Returns real or complex list of tile smaller of each pair of elements in listA and listB. [_ [LIST] MATH 1 :min( 11-16 min(value,list) Returns a real or complex list of the smaller of value or each list element. _ [LIST] MATH 1 :min( 11-16 Returns the number of combinations of valueA valueB at a time. [_ PRB 3:nOr 2-21 Returns a list of the combinations of value taken each element in list at a time. PRB 3:nCr 2-21 Returns a list of the combinations of each element in list taken value at a time. PRB 3:nCr 2-21 nCr valueB valueA value nCr list list nCr value listA nCr listB nDeriv(expression,variable, value[,e]) *Nom(ef_t_ct'ive compounding rate, pe/riods) Normal taken Returns a list of the combinations of each element in listA taken each element in listB at a time. [_TH] PRB 3:nOr Returns approximate numerical derivative of expression with respect variable at value, with specified e. [_ MATH 8:nDeriv( Computes rate. Sets normal the nominal display to 2-21 2-7 interest mode. [2_] [FINANCE] CALC B:*Nom( Normal A-16 Tables and Reference Information 14-12 i 1-1O Function or Instruction/ Arguments normalcdf(low_rbound, upperbound [, _,(_]) Key or Keys/ Menu or Screen/Item Result (;omputes tile normal distribution probability between low_rbound and upperbound for the specified and _. [_ [DISTR] D IST R 2:normalcdf( p 13-27 normalpdf(x[,p,(_]) (;omputes tile probability [_ [DtSTR] density function for the nornlal DISTR distribution at a specified x 1 :normalpdf( value for tile specified/_ and c_. not(value) Returns 0 if value is :/: 0. value can be a real number, expression, or list. [_ [TEST] LOG IC 4:not( 2-26 Returns tile number of permutations of volueA valueB at a time. taken [_TH] PRB 2:nPr 2-21 nPr list Returns a list of tile permutations of value taken each element in list at a time. [_TH] PRB 2:nPr 2-21 list nPr value Returns a list of tile permutations of each element in list taken value at a time. [_TH] PRB 2:nPr 2-21 Returns a list of tile permutations of each element in listA taken each element in listB at a time. [_TH] PRB 2:nPr npv(interest rate,CFO, CFList[,CFFreq]) Computes the sum of the present values for cash inflows and outflows. [2_] [FINANCE] CALC 7:npv( valueA Returns 1 if valueA or volueB is € 0. volueA and valueB can be realnumbers, expressions, or lists. [2_] [TEST] LOGIC 2:or valueA value listA nPr valueB nPr listB or volueB Tables and Reference 13-29 2-21 14-8 2-26 hfformation A-17 Function or Instruction/ Arguments Key or Keys/ Menu or Screen/Item Result Output(vow,coluran,"text") Displays specified text beginning at row and column. i [P_M] I/O 6:Output( 16-19 Output(row,column,value) Displays specified value begiJming at row and column. i [gggN] I/O 6:Output( 16-19 Param Sets parametric mode. Pause Suspends program until you press _. Pause ['value] Displays value; suspends program execution until you press [_. i Plot#(type,Xlistuame, YTistname,mark} Defines Plot# (1, 2, or 3) of type Scatter 05"xyLine for Xlistuame and Iqistuame using mark. 1 [2_] Plot#(type,Xlistuame, ,frvqlist) Defines Plot# (1, 2, 05"3) of type Histogram 05"Boxplot for Xlistuame _lth frequency fr_qlist. ; [2_] [STAT PLOT] PLOTS 1:Plot1( 2:Plot2( 3:Plot3( 12-37 Plot#(type,_istuame, .fr_qlist,mark) Defines Plot# (1, 2, or 3) of type ModBoxplot for Xlistname _lth frequency frvqlist using mark. -;-[_ [STAT PLOTS 1:Plot1( 2:Plot2( 3:Plot3( Plot#(type,datalistname, data axis,mark) Defines Plot# (1, 2, 05"3) of -;-[_ [STAT PLOT] type NormProbPIot for PLOTS datalistuame on data axis 1:Plot1( using mark. data axis can be X 2:Plot2( or Y. 3:Plot3( 12-37 PlotsOff [1,2,3] Deseleets all star plots or one or more specified stat [)lots (1, 2, 05"3). _ [STAT PLOT] STAT PLOTS 4:PlotsOff 12-35 PlotsOn [1,2,3] Selects all stat plots o1" one or more specified stat plots (1, 2, or 3). [_ [STAT PLOT] STAT PLOTS 5:PlotsOn 12-35 A-18 Tables and Reference Information graphing i Par execution 1-11 i [gggN] CTL 8:Pause CTL 8:Pause [STAT PLOTS 1:Plot1( 2:Plot2( 3:Plot3( 16-12 16-12 PLOT] 12-37 PLOT] 12-37 Function or Instruction/ Arguments Key or Keys/ Menu or Screen/Item Result Pmt_Bgn Specifies an mmuity due, where payments occur at the beginning of each payment period. F2Ta] [FINANCE] Pmt_End Specifies an ordinary annuity, where payments occur at the end of each payment period. F2na][FINANCE] CALC E:Pmt_End poissoncdf(,u,x) (;omputes a cumulative probability at x for the discrete Poisson distribution with specified mean ,u. [_ Computes a probabilii7 at x for the discrete Poisson distribution F2na][DtSTR] DISTR with the specified B:poissonpdf( poissonpdf(_,x) Polar eomplex Sets polar 'value i.Polar CALC F:Pmt_Bgn 14-13 nlean _. graphing Displays eomplex polar format. PolarGC Sets polar graphing coordinates fornmt. prgmname Executes DISTR C:poissoncdf( 13-34 Pol 1-11 CPX 7:_Polar 2-19 'value in ; r2_ [FORMAT] PolarGC 3-13 the program name. EPrn(pmtl,pmt2 [,roundvolue]) Computes the sum, rounded roundvalue, of the prineipal amount between pmtl and pint2 for an amortization schedule. prod(list[,sta,r¢,e/nd]) Returns product of list elements between start end. n] Prompts for value for variableA, then variableB, so on. Tables 13-33 i mode. i CTRL D:prgm Prompt variableA [,variableB,...,vaviable 14-13 [DtSTR] and to 16-15 [_ [FINANCE] CALC 0:EPrn( 14-9 and and Reference [_ [LIST] MATH 6:prod( 11-18 i [0ggM] I/O 2:Prompt 16-18 hfformation A-19 Function or Instruction/ Arguments Result 1-PropZlnt(x,n [,confidence level]) Computes a one-proportion z eonfidence interval. i 2-PropZlnt(xl,nl [,confidence Computes a two-proportion z eonfidence interval. i 1-PropZTest(pO,x,n [,alternative,drawflag]) Computes a one-proportion z test. olternative=-I is <; alternative=O is _; alternative=l is >. d'rmqflog=l draws results; drawflog=O calculates results. i 2-PropZTest(xl ,nl ,x2,n2 [,alternative,drawflog]) Computes a two-proportion z test. olternative=-I is <; alternative=O is €; alternative=l is >. drmqflog=l draws results; drawflog=O calculates results. i [g_g] TESTS 6:2-PropZTest( Pt-Change(x,y) Reverses [_ [DRAW] POINTS Pt-Off(x,y[,mark]) Erases mark. a point at (x,y) using Pt-On(x,y[,mark]) Draws mark. a point at (x,y) using PwrReg [Xlistname, Ylistname,freqlist, regequ] Fits a power regression model to Xlistname and Ylistname with frequencyfr_qlist, and stores the regression equation to regequ. ,x2,n2 level]) Key or Keys/ Menu or Screen/Item a point at (x,y). TESTS A:l-PropZlnt( 13-20 TESTS B:2-PropZlnt( 13-21 TESTS 5:1 -PropZTest( 13-14 13-15 3:Pt-Change( 2:Pt-Off( Tables and Reference Information 8-15 [_ [DRAW] POINTS l:Pt-On( A-20 8-15 [_ [DRAW] POINTS 8-14 [g_ CALC A:PwrReg 12-27 Function or Instruction/ Arguments Result Key or Keys/ Menu or Screen/Item Pxl-Change(row,column) Reverses pixel at (_w,column); 0 <_row <_62 and 0 _<column <_94. [_ [DRAW] POINTS 6:Pxl-Change( S-16 Pxl-Off(row,column) Erases pixel at (_vw,eolumn); 0 <- row <_62 and 0 <_column <_94. [_ [DRAW] POINTS 5:PxI-Off( 8-16 Pxl-On(row,column) Draws pixel at (row,column); 0 <- row <- 62 and 0 <_column <_94. [_ [DRAW] POINTS 4:PxI-On( 8-16 pxI-Test(row,column) Returns 1 if pixel (row, column) is on, 0 if it is oft'; 0 <_row <_62 and 0 <_column <_94. [_ [DRAW] POINTS 7:pxI-Test( P)Rx(r,0) Returns X, given polar coordinates r and O or a list of polar coordinates. [_ [ANGLE] ANGLE 7:P_.Rx( 2-24 P)Ry(r,O) Returns Y, given polar eoordflmtes r and O or a list of polar coordinates. [_ [ANGLE] ANGLE 8:P_.Ry( 2-24 QuadReg [Xlistname, Ylistname,fr_qlist, regequ] Fits a quadratic regression model to Xlistname and Iqist,name with frequency frvqlist, and stores the regression equation to regequ. [g_ CALC 5:OuadReg OuartReg [Xlistname, Iqistname,frvqlist, regequ] Fits a quartie regression model to Xlistname and Iqistname with frequeneyfrvqlist, and stores the regression equation to regequ. [gTfT] CALC 7:QuartReg Radian Sets radian angle mode. i 1_ Radian rand [(numtrials)] Returns a ral]dom nt:[mber between 0 and 1 for a speeified number of trials numtrials. randBin(numtrials,prob [,numsimulations]) Generates and displays a random real number from a specified Binonfial distribution. Tables and Reference 8-16 12-25 12-26 1-11 [_ PRB 1 :rand 2-20 PRB 7:randBin( 2-22 hfformation A-21 Function or Instruction/ Arguments Key or Keys/ Menu or Screen/Item Result randlnt( lower, upper [,numtrials]) Generates all(] displays a randoln integer withil] a range specified by lower and upper integer bounds for a specified number of trials numtrials. [_tH] PRB S:randlnt( randM(rows,columns) Returns a random matrix of rows (1-99) x columns (1-99). [_ MATH 6:randM( randNorm(p,c_[,numtrials]) Generates and displays a random real number from specified specified specified numtriols. 2-22 10-13 PRB a Normal distribution by p and _ for a number of trials 6:randNorm( 2-22 re^Oi Sets tile mode to polar complex number mode Real Sets inode to display complex results only when you enter complex numbers. i [M0_] Real real(value) Returns the real part of a complex number or list of complex numbers. [_ CPX 2:real( 2-18 [_ [DRAW] STO 4:RecallGDB 8-20 [_ [DRAW] STO 2:RecallPic S-1S CPX 6:_Rect 2-19 RecaIIGDB RecallPic complex n (re^Oi). Restores all settings stored tile graph database variable GDBn. n in Displays tile graph 31l(1 adds tile picture stored in Picn. 'value _Rect Displays complex 'value or list in rectangular format. RectGC Sets rectangular graphing coordinates format. ref(matrix) A-22 i Tables Returns tile row-echelon of a matrix. and Reference Inforination re^Oi 1-12 1-12 1 _ [FORMAT] RectGC 3-13 forln MATH A:ref( 10-15 Function or Instruction/ Arguments Result Key or Keys/ Menu or Screen/Item :Repeat condition :commands Executes condition eommands is true. until i [_ CTL :End :commands i [0ggM] CTL E:Return 16-15 Returns round(value[,#deeimals]) Returns a number, expression, list, or matrix rounded to #decimols (<_9). [_ NUM 2:round( *row(value,matrix,row) Returns a matrix matrix nmltiplied stored in row. MATH E:*row{ 10-16 MATH D: row+( 10-16 *row+(value,matrix, rowA,rowB) program. 16-11 Return row+(matrix,rowA,rowB) to tile calling 6:Repeat _lth row of by volue and Returns a matrix _lth rowA of matrix added to rowB and stored in rowB. Returns a matrix _lth rowA of matrix nmltiplied by volue, added to rowB, and stored in rowB. rowSwap(matrix,rowA, rowB) Returns matrix a matrix swapped rref(matrix) Returns echelon the reduced rowform of a matrix. R_Pr(x,y) R_PO(x,y) _lth _lth rowA of rowB. MATH F:*row+( 1O- 16 MATH C:rowSwap( 10-16 MATH B:rref( 10-15 Returns R, given reetanguhu" coordinates x and y or a list of rectangular coordinates. [2_ Returns 0, given rectangular coordinates x and y or a list of rectangular coordinates. [_ Tables and Reference 2-13 [ANGLE] ANGLE 5:R_Pr( 2-24 [ANGLE] ANGLE 6:R_PO( 2-24 hfformation A-23 Function or Instruction/ Arguments Result Key or Keys/ Menu or Screen/Item 2-SampFTest [listnameZ, listname2_fr_qlistl, fr_qlist2,alternative, drowflag] (Data list input) Performs a two-san]pie Ftest. alternative=-1 is <; alternative=O is _; alternative= l is >. drawflag= l draws results; drawflag=O calculates results. i 2-8ampFTest Sxl,nl, Sx2,n2[,alternative, drowflag] (Summary stats input) Performs a two-sample F test. alternative=-1 is <; alternative=O is _; alternative=l is >. drawflag=l draws results; drawflog=O calculates results. i 2-SampTInt [listnamel, listname2, frvqlistl _frvqlist2, canfidezwe level,pooled] (Data list input) Computes a two-sample t confidence intm_'al, pooled=l pools variances; pooled=O does not pool variances. i 2-SampTInt 21,Sx1,n1, 22,Sx2,n2 [,confidence level,pooled] (Sununary stats input) Computes a two-sample t confidence intm_,al, pooled=l pools variances; pooled=O does not pool variances. i 2-SampTTest [listnamel, listname2_frvqlistl , frvqlist2,alternative, pooled,draw flag] (Data list input) Computes a two-sample t test. alternative=-1 is <; alternative=O is _; alternative= l is >. pooled= l pools variances; pooled=O does not pool vm'iances, drawflog=l draws results; drawflog=O calculates results. i A-24 Tables and Reference TESTS D:2-SampFTest 13-23 TESTS D:2-SampFTest 13-23 TESTS 0:2-SampTInt 13-19 Information TESTS 0:2-SampTInt 13-19 TESTS 4:2-SampTTest 13-13 Function or Instruction/ Arguments Key or Keys/ Menu or Screen/Item Result _r_tq 2-Sam pTTest 5l,Sxl,nl, 22 ,Sx2 ,n2[ ,o lternative pooled,draw.flag] (Smmnary stats input) Computes a two-sample t test. alternative=-1 is <; alternative=O is _; alternative= l is >. pooled= l pools variances; pooled=O does not pool variances, drawflog=l draws results; drawflog=O calculates results. 2-SampZInt(_l,a, [,listnamel ,listname2 frvqlistl _frvqlist2, canfidence level]) (Data list input) Computes confidence 2-SampZlnt(_l,_, _1,nl ,_2,n2 [,confidence level]) (Smmnary stats input) Computes a two-sample z confidence intm_al. 2-SampZTest(_l,_ [,listnamel ,listname2 .frvqlistl ,frvqlist2, alternative,drowflag]) (Data list input) Computes a two-sample z test. alternative=-1 is <; alternative=O is _ ; alternative=l is >. drawflag=l draws results; drawflag=O calculates results. 2-SampZTest(61 ,_, _1 ,nl ,_2,n2 [,alternative,drawflog]) (Summary stats input) Computes a two-sample z test. alternative=-1 is <; alternative=O is ;_; alternative= l is >. draw.flag= l draws results; drawflog=O calculates results. i [gt_] TESTS 3:2-SampZTest( Sci Sets scientific mode. i [MODEl Sci Select(Xlistname, Iqistname) a two-sample intm_al. TESTS 4:2-SampTTest 13-13 z TESTS 9:2-SampZlnt( 13-18 TESTS 9:2-SampZlnt( 13-18 notation display Seleets one o1" more speeific data points from a scatter plot or xyLine plot (only), and then stores the selected data points to two new lists, Xlistname and Ylistname. Tables and Reference TESTS 3:2-SampZTest( 13-12 13-12 _ 1-10 [LIST] OPS 8:Select( 11-12 hfformation A-25 Function or Instruction/ Arguments Send(variable} Key or Keys/ Menu or Screen/Item Result Sends contents of variable to the CBL 2/CBL System or CBR. -;- seq(expression,variable, begin,end[,increment]) Returns list ereated by evaluating expression _lth regard to 'variable, from begin to end by incremez_t. _ Seq Sets sequence i Sequential Sets mode to graph ftmetions sequentially. SetUpEditor Removes all list names from the stat list editor, all(] then restores list names L1 through L6 to eolumns 1 through 6. graphing mode. I/O B:Send( OPS 5:seq( 11-11 Seq 1-11 Sequential 1-12 i EDIT 5:SetUpEditor 12-21 SetUpEditor listnamel [,listname2,..., listname20] Removes all list names from the stat list editor, then sets it up to display one or more listnames in the specified order, starting _lth eohmm 1. Shade(lowe:rfune, upperfunc[,Xleft_rqght, pattern,patres]) Draws lowerfune and upperfune in terms of X on the current graph and uses pattern and pat'r_s to shade the area bounded by lowerfunc, upperfunc, Xleft, and X'rqght. [_ Shadez2(lowerbound, upperbound,dy') Draws the density function the Z2 distribution specified degrees of freedom dfand shades tile area between [_ [DISTR] DRAW 3:Shade)_2( lowerbound A-26 Tables and Reference and upper_ound. Information 16-21 [LIST] for by EDIT 5:SetUpEditor 12-21 [DRAW] DRAW 7:Shade( 8-10 13-36 Function or Instruction/ Arguments ShadeF(lowerbound, upperbound, numerator df, denominator d,f) Key or Keys/ Menu or Screen/Item Result Draws the density function for the F distribution specified by numerator (lf and denorainator df and shades the area between lower'bound and _ [DISTR] DRAW 4:ShadeF( upperSound. 13-36 $hadeNorm(lower'bound, upper'bound[,p,G]) Draws the normal density function specified by p and (_ and shades the area between lower'bound and upper'bound. _ [DISTR] DRAW 1 :ShadeNorm( Shade_t(lower'bound, upperbound,dJ') Draws the density function for the Student-t distribution specified by degrees of freedom df, and shades the area between lower'bound and upperSound. [_ [DISTR] DRAW 2:Shade_t( Simul Sets mode to graph simultaneously. i [_Dg] S imul sin(volue) Returns number, tile sine of a real expression, or list. Ig]N] sin-l(volue) Returns number, tile m-csine expression, [_ sinh(volue) Returns tile hypet%olic sine of a real number, expression, or list. _ [CATALOG] sinh( Returns the hyperbolic arcsine of a real number, expression, or list. _ [CATALOG] sinh -1( sinh-l(value) Tables and functions of a real or list. Reference 13-35 13-36 1-12 2-3 [SIN-1] 2-3 15-10 15-10 hfformation A-27 Function or Instruction/ Arguments Key or Keys/ Menu or Screen/Item Result SinReg [iterations, Xlistname,I_istname, period,regequ] Attempts iterations times to fit a sJnusoJdal regression model to Xlistname and Iqistname using aperiod guess, and stores the regression equation to regequ. solve(expression,variable, guess,{lower',upper_) Solves expression for variable, given an initial guess and lower" and upper" bounds within which the solution is sought. i SortA(listuame) Sorts elements of listname ascending order. _ [LIST] OPS 1 :SortA( SortA(keylistuame, dependlistl [,dependlist2, ...,dependlist n]) Sorts SortD(listuame) Sorts elements of listname descending order. elements of in keylistuame in ascending order, then sorts each dependlist as a dependent list. in SortD(keylistuarae, Sorts de_er_dlistl dependlist in descending order, then sorts each dependlist as a dependent list. [,deper_dlist2,..., n]) elements of keylistuarae CALC C:SinReg 12-27 MATH 0:solve( 2-12 [2_] [LIST] OPS l:Sorth( [_ [LIST] OPS 2:SortD( [_ [LIST] OPS 2:SortD( stdDev(list[,frvqlist]) Returns the standard deviation of the elements in list with frequencyfrvqlist. [_ [LIST] MATH 7:stdDev( Stop Ends program execution; returns to home screen. i [gggM] CTL Store: value_variable Stores value _ StoreGDB Stores current graph datahase GDBn. F:Stop A-28 n Tables and Reference in variable. Information in [_ 11-10 12-20 11-10 12-20 11-10 12-20 11-10 12-20 ll-lS 16-15 1-14 [DRAW] STO 3:StoreGDB 8-19 Function or Instruction/ Arguments StorePic n String_*Equ(string,Y= Key or Keys/ Menu or Screen/Item Result Stores eun'ent pleture picture Picn. vat') in [_ [DRAW] STO l:StorePic Converts stt'ing iJlto an equation and stores it in Y: vat_ _ [CATALOG[ String_Equ( sub(string,begin,h_.ngth) Returns a string that is a subset of another string, from begin to length. [gffd][CATALOG] sub( sum(list[,stat't,end]) Returns the sum of elements list from start to end. [gffd][LIST] MATH 5:sum( tan(value) Returns nunlber, or list. the ttmgent expression, 8-17 15-8 of 15-9 11-18 of a real 2-3 tan-l(value) Returns the aretangent of a real nunlber, expression, or list. [gffd][TAN-1] Tangent(ea_ression,value) Draws a line tangent to expression at X=value. [gffd][DRAW] D RAW 5:Tangent( tanh(value) Returns hyperbolic tangent of a real number, expression, or list. [_ [CATALOG] tanh( 15-10 tanh-l(value) Returns the hyperbolic aretangent of a real number, expression, or list. _ [CATALOG] tanh-l( tcdf(lowerbound, upp_rbound,dJ_ Computes the Student-t distribution probability between lower_ound and upperSound for the specified degrees of freedom 4/: [2_ Text(row,column,textl, text2,...,text n) Writes text on graph at pixel (row,column), 0 <_row <_57 and 0 <_column <_94. beginning where [_ [DRAW] DRAW 0:Text( Tables Reference 2-3 8-8 15-10 [DISTR] DISTR 5:tcdf( 13-31 8-12 Then See If:Then and hfformation A-29 Function or Instruction/ Arguments Key or Keys/ Menu or Screen/Item Result Time Sets sequenee graphs with respect to time. Tlnterval [listname, .fr_qlist,eonfidence (Data list input) Computes inte_ral. a t confidence Tlnterval ;7,Sx,n [,confidence level] (Summary stats input) Computes inte_ral. a t confidence tpdf(x,df) Computes the probability" density" function (pdf) for the Student-t distribution at a specified x value _ith specified degrees of freedom ddq Trace Displays the graph TRACE mode. level] T-Test pO[,listname, frvqlist,alternative, d'r'o_ag] (Data list input) Tables and Performs a t test with frequeneyfrvqlist. alternative=-1 is < ; alternative=O is €: ; alternative=l is >. drawflag=l draws results; drawf!og=O ealeulates results. Reference Information -;-[_ [FORMAT] Time 6-8 i TESTS 8:Tlnterval 13-17 TESTS 8:Tlnterval 13-17 i [_ [DISTR] DISTR 4:tpdf( 13-30 and enters Performs a t test with frequeneyfrvqlist. alternative=-1 is <; alternative=O is €; alternative= l is >. drawflag= draws results; drawfiag=O calculates results. T-Test pO, _,Sx,n [,olternative,drawflag] (Summary stats input) A-30 to plot 3-18 i TESTS 2:T-Test l 13-11 i TESTS 2:T-Test 13-11 Function or Instruction/ Arguments Key or Keys/ Menu or Screen/Item Result tvm_FV[(N,I%,PV,PMT, P/Y,C/Y) ] Conlptltes tile ftlture va]ue. [_ [FINANCE] CALC 6:tvm_FV 14-7 tvm_I%[(N, PV,PMT,FV, PlY, C/Y)] (;omputes rate. tile annual [_ [FINANCE] CALC 3:tvm_I% 14-7 tvm_N[(I%,PV, PMT,FV, P/Y,C/Y)] (;omputes tile number payment periods. of tvm_Pmt[(N,I%,PV,FV, P/If, C/Y)] (;omputes payment. the amount tvm_PV[(N,I%,PMT,FV, P/Y,C/Y) ] (;omputes tile present uvAxes Sets sequence graphs to [)lot u(n)on the x-axis and v(n)on the y-axis. ; [2_] Sets sequence graphs to [)lot u(n) on the x-axis and w(n) on the y-axis. ; [2_] [Xlistname, Performs one-variable analysis on tile data in XTistname _ith frequeneyfrvqlist, [gT_] CALC l:l-Var 2-Mar Stats [Xlistname, Ylistnarae,fr_qlist] Performs two-variable analysis on the data in Xlistnarae and Iaistname with frequeney fr_qlist. [gT_] CALC 2:2-Mar Stats variance(list[,fr_qlist]) Returns the variance of the elements in list wlth frequeney frvqlist. [g_] [LIST] MATH 8:variance( Vertical Draws at x. [_ [DRAW] D RAW 4:Vertical uwAxes 1-Mar Stats .frwqlist] vwAxes Web x a vertical interest _ [FINANCE] CALC 5:tvm_N 14-7 of eaeh [_ [FINANCE] CALC 2:tvm_Pmt 14-6 value. [_ [FINANCE] CALC 4:tvm_PV 14-7 line [FORMAT] uv 6-8 [FORMAT] uw 6-8 Stats 12-25 Sets sequenee graphs to [)lot v(n) on the x-axis and w(n) on the y-axis. i- [2_] Sets sequence as webs. ; [2_] [FORMAT] Web Tables graphs to trace and Reference 12-25 11-18 S-6 [FORMAT] vw 6-8 hfformation 6-8 A-31 Function or Instruction/ Arguments Key or Keys/ Menu or Screen/Item Result :While condition :commands :End :command Executes condition valueA Returns 1 if only valueA or valueB = O. valueA and valueB can be real numbers, expressions, or lists. _ [TEST] LOGIC 3:xor Displays a graph, lets you draw a box that defines a new- -;- xor valueB ZBox commands is true. _ewing window, the window. ZDecimal while i CTL 5:While 2-26 ZOOM and updates 1:ZBox 3-20 Adjusts tile _dewing window so that aX=0.1 and AY=0.1, and displays tile graph screen with tile origin centered on the screen. i Redefines tile viewing window using these dimensions: AX=I XscI=10 AY=I YscI=I 0 i Zlnterval c_[,listname, .fr_qlist,confidence level] (Data list input) Computes intel_al. a z confidenee i Zlnterval c_,;7,n [,confidence level] (Summary stats input) Computes intel_al. a z confidenee Zoom In Magnifies tile part of the graph that surrounds the eursor location. i Displays a greater portion of the graph, centered on the cursor location. i Zlnteger Zoom Out A-32 Tables and Reference Inforination 16-11 ZOOM 4:ZDecimal 3-21 ZOOM 8:Zlnteger 3-22 TESTS 7:Zlnterval 13-16 i [_ TESTS 7:Zlnterval 13-16 ZOOM 2:Zoom In ZOOM 3:Zoom Out 3-21 3-21 Function or Instruction/ Arguments ZoomFit ZoomRcl ZoomStat Recalculates Ymin and Ymax to hmlude tile nlininluni and nlaxinmm Y values, between Xmin and Xmax, of the selected functions and replots tile functions. i Graphs tile selected functions in a user-defined _dewing window. i Redefines tile viewing window so that all statistical data i points ZoomSto ZPrevious ZSquare ZStandard Key or Keys/ Menu or Screen/Item Result ZOOM O:ZoomFit 3-22 MEMORY 3:ZoomRcl ZOOM are displayed. Immediately stores viewing window. tile current i Adjusts tile X or Y window settings so that each pixel represents m] equal width and height in the coordinate system, and updates the viewing window. i Replots the functions immediately, updating the window variables to the default values. i and Reference 9:ZoomStat 3-22 MEMORY 2:ZoomSto 3-23 i Replots tile graph using the window variables of the graph that was displayed before you executed the last ZOOM instruction. Tables 3-23 MEMORY 1:ZPrevious 3-23 ZOOM 5:ZSquare 3-21 ZOOM 6:ZStandard 3-22 Information A-33 Function or Instruction/ Key or Keys/ Menu or Screen/Item Arguments Result Z-Test(pO,_[,listname, f_qlist,elternative, drawflag]) (Data list input) Performs a z test with frequencyfreqlist. alterr_ative=-I is <; alterr_ative=O is €; alterr_ative= l is >. drawflag= draws results; drawflag=O calculates results. i [_ TESTS 1:Z-Test( l 13-10 Z-Test(pO,_,_,n [,olterr_ative,drawflag]) (Smmnary stats input) Performs a z test. alterr_ative=-I is <; alterr_ative=O is €; alterr_ative=l is >. draw.flag=l draws results; drawflog=O calculates results. i ZTrig Replots the functions immediately, updating i Factorial: value! Factorial: Degrees Radian: the ZOOM 7:ZTrig faetodal Returns factorial elements. notation: value ° angle r 13-10 window variables to preset values for plotting trig functions. Returns list! TESTS 1:Z-Test( 3-22 of value. PRB 4:! 2-21 PRB 4:! 2-21 of list Interprets designates fornlat. value as degrees; degrees in [)MS [_ Interprets angle as radim]s. [_ [ANGLE] ANGLE 1 :° ANGLE 3: r Transpose: A-34 matrix Tables T and Retrains a matrix in wltich each element (row, column) is swapped with tile corresponding element (cohmm, row) of matrix. Reference Information g-23 [ANGLE] g-24 MATH 2: T 10-12 Function or Instruction/ Arguments Result xt_ZrootX_value Retm'ns xtlZrootX_list Returns listAX_listB Cube Returns value 3 root: 3_(value) Equal: valueA=valueB Not equal: valueAcvalueB Less than: x_root Returns xthroot elements. listX_value Cube: Key or Keys/ Menu or Screen/Item valueA<valueB of value. 2-6 MATH 5:x-_ 2-6 MATH 5:x-_ 2-6 MATH 5:x-_ 2-6 of list list roots listA MATH 5:x_ of value. roots of listB. Returns the cube of a real or complex nmnber, expression, list, or square matrix. [_TH] MATH 3:3 Remms tile cube root of a real or complex nmnber, expression, or list. MATH 4:3_( Returns l lfvalueA = valueB. Returns 0 if valueA _ valueB. valueA and valueB can be real or complex numbers, expressions, lists, or matriees. [_ [TEST] TEST 1 := Returns 1 if valueA _ valueB. Returns 0 if valueA = volueB. valueA and volueB can be real or complex nmnbers, expressions, lists, or matrices. [_ [TEST] TEST 2:€ Returns 1 if volueA Returns 0 if volueA valueA and volueB [2T3] [TEST] TEST S:< o1"eomplex expressions, Tables < volueB. >_valueB. can be real 2-6 10-10 2-6 2-25 1O- 11 2-25 10-11 nunlbers, or lists. and 2-25 Reference hfformation A-35 Function or Instruction/ Arguments Greater than: valueA>valueB Key or Keys/ Menu or Screen/Item Result Returns 1 if valueA Returns 0 if valueA valueA and valueB O1" eonlplex [_ [TEST] TEST 3:> llUIslbers_ expressions, Less than or equal: volueA<_volueB > valueB. <_valueB. can be real or lists. Returns 1 if valueA Returns 0 if valueA valueA and volueB O1"eoIslplex expressions, 2-25 <_valueB. > volueB. can be real _ [TEST] TEST 6:_< nunlbers, or lists. 2-25 Greater than or equal: valueA>valueB Returns 1 if volueA 2 valueB. Retunls 0 if volueA < valueB. valueA and volueB can be real O1"eonlplex nunlbers, expressions, or lists. _ [TEST] TEST 4:> Inverse: Returns [] value -1 1 dix_ded by a real or eonsplex nunsber 2-25 or expression. Inverse: list -1 Inverse: matrix 2-3 Returns 1 divided elements. -1 Returns Squm'e: value 2 matrix by list [] inverted. [] 2-3 Returns value multiplied by itsel£ value can be a real or eonlplex nunlber expression. 10-10 [] or 2-3 Square: list 2 Returns list elements squared. [] Square: mat'ri:_ _ Returns itsel£ matrix by [] Powers: value^power Returns value raised to power. value can be a real 05"eoinplex number or expression. [] Powers: list^power Returns power'. [] Powers: value^list Returns value elements. 2-3 A-36 Tables and Reference multiplied 10-10 list elements Information raised to 2-3 2-3 raised to list [] 2-3 Function or Instruction/ Arguments Powers: mat'rix^pow_" Negation: -volue Key or Keys/ Menu or Screen/Item Result Returns matrix raised to power. elements [] 1O- 10 Returns the negative of a real o1"complex number, expression, list, o1"matrix. [] 2-4 10-9 Power of ten: lo^(volue) Returns 10 raised to tile value power, volue can be a real or conlplex ntlnlber or expression. _ [10x] Power of ten: lo^(list) Returns a list of 10 raised the list power. _ [10x] Square root: ,[(value) Returns square root of a real or complex number, expression, or list. _ [_] Multiplication: volueA*valueB Returns [] Multiplication: volue*list Returns element. Multiplication: list*value Returns each times volue. Multiplication: listA*listB Returns listA elements listB elements. Multiplieation: value*matrix Returns value times elements. Multiplication: matrixA*matrixB Returns matrixA matrixB. Division: valueA/valueB Returns valueB. Division: list/value Division: Division: volueA times to 2-4 2-4 volueB. 2-3 2-3 volue times each list [] 2-3 valueA list element [] 2-3 times [] 2-3 matrix [] 10-9 times [] 10-9 dMded by [] Returns list elements by value. dMded [] value/list Returns value elements. by list [] listA/listB Returns by listB 2-3 2-3 dMded 2-3 listA elements elements. Tables and dMded Reference [] 2-3 hfformation A-37 Function or Instruction/ Arguments Result Key or Keys/ Menu or Screen/Item Addition: valueA+valueB Returns Addition: list+value Returns list in which value added to each list element. Addition: listA+listB Returns listA elements listB elements. valueA plus valueB. [] is plus 2-3 [] 2-3 Addition: matrixA+matrixB Returns matrixA elements plus matrixB elements. [] Concatenation: string l +string2 Concatenates strings. [] Subtraction: valueA -valueB Subtracts valueB Subtraction: value-list Subtracts value. list elements Subtraction: list- value Subtracts elements. value Subtraction: listA-listB Subtracts listB listA elements. Subtraction: matrixA-matrixB Subtracts matrixB elements from matrixA elements. [] Minutes notation: degrees°minutes seeonds" [_ ' Interprets minutes angle nleasurement as minutes. Seconds notation: degrees°minutes seeonds" ' A-38 Tables 2-3 [] 10-9 two or more 15-6 from val'ueA. [] 2-3 from [] 2-3 from list [] 2-3 elements Interprets seconds angle nleasurenlent as seconds. from [] 2-3 10-9 [ANGLE] ANGLE 2:' @ 2-23 [.] 2-23 and Reference Information TI-83 Menu Map The TI-83 Menu tile keyboard Map layout I begins from at the top-left left to right. I (Func Plotl Plot3 ",,YI= ",,Y2= ",Y3= ",,Y4= ...... ",,Y9= ",,YO= mode) Plot2 and follows and settings are shown, I (Pol mode) Plotl Plot2 Plot3 ",rl= ",r2= ",r3= ",r4= ",rS= ",r6= ",X6T= Y6T= (Seq mode) Plotl Plot2 Plot3 nMin=l ",u(n)= u(nMin)= ",v(n)= v(nMin)= ",w(n)= w(nMin)= [_][STATPLOT] __1 I I I STAT PLOTS l:Plotl...Off _:L LI L2 m 2:Plot2...Off _:L LI L2 _ 3:Plot3...Off _:L LI L2 m 4:PlotsOff 5:PlotsOn I (PRGM editor) PLOTS l:Plotl( 2:Plot2( 3:Plot3( 4:PlotsOff 5:PlotsOn I I (PRGM editor) TYPE l:Scatter 2:xyLine 3:Histogram 4:ModBoxplot 5:Boxplot 6:NormProbPlot I I (Par mode) WINDOW Tmin=O Tmax=_2 (Pol mode) WINDOW Omin=O Omax=_2 Xscl=1 Ymin= 10 Ymax=10 Yscl=1 Xres=1 Tstep=_/24 Xmin= 10 Xmax=iO Xscl=1 Ymin= 10 Ymax=iO Yscl=1 Ostep=_/24 Xmin= 10 Xmax=iO Xscl=1 Ymin= 10 Ymax=iO Yscl=1 [TBLSET] iI TABLE SETUP TblStart=O (PRGM editor) MARK Z:D 2:+ 3:, I (Func mode) WINDOW Xmin= i0 Xmax=lO ATbI=I Indpnt:Auto Depend:Auto of the keyboard values I (Par mode) Plotl Plot2 Plot3 ",XIT= YIT= ",X2T= Y2T= [STATPLOT] corner Default (Seq mode) WINDOW nMin=1 nMax=10 PlotStart=1 PlotStep=1 Xmin= i0 Xmax=lO Xscl=l Ymin= i0 Ymax=lO Yscl=l _ [TBLSET] FI (PRGM editor) TABLE SETUP Ask Ask Indpnt:Auto Depend:Auto Tables Ask Ask and Reference Information A-39 i I I ZOOM 1:ZBox 2:Zoom In 3:Zoom Out 4:ZDecimal 5:ZSquare 6:ZStandard 7:ZTrig 8:Zlnteger 9:ZoomStat O:ZoomFit I MEMORY 1:ZPrevious 2:ZoomSto 3:ZoomRcl 4:SetFactors_ MEMORY (Set Factors,.,) ZOOM FACTORS XFact=4 YFact=4 [FORMAT] I I I (Func/Par/Po] modes) RectGC PolarGC CoordOn CoordOff GridOff GridOn AxesOn AxesOff LabelOff LabelOn ExprOn ExprOff (Seq mode) Time Web uv vw uw RectGC PolarGC CoordOn CoordOff GridOff GridOn AxesOn AxesOff LabelOff LabelOn ExprOn ExprOff [CALC] I I (Func mode) CALCULATE 1:value 2:zero 3:minimum 4:maximum 5:intersect 6:dy/dx 7:if(x)dx (Par mode) CALCULATE 1:value 2:dy/dx 3:dy/dt 4:dx/dt I (Pol mode) CALCULATE 1:value 2:dy/dx 3:dr/dO H Normal Sci Eng Float 0123456789 Radian Degree Func Par Pol Seq Connected Dot Sequential Simul Real a+bt re^Bt Full Horiz G T A-40 Tables and Reference Information I (Seq mode) CALCULATE 1:value I SEND 1:A11+... 2:All-... 3:Prgm... 4:List._ 5:Lists to 6:GDL 7:Pic._ 8:Matrix... 9:Real._ I RECEIVE 1:Receive T182... O:Complex._ A:Y Vars... B:String._ C:Back Up... i I EDIT 1:Edit._ 2:SortA( 3:SortD( 4:ClrList 5:SetUpEditor I I CALC 1:1Var Stats 2:2 Var Stats 3:Med Med 4:LinReg(ax+b) 5:QuadReg 6:CubicReg 7:QuartReg 8:LinReg(a+bx) 9:LnReg O:ExpReg A:PwrReg B:Logistic C:SinReg TESTS I:Z Test... 2:T Test... 3:2 SampZTest... 4:2 SampTTest... 5:1 PropZTest... 6:2 PropZTest... 7:Zlnterval... 8:Tlnterval... 9:2 SampZlnt._ 0:2 SampTlnt._ A:I PropZlnt._ B:2 PropZlnt._ C:Z 2 Test... D:2 SampFTest._ E:LinRegTTest... F:ANOVA( Tables and Reference Information A-41 [LIST] I 1 I NAMES l:listname 2:listname 3:listname 1 OPS l:SortA( 2:SortD( 3:dim( 4:Fill( 5:seq( 6:cumSum( 7:AList( 8:Select( 9:augment( O:List_matr( A:Matr_list( B:L I I 1 MATH l:_Frac 2:_Dec 3:3 4:3_r( 5: x_ 6:fMin( 7:fMax( 8:nDeriv( 9:fnlnt( O:Solver._ MATH 1:min( 2:max( 3:mean( 4:median( 5:sum( 6:prod( 7:stdDev( 8:variance( 1 NUM l:abs( 2:round( 3:iPart( 4:fPart( 5:int( 6:min( 7:max( 8:Icm( 9:gcd( CPX 1:conj( 2:real( 3:imag( 4:angle( 5:abs( 6:_Rect 7:_Polar [2nd][TEST] I I TEST i:= 2:_ 3:> 4:> 5:< LOGIC l:and 2:or 3:xor 4:not( 6:< A-42 Tables and Reference Information 1 PRB 1:rand 2:nPr 3:nCr 4:! 5:randlnt( 6:randNorm( 7:randBin( I I NAMES I:[A] 2:[B] 3:[C] 4:[D] 5:[E] 6:[F] 7:[G] 8:[H] 9:[I] O:[J] I I r_q [AN_LE] I MATH 1:det( 2: I 3:dim( 4:Fill( 5:identity( 6:randM( 7:augment( 8:Matr_list( 9:List_matr( O:cumSum( A:ref( B:rref( C:rewSwap( D:row+( E:*row( F:*row+( EDIT l:name 2:na_ 2:na_e I 6:Repeat 7:End 8:Pause 9:Lbl O:Goto A:IS>( B:DS<( C:Menu( D:prgm EDIT I:[A] 2:[B] 3:[C] 4:[D] 5:[E] 6:[F] 7:[G] 8:[H] 9:[I] O:[J] I EXEC l:nan_ (PRGM editor) CTL 1:If 2:Then 3:Else 4:For( 5:While F-- I 1: ° 2:' 3: r 4:_DMS 5:R_Pr( 6:R_PO( 7:P_Rx( 8:P_Ry( I NEW 1:Create I (PRGM editor) I/0 1:Input 2:Prompt 3:Disp 4:DispGraph 5:DispTable 6:Output( 7:getKey 8:ClrHeme 9:ClrTable O:GetCalc( A:Get( B:Send( ANGLE New I (PRGM editor) EXEC m:name 2:name E:Return F:Stop G:DelVar H:GraphStyle( Tables and Reference Information A-43 I I DRAW l:C]rDraw 2:Line( 3:Horizontal 4:Vertical 5:Tangent( 6:DrawF 7:Shade( 8:Drawlnv 9:Circle( O:Text( A:Pen I POINTS 1:Pt On( 2:Pt Off( 3:Pt Change( 4:Pxl On( 5:Pxl Off( 6:Pxl Change( 7:pxl Test( 1 STO 1:StorePic 2:RecallPic 3:StoreGDB 4:RecalIGDB I VARS 1:Window._ 2:Zoom._ 3:GDB... 4:Picture._ 5:Statistics... 6:Table... 7:String._ Y VARS 1:Function._ 2:Parametric... 3:Polar._ 4:On/Off... VARS i I I (Window...) X/Y l:Xmin 2:Xmax 3:Xscl 4:Ymin 5:Ymax 6:Yscl 7:Xres 8:AX 9:AY 0:XFact A:YFact A-44 Tables I (Window...) T/e 1:Tmin 2:Tmax 3:Tstep 4:emin 5:6max (Window...) U/V/W 1:u(nMin) 2:v(nMin) 3:w(nMin) 4:nMin 5:nMax 6:6step 6:PlotStart 7:PlotStep and Reference Information VARS I I I (Zoom...) ZX/ZY (Zoom...) ZT/Ze (Zoom...) ZU l:ZXmin 2:ZXmax l:ZTmin 2:ZTmax l:Zu(nMin) 2:Zv(nMin) 3:ZXscl 4:ZYmin 5:ZYmax 3:ZTstep 4:ZOmin 5:[email protected] 3:Zw(nMin) 4:ZnMin 5:ZnMax 6:ZYscl 7:ZXres 6:[email protected] 6:ZPlotStart 7:ZPlotStep VARS I I (GDB...) GRAPH DATABASE I:GDB1 2:GDB2 (Picture...) PICTURE 1:Picl 2:Pic2 9:GDB9 O:GDBO 9:Pic9 O:PicO VARS I (Statistics...) XY l:n 2:_ 3:Sx 4:_x I (Statistics...) Z I:Zx 2:Zx 2 3:Zy 4:Zy 5:Zxy 6:Sy 7:_y 8:minX 9:maxX O:minY 2 I I I (Statistics...) EQ (Statistics...) TEST (Statistics...) PTS I:RegEQ 2:a 3:b 1:p 2:z 3:t i:xl 2:yi 3:x2 4:c 5:d 4:Z 2 5:F 4:y2 5:x3 6:e 7:r 8:r 2 9:R 2 6:df 7:# 8:#1 9:#2 O:s 6:y3 7:Q1 8:Med 9:Q3 A:maxY A:_I B:_2 C:Sxl D:Sx2 E:Sxp F:nl G:n2 H:lower I:upper Tables and Reference Information A-45 VARS I I (Table...) TABLE 1:TblStart (String...) STRING 1:Strl 2:ATbl 2:Str2 3:TbIInput 3:Str3 4:Str4 9:Str9 O:StrO Y VARS I I I (Function...) FUNCTION I:YI 2:Y2 3:Y3 4:Y4 (Parametric...) PARAMETRIC I:XIT 2:YIT 3:X2T 4:Y2T I (Polar...) POLAR i:ri 2:r2 3:r3 4:r4 5:r5 O:Yo A-46 B:Y6T Tables and Reference Information I (On/Off._) ON/OFF 1:FnOn 2:FnOff [_ [DISTR] I I I DISTR 1:normalpdf( 2:normalcdf( 3:invNorm( 4:tpdf( 5:tcdf( 6:z2pdf( 7:z2cdf( 8:Fpdf( 9:Fcdf( O:binompdf( A:binomcdf( DRAW 1:ShadeNorm( 2:Shade t( 3:Shadez2( 4:ShadeF( B:poissonpdf( C:poissoncdf( D:geometpdf( E:geometcdf( I_ [FINANCE] I I CALC I:TVM Solver... 2:tvm Pmt 3:tvm I% 4:tvm PV 5:tvm N 6:tvm FV 7:npv( 8:irr( 9:hal( O:XPrn( A:glnt( B:_Nom( C:_Eff( D:dbd( E:Pmt End F:Pmt Bgn I VARS I:N 2:1% 3:PV 4:PMT 5:FV 6:P/Y 7:C/Y Tables and Reference Information A-47 MEMORY [MEM] i--J I I MEMORY l:Check RAM_ 2:Delete._ 3:Clear Entries 4:ClrAllLists 5:Reset... MEMORY I I (Check RAM...) MEM FREE 27225 Real 15 (Delete...) DELETE FROM... 1:All... Complex List Matrix Y Vars 2:Real._ 3:Complex._ 4:List... 5:Matrix... 0 0 0 240 Prgm Pic GDB 14 0 0 String 0 6:Y Vars... 7:Prgm... 8:Pic... 9:GDB... O:String... (Reset...) I Resetting erases all 12_]_ALOG] I (All Memory...) RESET MEMORY 1:No 2:Reset (Defaults...) RESET DEFAULTS 1:No 2:Reset memory data CATALOG cosh( cosh-l( Equ_String( expr( and inString( programs• length( sinh( sinh-1( String_Equ( sub( tanh( tanh-1( A-48 Tables and Reference Information I (Reset...) RESET 1:All Memory... 2:Defaults._ Variables User Variables The TI-83 Some uses variables the variables listed are restricted below to specific in various data ways, types. The variables A through Z and 0 are defined as real or complex numbers. You may store to them. The TI-83 can update X, Y, R, 0, and T dm'ing graphing, so you may want to avoid using these varial)les to store nongraphing data. The variables (list nalnes) L1 through LS are restricted lists; you cannot store another type of data to them. The wu'iables (matrix names) to matrices; you cannot store The vm'iables Pie1 through pictures; you cannot store to [A] through [J] are restricted another type of data to them, Pie9 and Pic0 are restricted to another type of data to them. The variables GDB1 through GDB9 and GDB0 are restricted to graph databases; you cannot store another type of data to them, The variables Strl through Str9 and StrO m'e restricted to strings; you cannot store another type of data to them. You can store any string of characters, functions, instructions, or vm'iables to the functions Yn, (1 through 9, and 0), XnT/YnT (1 through 6), rn (1 through 6), u(n), v(n), and w(n) directly or through the Y= editor. The validity string is determined when the function is evaluated. System Variables of the The variables below nmst be real numbers. You may store to them. Since the TI-83 can update some of them, as the result of a ZOOM, for example, you nlay want to avoid using these variables to store nongraphing data. • Xmin, Xmax, Xsel, AX, XFact, Tstep, PlotStart, nMin, and ()tiler window variables, • ZXmin, ZXmax, ZXscl, ZTstep, ZPIotStart, other ZOOM variables. The variables cannot store below are resetwed to them. Zu(nMin), for use by the TI-83. and You n, _, Sx, _x, minX, maxX, Ey, Ey 2, Exy, a, b, e, RegEQ, xl, x2, yl, z, t, F, Z2, p, xl, Sxl, nl, lower, upper, r2, R 2 aft(] other statistical variables, Tables and Reference hfformation A-49 Statistics Formulas This section contains statistics fornmlas for the Logistic and SinReg regressions, ANOVA, 2-SampFTest, and 2-SampTTest. Logistic The logistic regression algorithm applies nonlinear t_cursive least-squares techniques to optimize the following cost function: N j :z(-i÷o>, 4 c which is the sunl of the squares where: of the residual errors, x = the independent variable list y = the dependent variable list N = the dimension of the lists This technique attempts to estimate the constants e t_cursively to make J as small as possible. SinReg a, b, and The sine regression algorithm applies nonlinear recut_ive least-squares techniques to optimize the following cost function: N J= E[a i=1 siyt(bxi + e)+ d- yi]2 which is the sunl of the squares where: of the residual errors, x = the independent variable list y = the dependent variable list N = the dimension of the lists This technique attempts to recursively estimate the c()nstants a, b, c, and d to make J as small as possible. A-50 Tables and Reference Inforination ANOVA( The ANOVA F F statistic is: Factor MS' Error MS The mean Factor Error squares MS' MS' = The sum are: (MS) that Factor SS Factor df Error SS Error df of squares make (SS) that up F are: make up the mean squares I Factor SS = E ni(xi - 2) 2 i=1 I Error SS = E (ni - 1)Sxi 2 i=l The degrees of freedoln dfthat make up the mean squares are: Factor df = I - 1 = numerator df for V I Ermrdf where: = E i=l (hi - 1) = denolninator I = number _:i Sxi if)r = the length _: = the mean and F of populations = the mean of each list = the standard deviation ni Tables df of each of each list list of all lists Reference Information A-51 Below 2-SampFTest for the 2-SampFTest. is the definition Sxl, Sx2 = Sample nl-1 standard and n2-1 deviations degrees having of freedom df, respectively. F = F-statistic dr(x, nl-1 , n2-1 ) [ Sx2 ) = Fpdf( ) with fl'eedom p = reportedp 2-SampFTest p = i f(x, for the alternative degrees of df, hi-1 , and n2-1 wdue hypothesis (s 1 > (s 2. hypothesis (_1< (_2- hypothesis (_1 :_ (_2.Limits nl - 1,n 2 - 1)dx 2-SampFTest for the alternative F p = ff(x,n 0 1-1,n 2-1)dx 2-SampFTest for the alternative nmst satisfy the following: Lb nd /92= f f(x'nl0 where: l'n2-1)dx= [Lbnd, Ubnd] ff(x,n U_,_ 1-1,n 2-1)dx = lower and upper limits The F-statistic is used as the bound producing the smallest integral. The reinaining bound is selected to achieve the preceding integral's equality relationship. A-52 Tables and Reference Information 2-SampTTest The following is the definition for the 2-SampTTest, The two-sample t statistic with degrees of freedom dfis: t= Xl--X2 s where tile computation whether the variances pooled: S = ]_/$2b'12q V nl d f- l nl-lk of S and df are dependent are pooled. If the variances on are not SX22 n2 S:t;12 + ,gXd2 )2 nl } nz-lk l (s.s/,, nz ) otherwise: (n I - 1)SXl _:t;p = 2 + (n 2 - 1)SX2 2 df S = J1 + 1 Sxp V)'_I n2 df = nl+n2-2 and Sxp is the pooled Tables variance. and Reference Information A-53 Financial This Formulas section contains amortization, Time Value Money cash of financial flow, fommlan interest-rate for computing conve_\sions, time and days value of money, between dates. i=[e(y×ln(x+l))]_l where: PMT € 0 y = C/Y + P/Y x = (.01 ×1%) = compounding P/Y = payment I% = interest i = (-FV + PV)( 1+ N) _ PMT = 0 The used to compute 0 = PV + PMT 1% = 100 × C/Y where: periods periods rate per per year per year yem" 1 where: iteration + C/Y C/Y x G i [1-(1+i) i: NI+FV×(I+i) N × [e(Y × ln(x + 1)) _ 1] x = i y = P/Y+C/Y G i = l+i×k where: k = 0 for end-of-period payments k = 1 for beginning-of-period N- where: [PMTxGi+PVxi) ln(1 + i) i € 0 N = -(PV + FV) + PMT where: A-54 Tables and Reference i = 0 Information payments PMT=-ix[PV_ Gi PV+FV (I+i)N- [ where: PMT i € 0 = -(PV + FV) where: + N i = 0 J where: + PMT where: PMT x Gi i × N) i = 0 PMT i x G i where: FV = -(PV where: (l+i) i € 0 PV = -(FV FV ] lJ (l+i)N× ( PV-_ PMT×Gi.) i € 0 + PMT x N) i = 0 Tables and Reference Information A-55 Amortization If computing Let hal(O) Iterate bal(), pint2 = npmt = RND(PV) fronl m = 1 to pint2 Lm = RND[RND12(-i x bal(m - 1))] hal(m) = bal(m - 1) -[m+ RND(PMT) then: hal() E Prn( Z Int( where: = hal(pint2) ) = bal(pmt2) ) = (pint2 RND - bal(pmtl) - pmtl = round + 1) x RND(PMT) the display- decimal RND12 = round places A-56 Tables and Reference Information to the number selected to 12 decimal Balance, principal, and interest values of PMT, PV, I°/o,and pmtl - Z Prn( places are dependent and pint2. on the ) of Cash Flow N npv() = CF0 + _CFj(1 j=l where:Sj= ni +/) & _(1 - (1 _/) rq) J >-1 j= 0 Net present value is dependent on the values of the initial cash flow (CFII), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i), irr() = 100 × i, where i satisfies npv() =0 Internal rate of return is dependent on the values of the initial c_h flow (CFo) and subsequent cash flow. (CFj), i = I% + 100 Interest Rate Conversions VEff( ) = 100 × (e cT × Zn(x+ 1) _ 1) where: x = ,01 x NOM+ CP _Nom( ) = 100 × CP × [ei + cP × z,.(x+ 1)_ 1] where: x = ,01 × EFT" EFF = effective rate CP = compounding NOM = nominal rote Tables and Reference periods Information A-57 Daysbetween Withthedbd(function, youcanenterorcompute adate Dates within the range Jan. 1, 1950, through Actual/actual day-count number of days per month Dec. 31, 2049. method (assunles and actual number actual of day-s per year): dbd( (days Number between Number of Days dates) of Days = II - Number I = (Y1-YB) of Days I × 365 + (number + DT1 of days MB to M1) (Y1 - YB) + 4 Number of Day-s II = (Y2-YB) x 365 + (number + DT2 of days MB to 11//2) (Y2 - YB) + 4 where: M1 DT1 = month of first = day of first date date Y1 = year of first date M2 = month of second DT2 = day of second Y2 = year = base month DB = base day (1) YB = base A-58 Tables and Reference Information date of second MB year date date (January) (first year _ter leap year) B Contents GeneralInformation Batte_" Infommtion ...................................... In Case of Difficulty ..................................... Error Conditions ......................................... Accuracy Infomlation .................................... Support and Sep_iee Information ......................... Warranty Infornlation .................................... General Information B-2 B-4 B-5 B-10 B-12 B-13 B-1 Battery Information When to Replace the Batteries The TI-83 uses five batteries: and one lithium auxilimTF power AAA batteries. When the battery the TI-83 displays _Jour four AAA alkaline batteries battery-. The lithium battery pro_qdes to retain menlot T while you replace voltage level this message the drops below a usable level, when you turn on the unit. batteries are low. Reco_r_end change o? batteries. Alter this message is first displayed, you can expect the batteries to function for about one or two weeks, depending on usage. (This one-week to two-week period is based on tests with alkaline batteries; the performance of other kinds of batteries may vm3z.) The time you the you low-battery message continues to be displayed each you turn on the unit until you replace the batteries. If do not replace the batteries within about two weeks, calculator may turn off by itself or fail to turn on until install new batteries. Replace Effects of Replacing Batteries the Battery Precautions Take these precautions • • • • • General batte_y- eve_3z three or four years. Do not remove both types of batteries (AAA and lithium auxiliat_F) at the same time. Do not allow the batteries to lose power completely. If you follow these guidelines and the steps for replacing batteries on page B-3, you can replace either type of batter T without losing any information in memo_7. • B-2 the lithimn when replacing batteries. Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries. Do not mix rechm'geable and nonrechargeable batteries. Install batteries according to polarity (+ and -) diagrams. Do not place nonreehargeable batteries in a battery recharger. Properly dispose of used batteries immediately. Do not leave them within the reach of children. Do not incinerate batteries. hfformation Replacing Batteries the To replace the batteries, follow these steps. 1. Turn offthe calculator. Replacethe slide cover over the keybom'd to avoid inadvertently turning on the calculator. Turn the back of the calculator toward you. Hold the cMeulator upright. Place your thumb on the oval indentation on the battetsz cover. Push down and toward you to slide the cover al_out IAinch (6 nlnl). Lift off the cover to expose the batte_3z eolnpartment. Note: To avoid loss of infornmtion memory, you nmst turn off the remove the AAA batteries and simultaneously. 3. Replace all four time. Or, replace stored calculator. the lithium AAA alkaline batteries the lithium batte_Ty-. in Do not battery at the same • To replace the AAA alkaline batteries, remove all four discharged AAA batteries and install new ones according to the polm'ity (+ and -) diagrams in the batte_3z compartment. • To remove the lithimn batte_Ty-,place your index finger on the battet3z. Insert the tip of a ball-point pen (or similar instrument) under the battery at the small opening provided in the batte_sz compartment. Carefully P_TY" the battetsz upward, holding it with your thumb and finger. (There is a spring that pushes against the underside of the battet3z.) • Install the new batte_sz, + side up, by inserting the batte_3z and gently- snapping it in with your finger. Use a CR1616 or CR1620 (or equivalent) lithium batte_y-. 4. Replace the batte_y- compartment cover. Turn the calculator on and adjust the display contrast, if necessmTy- (step 1; page B-4). General Information B-3 In Case of Difficulty Handling a Difficulty To handle a difficulty, follow these steps. 1. If you cannot see anything nlay need to be adjusted. on the screen, the contrast To darken the screen, press and release [2_, and then press and hold [] until the display- is sufficiently dark. To lighten the screen, press and release [_], and then press and hold [] until the display is sufficiently light. 2. If an error menu is displayed, follow the steps in Chapter 1. Refer to pages B-5 through B-9 for details about specific errors, if necessatT. 3. If a checkerboard cursor ( N ) is displayed, then either you have entered the nlaxinlunl number of characters in a prompt, or nlenlory is full. If nlenlory is full, press [_ [MEM]2 to select 2:Delete, and then delete some items fronl nlenlory (Chapter 18). 4, If the busy indicator (dotted line) is displayed, a graph or program has been paused; the TI-83 is waiting for input, Press [gNT_ to continue or press [_] to break, 5, If the calculator does not seem to work at all, be sure the batteries are flesh and that they are installed properly. Refer to battew information on pages B-2 and B-3. B-4 General Information Error Conditions When the TI-83 detects an error, it displays ERR:message and an error menu. Chapter 1 describes the general steps for eotTeeting errors, This table contains each etTor type, possible causes, and suggestions for correction, Error Type ARCHIVED VAR ARGUMENT BAD GUESS Possible Causes and Suggested Remedies A function or instruction is archived and therefore cannot be executed or edited. [ _se the unto'chive command to mmrehive the variable before using it. A function or instruction does not have the co_Tect number of arguments. See Appendix A and the appropriate chapter. • In a CALC operation, you specified a Guess that is not between Left Bound and Right Bound. • For the solve( function or the equation solver, you specified a guess that is not between lower and upper. • Your guess and severM points around it are undefined. Exa]nine a graph of the function. If the equation has a solution, change the bounds and/or the initial guess. BOUND • In a CALC operation or with Select(, you defined Left Bound > Right Bound, • In fMin(, fMax(, solve(, or the equation entered lower >_upper. solver, you BREAK You pressed the [ON]key to break execution of a prograln, to halt a DRAW instruction, or to stop evaluation of an expression. DATATYPE You entered a value or variable that is the wrong data type. • For a function (including implied lnultiplication) or an instruction, you entered an argument that is an invalid data type, such _ts a complex number where a real number is required. See Appendix A and the appropriate chapter. • In an editor, you entered a type that is not allowed, such as a matrix entered as an element in the stat list editor. See the appropriate chapter. • You attelnpted to store to an incorrect a nmtrix, to a list. data type, such as DIMMISMATCH You attempted to perform an operation that references more than one list or lnatrix, but the dimensions do not lnateh. DIVIDE BY 0 • You attempted to dixqde by zero. This error is not returned during graphing. The TI-83 allows for undefined values on a graph. • You attelnpted a linear regression with a vertical General Infornmtion line. B-5 Error Type Possible DOMAIN • You specified an argument to a function or instruction outside the wdid range, This elTor is not returned during graphing. The TI-83 allows for undefined values on a graph, See Appendix A and tile appropriate chapter. • You attempted a logarithmic or power regression with -X or an exponential or power regression with a -Y. • You attempted pint2 < pint1. Duplicate Name Error in Xmit Causes and Suggested to compute A variable you attempted because a variable with receiving unit. Remedies a XPrn( or Xlnt( with to transmit cannot be translnitted that name already exists in the • The TI-83 was unable to transmit an item. Check to see that the cable is firnfly connected to both units and that the receiving unit is in receive mode. • You pressed • You attempted TI-83. • You attempted to transfer data 1.6) from a TI-83 to a TI-82. • You attempted a TI-82 without [_ to break to perform during transmission. a backup (()tiler from than a TI-82 to a kl through to transfer kl through L6 from a TI-83 to using 5:Lists to TI82 on the LINK SEND nlenu, ILLEGAL NEST You attempted to use an invalid function a function, such as seq( within e_ression INCREMENT • The increment in seq( is 0 or has the wrong sign. This error is not returned during graphing. The TI-83 allows for undefined values on a graph, • The increment • You attempted to refel_nce a variable or use a function where it is not valid. For example, Yn cannot reference Y, Xmin, AX, or TblStart, • You attempted was transferred INVALID in a For( loop in an argument for seq(. is 0, to reference a variable or function that from the TI-82 and is not valid for the TI-S3. For example, you may have transfen'ed U n-1 to the TI-83 from the TI-82 and then tried to reference it. • B-6 General In Seq mode, you attempted to graph a phase without defining both equations of the phase hfformation plot plot. to Error Type Possible Causes and Suggested Remedies INVALID (cont.) • In Seq nlode, you attempted to graph a recursive sequence without having input the correct number initial conditions. • In Seq mode, you attempted than (n-l) or (n-2). to reference of terms other You attelnpted to designate a graph style that is invalid within the eutTent graph mode. You attempted to use Select{ without having selected (turned on) at least one xyLine or scatter plot. INVALIDDIM You specified dimensions for an argument appropriate for the operation. You specified a list dimension as something an integer between 1 and 999. that are not other than You specified a matrix dimension as something than an integer between 1 and 99. You attempted ITERATIONS to invert a matrix other that is not square. • The solve( function or the equation solver has exceeded the nmximum number of permitted iterations. Examine a graph of the function. If the equation has a solution, change the bounds, or the initial guess, or both. • irr( has exceeded the nmxinmm number of permitted iterations. • When computing was exceeded. 1%,the nl_Lxinlunl number is not defined of iterations LABEL The label in the Goto instruction instruction in the program. with a Lbl MEMORY Memory is insufficient to perform the instruction or function. You nmst delete items from memory (Chapter before executing the instruction or function. 18) Reeursive problems return this error; for example, graphing the equation YI=Y1. Branching out of an If/Then, For(, While, or Repeat loop with a Goto also can return this error because the End statelnent that terminates the loop is never reached. General Information B-7 Error Type MemoryFull Possible Causes and Suggested Remedies • You are unable to transmit an item because tile receiving unit's available lnelnol_y- is insufficient. You lnay skip the iteln or exit receive triode, • During a lnelnol_y- backup, the receiving unit's available nlenlory is insufficient to receive all itelns in the sending unit's lnelnot_yL A lnessage indicates the number of bytes the sending unit nmst delete to do the lnetnol_- backup. Delete items and try again. MODE You attempted to store to a window variable in another graphing mode or to perform an instruction while in the wrong nlode; for exaInple, Drawlnv in a graphing nlode other than Func. .............................. The saiv;{ function a sign change. _;i the equation ...... • You atteinpted to compute I%when FV, (N*PMT), and PV are all _>O, or when FV, (N*PMT), and PV are all _<O. • You attempted to eonlpute irr( when neither CFList nor CFO is > O, or when neither CFList nor CFO is < O. NONREAL ANS In Real mode, the result of a calculation yielded a complex result. This error is not returned during graphing. The TI-83 allows fox"undefined values oil a graph. OVERFLOW You attempted to enter, or you have calculated, a number that is beyond the range of the calculator. This error is not returned during graphing. Tile TI-83 allows for undefined wdues on a graph. RESERVED You attempted to use a wsteln See Appendix A. SINGULAR MAT • A singular matrix (determinant argument for % variable inappropriately. = 0) is not valid as the • The 8inReg instruction or a polynomial regression generated a singular matrix (determinant = 0) because could not find a solution, or a solution does not exist. This error is not returned during graphing. allows for undefined values on a graph. B-8 General hfformation Tile TI-83 it Error Type Possible Causes and Suggested Remedies SINGULARITY expression ill the solve( function or the equation solver contains a singularity (a point at which the function is not defined). Examine a graph of the function. If the equation h_s a solution, change the bounds or the initial guess or both. STAT You attempted appropriate. • Statistical • Ned-Ned partition. a stat calculation analyses with lists that are not must have at least two data points. must have at least three points in each • When you use a frequency list, its elements must be _>0. • (Xmax - Xmin) / Xscl nmst be <_47 for a histogram. STAT Pt_OT Y0u atte;_pted to display a graph when a stat plot that uses an undefined list is turned on. SYNTAX The connnand contains a syntax error. Look for lnisplaced functions, arguments, parentheses, or colnnlas. See Appendix A and the appropriate chapter, TOL NOT MET You requested a tolerance retum an accurate result. UNDEFINED You referenced a variable that is not currently defined. For example, you referenced a stat variable when there is no current calculation because a list has been edited, or you referenced a variable when the variable is not valid for the current calculation, such as a 'after Med-Med. WINDOW RANGE A probleln exists with the window variables. • You defined Xmax _<Xmin or Ymax _<Ymin. • You defined • You attempted • You defined to which the algorithln cannot 0max _<0min and 0step > 0 (or xqce versa). to define Tstep=0. Tmax _<Train and Tstep > 0 (or vice versa). • Window variables are too SLUM1 or too large to graph correctly. You may have attempted to zoom in or zoom out to a point that exceeds tile TI-83's nulnerical range. ZOOM • A point or a line, instead • A ZOOM operation of a box, is defined returned in ZBox. a math error. General Information B-9 Accuracy Computational Accuracy Information To maximize accuracy-, internally than it displays. using up to 14 digits with the TI-83 carries more digits Values m_ stored in nlemo_a two-digit exponent. • You can store a value in the window to 10 digits (12 for Xscl, Yscl, Tstep, vm'iables using and 0step). • Displayed values are rounded as specified by the mode setting with a nlaxinmln of 10 digits and a two-digit exponent. • ReflEO displays up to 14 digits in Float mode. [ Mng a fixed-decilnal setting other than Float causes ReflEO results to be rounded and stored with the specified number of decimal places. Graphing Xmin is the center Accuracy of the next-to-the-rightmost pixel. (The rightmost reserved for the busy indicator,) AX is the distance between the centers of two adjacent pixels. • • of the leffmost pixel, up Xmax is the center In Full screen mode, AX is calculated zks (Xmax - Xmin) / 94. In G-T split-screen mode, calculated as (Xmax - Xmin) / 46. pixel is AX is If you enter a value ff)r AX from the home screen or a program in Full screen mode, Xmax is calculated as Xmin + AX * 94. In G-T split-screen mode, Xmax is calculated as Xmin + AX * 46, Ymin is the center of the next-to-the-bottom pixel; Ymax is the center of the top pixel. AY is the distance between the centers of two adjacent pixels. • • B-IO General In Full screen mode, AY is calculated as (Ymax - Ymin) / 62. In Horiz split-screen nlode, AYis cMculated as (Ymax - Ymin) / 30. In G-T split-screen mode, AY is c'Mculated as (Ymax - Ymin) / 50. If you enter a vMue for AYfronl the home screen or a program in Full screen mode, Ymax is calculated as Ymin + AY * 62. In Horiz split-screen nlode, Ymax is eMculated as Ymin + AY * 30. In G-T split-screen nlode, Ymax is calculated _ksYmin + AY* 50, Information Cursor coordinates aredisplayed aseight-character numbers (whichmayinclude anegative sign,decimal point,andexponent) whenFloatmode isselected. XandY areupdated withanlaxinmln accuracy ofeightdigits. minimum and maximum on the CALCULATE are menu calculated with a tolerance of 1E-5; _f(x)dx is calculated at 1E-3. Therefore, the result displayed nlay not be accurate to 'all eight displayed digits. For most functions, at least five accurate digits exist. For fMin(, fMax(, and fntnt( on the MATH menu and solve( in the CATALOG, the tolerance can be specified. Function Limits Function sn Range of Input Values cos. " .................... 0 sin -1 2a', COS-1 X ........... -1 < x <_1 ....... ............................... ex -10100< x -<230.25850929940 1_ -10 i00 < x < 100 sinh x, cosh w tanh x Ixl _<230.25850929940 Ixl < 10 i°° sinh :_ x Ixl < 5 x 109!_ .............................. cosh-1 .%, l_<x < 5x 1() 9!_ tanh :_ x ........................................................... -1 <x< ......................... 1 _x (real lnode) _X (complex Function Results 0 < x < 10100 mode) Ixl < 10 t°° x! -.5 -< x -< 69, where x is a multiple Function 1 1 tan- x -90 Range of Result o o to 90 or-_/2 ) cos-1x 0° to 180° t0_/2 of .5 (radians) or 0 to x (radians) General Information B-11 Support and Service Information Product Support Customers For general in the U.S., Canada, Puerto Rico, and the Virgin Islands questions, contact questions, phone: Customers Contact Instrunmnts 1-800-TI-CARES [email protected] phone: e-mail: For technical Support: Texas Customer Support: (1-800-842-2737) call the Progrannning Assistance Group of Custonler 1-972-917-8324 outside the U.S., Canada, Puerto Rico, and the Virgin Islands TI by e-mail or visit the TI calculator home page on the World Wide Web. [email protected] education.ti.com e-mail: Internet: Product Service Customers in the U.S. and Canada Only Always contact for service. Customers Texas Instrmnents Customer Support before returning a product outside the U.S. and Canada Refer to the leaflet enclosed Instruments retaileddistributor. with this product or contact your local Texas your local Texas Other TI Products and Services Visit the TI calculator honle page on the World Wide Web. education.ti.com Refer to the leaflet enclosed Instruments retailer/distributor. B-12 General Information with this product or contact Warranty Information Customersin the U,S.and CanadaOnly One-Year Limited Warranty for Electronic Product This Texas Instruments ("TI") electronic purchaser and user of the product. product warranty extends only to the original Warranty Duration. This TI electronic product is warranted to the original purchaser for a period of one (1) year fl'om the original purchase date. Warranty (;overage. This TI electronic product is warranted against defective rnaterials and construction. THIS WARRANTY IS VOID IF THE PRODUCT HAS BEEN DAMAGED BY ACCIDENT OR UNREASONABLE USE, NEGLECT, IMPROPER SERVICE, OR OTHER CAUSES NOT ARISING OUT OF DEFECTS IN MATERIALS OR CONSTRUCTION. Warranty Disclaimers. ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE, INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE LIMITED IN DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS INSTRUMENTS SHALL NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL OR CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE CONSUMER OR ANY OTHER USER. Sortie states/provinces do not allow the exclusion or limitation consequential damages, so the above limitations or exclusions of implied warranties or may not apply to you. Legal Remedies. This warranty gives you specific legal rights, mid you may also have other rights that vat_ fl'om state to state or province to province. Warranty Performance. [)tiring the above one (1) year warranty period, your defective product will be either repaired or replaced with a reconditioned model of an equivalent quality (at TI's option) when the product is returned, postage prepaid, to Texas Instruments Service Facility. The warranty of the repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than the postage requirement, no charge will be made for such repair and/or replacernent. TI strongly recommends that you insure the product for value prior to rnailing. Software. Software is licensed, not sold. TI and its licensom do not warrant that the software will be free fl_m errom or rneet your specific requirements. All software is provided "AS IS." Copyright. The software protected by copyright. and any docurnentation supplied with this product General are Information B-13 Australia One-Year & New Zealand Limited Customers Warranty only for Commercial This Texas Instruments electronic product original purchaser and user of the product. Electronic wmTanty Product extends only to the Warranty Duration. This Tex_Ls Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This against defective materials product luks been damaged set_ice, or other causes not Texas Instruments electronic product is warranted and construction. This warranty is void if the by accident or unreasonable use, neglect, improper arising out of defects in materials or construction. Warranty Disclaimers. Any implied warranties arising out of this sale, including but not limited to tile implied warranties of merchantability and fitness for a particular purpose, are limited in duration to tile above one-year period. Texas Instruments shall not be liable for loss of use of the product or other incidental or consequential costs, expenses, or danlages incm'red by the consuiner or any other user. Sonic jurisdictions do not allow the exclusion or limitation of implied warranties or consequential damages, so the al)ove limitations or exclusions nlay not apply to you. Legal Remedies. also have other This rights warranty gives you specific that vm_- from jurisdiction legal rights, to jm'isdiction. and you nlay Warranty Performance. Dm'ing the above one (1) year warranty period, your defective product will be either repaired or replaced with a new or reconditioned model of an equivalent quality (at TI's option) when the product is returned to the original point of purchase. The repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than your cost to return the product, no charge will be made for such repair and/or replacement. TI strongly recommends that you insm'e the product for value if you mail it. Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. All software is provided "AS IS." Copyright. are protected The software by copyright. and any documentation supplied with this product All CustomersOutsidethe U.8. 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. B-14 General Information Index + (addition), 2-3, A-38 z2cdf( (chi-square cdf), 13-31, A-3 x2pdf( @hi-square pdf), 13-31, A-4 x2-Test (ehi-square test), 13-22, A-4 : (colon), 6, 16-5 + 3 3_( (concatenation), 15-6, A-38 (cube), 2-6, A-35 (cube root), 2-6, A-35 ° / = (degrees notation), 2-3, A-34 (division), 2-3, A-37 (equal-to relational test), 2-25, A-35 ! 0 '. ".. > > (factorial), 2-21, A-34 (graph style, animate), 3-9 (graph style, (lot), 3-9 (graph style, line), 3-9 (greater than), 2-25, A-35 (greater than or equal to), 2-25, A-35 -1 < < {} [] • . (mx.erse), 2-3,o 8-9, 10-10, A-36 (less than), 2-25, A-35 (less than or equal to), 2-25, A-36 (list indicator), 11-4 (matrix indicator), 10-7 (minutes notation), 2-23, A-38 (multiplication), 2-3, A-37 (negation), 1-23, 2-4, A-37 (not equal to), 2-25, A-35 (parentheses), 1-23 (pi), 2-4 (pixel mark), 8-15, 12-34 (pixel mark), 8-15, 12-34 * () [] + (pixel mark), 8-15, 12-34 _::> (plot type, box), 12-33 2m= (plot type, histogram), 12-32 _:>'_" (plot type, modified box), 12-32 __ (plot type, normal probability), 12-33 ^ (power), ~-3, A-36, A-37 10"( (power often), 2-#,A-37 ×/ (root), 2-6, A-35 2 _( --> .... (seconds (square), notation), 2-23, A-38 2-3, A-36 (square root), 2-3, A-37 Store, 1-1]-_, A-28 (string indicator), 15-3 (subtraction), 2-3, A-38 -Aa+bl (rectangular complex 1-12, 2-16, A-3 above graph style(N), 3-9 abs( (absolute value), 10-10,A-2 mode), 2-13, 2-19, accuracy information computational and graphing, B-10 graphing, 3-17 function limits and results, B-11 addition (+), 2-3, A-38 alpha cursor, 1-5 alpha key, 3 alpha-lock, 1-8 alternative hypothesis, amortization hal( (amortization A-3 13-7 balanee), 14-9, calculating schedules, 1]-t-9 fornmla, A-56 Elnt( (sum of interest),14-9, A-12 EPrn( (sum of principal), lJ.t-9, A-19 and (Boolean operator), 2-26, A-2 angle(, 2-19, A-2 ANGLE menu, 2-23 angle modes, 1-11 animate graph style (_), 3-9 ANOVA( (one-way variance analysis), 13-25, A-2 fornmla, A-51 Ans (last answer), 1-18, A-2 APD TM (Automatic Power Down__), applications. ,fee examples, applications areeosine (cos < 0, 2-3 aresine (sin<0, 2-3 aretangent (tan "10, 2-3 1-2 augment(, 10-1J-t, 11-15,A-3 Automatic Power Down _xt(AP[Y_), 1-2 automatic regression equation, 12-22 automatic residual list (RESID), 12-22 axes fommt, sequence graphing, 6-8 axes, displaying (AxesOn, AxesOff), 3-14, A-3 AxesOff, AxesOn, 3-14t, A-3 3-14t, A-3 Index-1 -Bbacking - C (continued) up calculator 19-10 memmTy, 19-4, bal( (amortization balance), batteries, 1-2, B-2 below- graph style (6), 3-9 14-9, A-3 C calculating, 14-8 fornmla, A-57 irr( (internal rate of return), A-13 1-12, 2-16, A-3, 1-12, 2-16, 2-18, A-22 variable coneatenation (+), 15-6, A-38 confidenee intervals, 13-8, 13-16 13-21 - conj((conjugate), 2-18, A-4 Connected (plotting mode), 1-11, A-4 contrast (display), 1-3 convergence, sequence graphing, 6-12 conversions 13-8 14-8, Circle( (draw" circle), & l 1, A-4 Clear Entries, 1&4 , A-4 clearing entries (Clear Entries), 18-4, A-4 all lists (ClrAIIkists), 1&4, A-4 draw3ng (ClrDraw), 8-4, A-4 home screen (ClrHome), 16-20, A-4 list (Clrkist), 12-20, A-4 table (ClrTable), 16-20, A-4 ClrAIIkists (dear all lists), 1&4, A-4 ClrDraw (clear drawing), &4, A-4 ClrHome (clear home screen), 16-20, A-4 Clrkist (elear list), 12-20, A-4 ClrTable (elear table), 16-20, A-4 coefficients of determination (r 2, R2), 12-23 Index-2 re^01), (c/Y), 14-4, 14-14 npv( (net present value), 14-8, A-17 CATALOG, 15-2 CBL 2/CBL System, 16-21, 19-3, A-IO CBR, 16-21, 19-3, A-IO Check RAM (memol_y screen), 18-2 old-square cdf 0_2cdf0,13-31, A-3 old-square pdf (z2pdf(), 13-31, A-4 eld-squm'e test (z2-Test), 13-22, A-4 colon separator (:), 6, 16-5 combinations (nCr), 2-21, A-16 modes (a+bl, A-22 numbers, - CALCULATE metal, 3-25 Calculate output option, 13-6, cash flow" complex compounding-periods-per-year binomcdf(, 13-33, A-3 binompdf(, 13-33, A-3 Boolean logie, 2-26 box pixel mark ([]), 8-15, 12-34 Boxplot plot type (_), 12-33 busy indicator, 1-4 - - )Dec (to deeimal), 2-5, A-5 _DMS (to degree_minute_ seeonds), 2-24, A-7 _Eff (to effeetwe interest rate), 14-12, A-7 Equ_String( (equation-to-string conversion), 15-7, A-8 _Frac (to fraction conversion), 2-5, A-IO kist_matr( (list-to-matrix conversion), 10-14, 11-15, A-14 MatrHist((matrix-to-list conversion), 10-14, 11-16, A-15 )Nora (to nominal interest rate conversion), 14-12, A-16 )Polar (to polar A-19 eonversion), 2-19, PH_x(, P)Ry( (polar-to-reetangular conversion), 2-24, A-21 _Rect (to rectangular conversion), 2-19, A-22 R_Pr(, R_Pe( (reetangular-to-polm" conversion), 2-24, A-23 String)Equ( (string-to-equation conversion), 15-8, A-29 CoordOff, 3-14, A-5 CoordOn, 3-14, A-5 correlation eoefficient (r), 12-23, to 12-27 12-25 cos((cosine), 2-3, A-5 cos'l((areeosine), 2-3, A-5 cosh( (hyperbolic cosine), 15-10, A-5 - D (continued)cosh'l( (hyperbolic A-5 - D (continued) arceosine), cosine (cos(), 2-3, A-5 cross pixel mark (+), 8-15, cube (3), 2-6, A-35 cube root (3_(), 2-6, A-35 15-10, 12-34 CubicReg (cubic A-5 regression), 12-26, cubic regression A-5 (CubicReg), 12-26, eunmlative sum (cumSumO, 10-15, 11-12, A-5 cumSum( (cumulative sum), 10-15, 11-12, A-5 cursors, 1-5, 1-8 C/Y (compounding-periods-per-year variable), 124-Y4,124-124 - D- Data input option, 13-6, 13-7 days between dates (dbd0, 14-13, A-5, A-58 dbd( (days between A-58 dates), 14-13, A-5, _Dec (to decimal conversion), 2-5, A-5 decimal mode (float or fixed), 1-10 decrement and skip (DS<(), 16-14, A-7 definite integral, 2-7, 3-28, 4-8, 5-6 Degree angle mode, 1-11, 2-23, A-6 degrees notation (°), 2-3, A-3J4 DELETE FROM menu, 18-3 delete vm'iable contents (DelVar), 16-15, A-6 DeWar (delete vm'iable contents), 16-15, A-6 DependAsk, 7-3, 7-5, A-6 DependAuto, 7-3, 7-5, A-6 derivative. See numerical derivative det((determinant), 10-12, A-6 determinant (det0, 10-12, A-6 DiagnostieOff, 12-23, A-6 DiagnostieOn, 12-23, A-6 diagnostics display mode(r, r2, R2), 12-23 differentiation, dimensioning - a list or matrix, 10-13, 11-11, A-6 dim((dimension), 10-12, ->dim( (assign dimension), 11-11, A-6 10-12, 11-11, A-6 10-13, Disp (display), 16-18, A-6 DispGraph (display graph), display contrast, 1-3 display cursors, 1-5 16-19, A-7 DispTable (display table), 16-19, A- 7 DISTR (distributions memO, 13-29 DISTR DRAW (distributions drawing menu), 13-35 distribution functions binomedf(, 13-33, A-3 binompdf(, 13-33, A-3 z2cdf(, 13-31, A-3 z2pdf(, 13-31, A-4 Fcdf(, 13-32, A-8 Fpdf(, 13-32, A- 9 geometcdf(, 13-34, A- I O geometpdf(, 13-34, A-11 invNorm(, 13-30, A-12 normalcdf(, 13-30, A-1 7 normalpdf(, 13-29, A-17 poissoncdf(, 13-324, A-99 poissonpdf(, 13-33, A-19 tcdf(, 13-31, A-29 tpdf(, 13-30, A-29 distribution shadh]g instructions Shadex2(, 13-36, A-26 ShadeF(, 13-36, A-27 ShadeNorm(, 13-35, A-27 Shade_t(, 13-36, A-27 dhqsion (/), 2-3, A-37 [)MS (degrees/minutes/seconds notation), 2-23, A-38 _DMS (to degreegminutes/seconds), 2-224, A- 7 entity" dot graph style ('..), 3-9 dot pixel Inark (.), 8-15, 12-324 Dot (plotting mode), 1-11, A-7 DrawF (draw- a function), &9, A-7 2-8, 3-28, 4-8, 5-6 Index-3 - D (continued)drawing - E (continued) on a graph circles (Circle(), 8-11 flmetions and inverses (DrawF, Drawlnv), 8-9 lines (Horizontal, Line(, Vertical), 8-6, 8-7 line segments (Line(), 8-5 pixels (PxI-Change, Pxl-Off, Pxl-On, pxI-Test), 8-16 points (Pt-Change, Pt-Off, Pt-On), 8-14 tangents (Tangent), 8-8 text (Text), 8-12 using Pen, 8-13 Drawlnv (draw" inverse), 8-9, A-7 DRAW menu, 8-3 DRAW instructions, 8-3 - 8-16 [)raw- output option, 13-6 - 13--8 DRAW POINTS menu, 8-14 DRAW STO (draw" store menu), 8-17 dr/d0 operation on a graph, 5-6 DS<( (decrement and skip), 16-14, A-7 DuplicateName menu, 19-5 dx/dt operation on a graph, 3-28, 4-8 dy/dx operation on a graph, 3-28, 4-8, 5-6 - E- e (constant), 2-4 e^((exponential), 2-4, A- 7 E (exponent), 1-7, 1-10, A-7 edit keys table, 1-8 t.Eff( (to effective A-7 Else, 16-10 End, 16-12, rate), 14-12, A-8 Eng (engineering A-8 entry cm'sor, interest notation mode), 1-10, 1-5 ENTRY (last entry key), 1-16 EOS TM (Equation Operating System), 1-22 eqn (equation variable), 2-8, 2-12 equal-to relational test (=), 2-25, A-35 Equation Operating System (EOSTM), 1-22 Equation Solver, 2-8 equations with nmltiple Index-4 roots, 2-12 - Equi_String( (equation-to-string conversion), 15-7, A-8 errors diagnosing and correcting, 1-24 messages, B-5 example _-applieations m'ea between cm_es, 17-11 m'eas of regular 17-16 n-sided polygons, box plots, 17-2 cobweb attractors, 17-8 fundamental theorem of calculus, 17-14 guess the coefficients, 17-9 inequalities, 17-5 mortgage payments 17-18 parametric equations: ferris wheel problem, 1 7-12 pieeewise functions, 1 7-4 Sierpinski triangle, 1 7- 7 solving a system of nonlinear equations, 17-6 unit circle and trig curves, 17-10 examples_--Getting Started box w_th lid 9 to 16 defining a, 9 defining a table of values, 10 finding calculated maxinmm, 16 setting the viewlng window, 12 tracing the graph, 13 zooming in on the graph, 15 zooming in on the table, 11 coin flip, 2-2 compound interest, 14-3 drawing a tangent line, 8-2 financing a era', 14-2 forest and trees, 6-2 generating a sequence, 11-2 graphing a circle, 3-2 mean height of a population, 13-2 path of a ball, J-t-2 pendulum lengths and periods, 12-2 polar rose, 5-2 - E (continued) exalnp]es_--Getting Started quadratic formula (continued) converting to a fraction, g displaying eomplex results, 8 entering a calculation, 6 roots of a, 7-2 sendHlg variables, 19-2 solving a system of linear equations, 10-2 unit circle, 9-2 volume of a cylinder, 16-2 examples_-nliseellaneous convergence, 6-12 daylight hours in Alaska, 12-28 calculating outstanding loan balances, l J-t-l O predator-prey model, 6-13 exponential regression (ExpReg), 12-26, A-8 expr( (string-to-expression conversion), 15-7, A-8 ExpReg (exponential regression), 12-26, A-8 expression, 1-6 converting front string (expr(), 15- 7, A-8 turning on and off (lllxprOn, lllxprOff), 3-1].t , A-8 lllxprOff (expression lllxprOn (expression off), 3-1].t, A-8 on), 3-1].t, A-8 - F- ff(x)dx operation on a graph, 3-28 factorial (!), 2-21, A-3]._ fandly of eut_es, 3-16 Fcdf(, 13-32, A-8 Fill(, 10-13, A-8 FINANCE CALC menu, 14-5 FINANCE VARS menu, 1]-t-1]-t financial functions amortization schedules, 10.-9 cash flows, 14-8 days between dates, 14-13 interest rate conversions, 14-12 payment method, 14-13 time value of money (TVM), 14-6 - F (continued) Fix (fJxed-deeimal - mode), 1-10, A-8 fixed-deeimal mode (Fix), 1-10, A-8 Float (floating-decimal mode), 1-10, A-8 floating-decimal A-8 mode (Float), 1-10, fMax( (function maximum), 2-6, A-9 fMin( (function ndnimum), 2-6, A-9 fnlnt( (function integral), 2-7, A-9 FnOff (function off), 3-8, A-9 FnOn (function on), 3-8, A-9 For(, 16-10, k-9 format settings, 3-13, 6-8 formulas amortization, A-56 ANOVA, A-51 cash flow, A-57 days between dates, A-58 factorial, 2-21 interest rate conversions, A-57 logistic regression, A-50 sine regression, A-50 time value of money, A-5].t two-sample T-Test, A-52 two-sample t test, A-53 fPart( (fractional part), 2-1& 10-11, A-9 Fpdf(, 13-32, A-9 )Frac (to fraction), 2-5, A-IO free-moving cursor, 3-17 frequency, 12-2].t Full (full-screen mode), 1-12, A-IO full-screen mode (Full), 1-12, A-IO Func (function A-IO function, graphing definition function graphing, accuracy, 3-17 mode), 1-11, of, 1-7 3-1 to 3-28 CALC (calculate menu), 3-25 defining and displaying, 3-3 defining in the Y= editor, 3-5 defining on the home screen, in a program, 3-6 deselecting, 3- 7 displaying, 3-3, 3-11, 3-15 evaluating, 3- 6 family of cmxres, 3-16 format settings, 3-13 Index-5 - F (continued) Ftmction graphing - - G (continued) (continued) graph free-moving cursor, 3-17 graph styles, 3-9 maximunl of (fMax0, 2-6, A-9 minimmn of (fMin0, 2-6, A-9 modes, 1-11, 3-4,A-10 moving the cursor to a value, 3-19 overlaying functions on a graph, 3-16 panning, 3-19 pausing or stopping a graph, 3-15 Quick Zoom, 3-19 selecting, 3-7, 3-8, A- 9 shading, 3-10 Snmrt Graph, 3-15 tracing, 3-18 window variables, 3-11, 3-12 Y= editor, 3-5 _ewing window, 3-11 AX and AY window variables, 3-12 ZOOM menu, 3-20 ZOOM MEMORY menu, 3-23 function integral (fnlnt0, 2-7, A-9 functions and instructions table, A-2 to A-2 future vahle, 14-5, 14-7, l J-t-l J-t present value, 14-5, 14-7, 1J-t-l}-t FV (future-value vm'iable), 1J4-J4, 1J4-1J4 -G gcd( (greatest A-IO common - divisor), 2-15, GDB (graph database), 8-19 geometcdf(, 13-34, A- I O geometpdf(, 13-34, A- I O Get( (get data from CBL 2/CBL or CBR), 16-21, A-IO GetCalc( (get data from TI-83), 16-21, A-IO getKey, 16-20, A-IO Getting Started, 1 to 18. See also examples, Getting Started Goto, 16-13, A-IO database (GDB), 8-19 graphing modes, 1-11 graphing-order modes, 1-12 GraphStyle(, 16-15, A-11 graph styles, 3-9 graph-table split-screen mode 1-12, 9-5, A-11 (G-T), greater than (>), 2-25, A-35 greater than or equal to (>), 2-25, A-35 greatest common divisor (gcd0, 2-15, A-IO greatest integer A-12 (intO, 2-14, GridOff, 3-14, A-11 GridOn, 3-14, A-11 G-T (graph-table split-screen 1-12, 9-5, A-11 - H 10-11, mode), - Histogram plot type (2m_), 12-32 home screen, l-J4 Horiz (horizontal split-screen mode), 1-12, 9-4, A-11 hyperbolic functions, 15-10 Horizontal (draw- line), &6 - 8-7, A-11 hypothesis tests, 13-10 - 13"-15 i (complex number constant), 2-17 1%(annual interest rate variable), 14-4, 14-14 identity(, 10-13, A-11 if instructions If, 16-9, A-11 If-Then, 16-9, A-11 If-Then-Else, 16-10, A-11 imag( (imaginmTy" pm't ), 2-18, imaginary part (imagO, 2-18, implied nmltiplieation, 1-23 A-11 A-11 increment and skip (IS>(), 16-13, A-13 IndpntAsk, 7-3, A-12 IndpntAuto, 7-3, A-12 independent variable, 7-3, A-12 inferential Index-6 - stat editors, 13-6 - I (continued) -K- - inferential statistics. See also stat tests; confidence intervals alternative hypotheses, bypassing calculating 13-8 editors, 13-8 test results (Calculate), 13- 7 keyboard layout, 2, 3 ninth operations, key-code 2-3 diagrmn, 16-20 - L- confidence interval calculations, 13-8, 13-16 - 13-21 data input or stats input, 13-7 L (user-created list nmne 11-16, A-13 LabelOff, 3-14, A-13 entering argument values, 13- 7 graphing test results (Draw), 13-8 input descriptions table, 13-26 pooled option, 13-8 STAT TESTS menu, 13-9 test and interval output variables, 13-28 LabelOn, labels Input, 16-16, 16-17, A-12 insert cursor, 1-5 inString( (in string), 15-7, A-12 instruction, definition of, 1-7 int( (greatest integer), 2-1#, 10-11, A-12 Elnt( (sum of interest), 1#-9, A-12 integer part (iPart0, 2-1#, 10-11, A-12 integral. See nmnerical integral interest rate conversions eMeulating, 14-12 _Eff( (compute effective rate), 14-12, formula, A-57 _Nom( (compute rate), 1#-12, interest A-7 nondnal A-16 interest internal rate of return (irr(), 1#-8, A-13 intersect operation on a graph, 3-27 inverse (-1), 2-3, 8-9, 10-10, A-36 inverse eunmlative normal distribution (invNorm0, 13-30, A-12 inverse trig functions, 2-3 invNorm( (inverse eunmlative normal distribution), 13-30, A-12 iPart( (integer part), 2-14, 10-11, A-12 irr( (internal rate of return), 14-8, A-13 I$>( (increment and skip), 16-13, A-13 symbol), 3-14, A-13 graph, 3-14, A-13 program, 16-13, A-13 Last Entry, 1-16 Lbl (label), 16-13, A-13 Icm( (least common multiple), A-13 least common A-13 nmltiple (Icm(), 2-15, 2-15, length( of string, 15-8, A-13 less than (<), 2-25, A-35 less than or equal to (<), 2-25, A-36 line graph style C'), 3-9 Line( (draw line), 8-5, A-13 line segments, drawing, &5 lines, drawing, 8-6, & 7 linking receMng items, 19-5 to a CBL 2/CBL System or CBR, 19-3 to a PC or Macintosh, 19-3 to a TI-82, 19-3, 19-8 transndtting items, 19- 6 two TI-83 units, 19-3 LINK RECEIVE menu, 19-5 LINK SEND menu, 19-4 kinReg(a+bx) (linear 12-26, A-14 LinReg(ax+b) (linear 12-25, A-14 regression), regression), LinRegTTest (linear regression 13-2#, A-14 AList(, 11-12, A-14 LIST MATH menu, 11-17 t test), List_matr( (lists-to-matrix conversion), 10-14, 11-15, A-14 LIST NAMES menu, 11-6 LIST OPS menu, 11-10 Index-7 - L (continued) - - M (continued) lists, 11-1 to 11-18 matriees, aeeessing an element, 11-5 attaehing fornmlas, 11-7, 12-14 clearing all elements, 12-12, 12-20 eopying, 11-5 creating, 11-3, 12-12 deleting from memory, 11-5, 18-3 detaching fommlas, 11-8, 12-16 dimension, 11-4, 11-11 entering list names, 11-6, 12-11 indicator ({ }), 11-4. naming lists, 11-3 storing and displaJAng, 11-4. transmitting to and from TI-82, 19-4 using in expressions, 11-9 using to graph a family of curves, 3-16, 11-5 using to select data points from a plot, 11-13 using ,_th math functions, 11-9 using _th ninth operations, 2-3 In(, 2-4, A-14 LnReg (logarithmic regression), 12-26, A-14 log(, 2-4, A-14 logic (Boolean) operators, 2-26 Logistic (regression), 12-27, A-15 logistic regression fornmla, A-50 - MATH CPX (eomplex MATH menu, 2-5 M - menu), 2-18 MATH NUM (number menu), 2-13 math operations, keyboard, 2-3 MATH PRB (probability menu), 2-20 MatrHist( (nmtrix-to-list conversion), 10-14, 11-16, A-15 matrices, 10-1 to 10-16 accessing elements, 10-8 copying, 10-8 defined, 10-3 deleting from memory, 10-4 dimensions, 10-3, 10-12, 10-13 displaying a nmtrix, 10-8 displaying matrix elements, 10-4 editing matrix elements, 10-6 Index-8 - (eontinued) indicator ([ ]), 10-7 inverse (-1), 10-10 math functions, 10-9 to 10-11 matrix math functions (det(, T, dim(, Fill(, identity(, randM(, augment(, MatrHist(, List_matr(, cumSumO, 10-12 to 10-16 reDreneing in expressions, 10- 7 relational operations, 10-11 row operations(ref(, rref(, rowSwap(, row+(, *row(, *row+(), 10-15 selecting, 10-3 xqewing, 10-5 MATRX EDIT menu, 10-3 MATRX MATH menu, 10-12 MATRX NAMES menu, 10-7 max((maximum), 2-15, 11-17, A-15 maximum of a funetion (fMax0, 2-6, A-9 maximum operation on a graph, 3-27 mean(, 11-17, A-15 median(, 11-17, A-15 Meal-Meal (median-median), 12-25, A-15 inenlolTy" backing up, 19-10 checking available, 18-2 clearing all list elements from, elem'tng entries from, 18-4 deleting items from, 18-3 insufficient during transmission, 19-5 18-4 resetting defaults, 18-6 resetting memory, 18-5 MEMORY menu, 18-2 Menu( (define menu), menus, 4, 1-19 16-14, A-15 defining (Menu(), 16-14, A-15 nmp, A-39 scrolling, 1-19 min( (minhmm0, 2-15, 11-17, A-16 minimum operation on a graph, 3-27 minimum of a function (fMin0, 2-6, minutes notation ('), 2-23, A-38 ModBoxplot plot type (4>.), 12-32 A-9 - M (continued) modified - box [)lot type (o..), - N (continued) 12-32 mode settings, 1-9 a+bl (complex rectangular), 2-16, A-3 re^Of (complex A-22 polar), 1-12, 1-12, 2-16, Connected (ploning), 1-11, A-4 Degree (angle), 1-11, 2-24, A-6 Dot (plotting), 1-11, A-7 Eng (notation), 1-10, A-8 Fix (decimal), 1-10, A-8 Float (decimal), 1-10, A-8 Full (screen), 1-12, A-IO Func (graphing), 1-11, A-IO G-T (screen), 1-12, A-11 Horiz (screen), 1-12, A-11 Normal (notation), 1-10, A-16 Par/Param (graphing), 1-11, A-18 Pol/Polar (graphing), 1-11, A-19 Radian (angle), 1-11, 2-24, A-21 Real, 1-12, A-22 Sci (notation), 1-10, A-25 Seq (graphing), 1-11, A-26 Sequential (graphing order), A-26 1-12, Simul (graphing order), 1-12, A-27 modified box [)lot type (o..), 12-32 multiple entries on a line, 1-6 multiplication multiplieative N - N (number of payment periods variable), 14-4, 14-14 nCr (number of combinations), A-16 nDeriv( (numerical A-16 negation (-), 1-23, _Nom( (to nominal A-16 derivative), (normal distribution probability), 13-30, A-17 normalpdf( (probability density function), 13-29, A-17 NormProbPIot plot type ([__), 12-33 not( (Boolean operator), 2-26, A-17 not equal to (_), 2-25, A-35 nPr (pernmtations), 2-21, A-17 npv( (net present value), 14-8, A-17 numerical derivative, 2- 7, 3-28, 4-8, 5-6 numerical integral, 2- 7, 3-28 - O- one-proportion z confidence inte_ral (1-PropZInt), 13-20, A-20 one-proportion z test (1-PropZTest), 13-14, A-20 one-sample t confidence inte_al (Tlnterval), 13-17, A-30 one-variable statistics (1-Var Stats), 12-25, A-31 or (Boolean) operator, 2-26, A-17 order of evaluating equations, 1-22 Output(, 9-6, 16-19, A-18 panning, 3-19 Par/Param (pm'ametrie graphing mode), 1-9, 1-11, A-18 parametric equations, 4-5 parametric graphing CA/C (calculate operations on a (*), 2-3, A-37 inverse, 2-3 - normalcdf( - 2-21, 2-7, 2-4, A-37 interest rate), nonrecursive sequences, 6-5 normal distribution probability (normalcdf(), 13-30, A-17 Normal notation mode, 1-10, A-16 normal probability plot type (__), 12-33 14-12, graph), 4-8 defi_ling and editing, 4-4 free-moving cursor, 4- 7 graph format, 4-6 graph styles, 4-4 moving the cursor to a value, 4-8 selecting and deseleeting, 4-5 setting parametric mode, 4-4 tracing, 4- 7 window variables, 4-5 Y= editor, 4-4 zoom operations, 4-8 parentheses, 1-23 path (_.)) graph style, 3-9 Index-9 - P (continued) - - P (continued) - Pause, 16-12, A-18 pooled pausing a graph, Pen, 8-13 power (^), 2-3, A-36, A-37 power of ten (10^0, 2-& A-37 present vahle, 1].t-5, 1].b7, 14-1].t pernmtations phase plots, 3-15 (nPr), 2-21, A-17 6-13 Pi (_), 2-4 Pic (pictures), 8-17, pictures (Pic), 8-17, pixel, 8-16 9-6 14-4, Pmt_Bgn (payment beghming variable), 14-13, A-19 Pmt_End (payment end variable), 14-13,A-19 poissoncdf(, 13-324, A-19 poissonpdf(, 13-33, A-19 Pol/Polar (polar graphing mode), 1-9, 1-11,A-19 polar equations, 5-4 polar form, complex numbers, 2-17 *Polar (to polar), 2-19, A-19 polar graphing CALC (calculate operations on a 5-3 5-6 graph format, 5-5 graph styles, 5-3 moving the cursor to a value, 5-6 selecting and deselecting, 5-4, mode (Pol/Polar), 1-9, 1-11, 5-3, A-19 tracing, 5-6 window variables, 5-]-_ Y= editor, 5-3 ZOOM operations, 5-6 PolarG¢ (polm" graphing coordinates), 3-13, A-19 Index-lO 13-8 PRGM EDIT menu, 16-7 PRGM EXEC menu, 16-7 pixels in Horiz/G-T modes, 8-16, Plot4 (, 12-34, A-18 Plot2(, 12-34, A-18 Plot3(, 12-34, A-18 PlotsOff, 12-35, A-18 PlotsOn, 12-35, A-18 plotting modes, 1-11 plotting stat data, 12-31 PMT (payment amount variable), 14-14 free-moxqngcursor, 13-6, prexqous entlT (Last Entry), 1-16 PRGM CTL (program control menu), 16-8 8-18 8-18 graph), 5-6 defining and displaying, equations, 5-4 option, P RGM I/O (Input/Output menu), 16-16 prgm (program name), 16-15, A-19 PRGM NEW menu, 16-0. ZPrn( (sum of principal), 12.t-9, A-19 probability, 2-20 probability density" function (normalpdfO, 13-29, A-17 prod((product), 11-18, A-19 programming copying and renaming, 16-7 creating new-, 16J._ defined, 16J.t deleting, 16J-_ deleting command lines, 16-6 editing, 16-6 entering command lines, 16-5 executing, 16-5 instructions, 16-9 - 16-21 inserting command lines, 16-6 (prgm), 16-15, renaming, 16- 7 name A-19 stopping, 16-5 subroutines, 16-22 Prompt, 16-18, A-19 1-PropZlnt (one-proportion z confidence interval), A-20 13-20, 1-PropZTest (one-proportion 13-1].t, A-20 2-PropZlnt (two-proportion z confidence interval), A-20 z test), 2-PropZTest (two-proportion 13-15, A-20 z test), 13-21, P)'Rx(, P)'Ry( (polar-to-rectangular conversions), 2-24, A-21 Pt-Change(, 8-15, A-20 Pt-Off(, 8-15, A-20 Pt-On(, 8-10, A-20 - P (continued) PV (present value 114-114 p-value, 13-28 PwrReg (power A-20 - - R (continued) variable), lJ4-J4, regression), 12-27, Pxl-Change(, 8-16, A- 21 PxI-Off(, 8-16, A-21 PxI-On(, 8-16, A-21 pxI-Test(, 8-16, A-21 PlY (nunlber-of-payment-periods-peryear variable), l J4-J4, l J4-1J4 QuadReg (quadratic regression), 12-25, A-21 QuartReg (quartic regression), 12-26 Quick Zoom, 3-19, A-21 - R- r (radian notation), 2-2/4, A-3J4 r (correlation coefficient), 12-23 r2, R 2 (coefficients of determination), 12-23 Radian angle mode, 1-11, 2-2J4, A-21 radian notation (r), 2-24, A-34 rand (random number), 2-20, A-21 randBin( @andom binomial), 2-22, A-21 randlnt( (random integer), 2-22, A-22 randM( (random matrix), 10-13, A-22 randNorm( (random Normal), 2-22, A-22 random seed, 2-20, 2-22 RegEQ (regression equation 12-22, 12-29 regression model automatic regression 12-22 automatic 12-22 vm'iable), equation, residual list feature, diagnostics display models, 12-25 mode, 12-23 relational operations, 2-25, 10-11 Repeat, 16-11, A-23 RESET menu, 18-5 resetting defaults, 18-6 memmTy', 5, 18-5 resklual list (RESID), 12-22 Return, 16-15, A-23 root (x?), 2-6, A-35 root of a function, 3-26 round(, 2-13, 10-10, A-23 row+(, 10-16, A-23 *row(, 10-16, A-23 *row+(, 10-16, A-23 rowSwap(, 10-16, A-23 RH=r(, I_P0( (reetangular-to-polm" conversions), 2-2J4, A-23 rref( (reduced-row-echelon form), 10-15, A-23 -S 2-SampFTest 13-23, - (two-sample A-2J4 g-Test), RecallPic, 8-18, A-22 _Rect (to rectangulm'), 2-19, A-22 rectangular form, complex numbers, 2-17 2-SampTInt (two-sample t confidence illtel_ral), 13-19, A-24 2-SampTTest (two-sample t test), 13-13, A-2J4, A-25 2-SampZlnt (two-sample z confidence inte_5,al), 13-18, A-25 2-SampZTest (two-sample z test), 13-12, A-25 Scatter plot type (L_), 12-31 Sci (scientific notation mode), 1-10, A-25 RectGC (rectangular graphing coordinates), 3-13, A-22 recursive sequences, 6-6 ref( (row-echelon form), 10-15, A-22 scientific notation, 1 -7,1-10 screen modes, 1-12 second cursor (2nd), 1-5 second key (2nd), 3 RCL (recall), 1-15, 11-9 re^Oi (polm" complex mode), 2-16, A-22 Real mode, 1-12, A-22 1-12, real( (real part), 2-18, A-22 RecalIGDB, 8-20, A-22 Index- 11 - S (continued) seconds DMS notation - ('), - S (continued) program, 3-8 functions in tile Y= editor, items from stat plots nlenus, SetUpEditor, 12-21, A-26 shade above (7) graph style, 3-9 shade below- (6) graph style, 3-10 2-23 Select(, 11-12, A-25 selecting data points from a plot, 11-13 functions from the home screen or a 3-7 J4 from tile Y= editor, 3-7 Send( (send to (BL 2/('BL or CBR), 16-21, A-26 sending. See trtmsmitting Seq (sequence graphing mode), 1-11, A-26 seq((sequence), 11-12, A-26 sequence graphing axes fommt, 6-8 CALC (calculate memO, 6-10 defining and displaying, 6-3 evaluati]lg, 6-10 free-mo_ng cursor, 6-9 graph fommt, 6-8 graph styles, 6-J4 moving the cursor to a value, 6-9 nonreeursive sequences, 6-5 phase plots, 6-13 recursive sequences, 6-6 setting sequence mode, 6-3 selecting and deseleeting, TI-83 versus TI-82 table, tracing, 6-9 web plots, 6-11 window variables, 6- 7 Y= editor, 6-J4 6-4 6-15 Index-12 from a program, 7-3 ShadeF(, 13-36, A-27 ShadeNorm(, 13-35, A-27 Shade_t(, 13-36, A-27 shading graph areas, 3-10, 8-10 Simul (simultaneous graphing order mode), 1-12, A-27 sin((sine), 2-3, A-27 sin'1((m-csine), 2-3, A-27 sine (sin(), 2-3, A-27 sine regression formula, A-50 sinh( (hyperbolic sine), 15-10, A-27 sinh'l( (hyperbolic m'csine), 15-10, A-27 SinReg (sinusoMal A-28 3-10 regression), 12-27, Smart Graph, 3-15 solve(, 2-12, A-28 Solver, 2-8 solving for variables in tile equation solver, 2-10, 2-11 SortA( (sort ascending), 11-10, 12-20, A-28 SortD( (sort A-28 descending), 11-10, 12-20, mode, 9-5 mode, 9-# setting, 9-3, 9-6 split-screen values, 8-12, 8-16, square (2), 2-3, A-36 square root (_(), 2-3, A-37 STAT CALC menu, 12-2J-t STAT KDIT menu, 12-20 stat list editor attaching formulas 12-1J.t modes from a program, 1-9 split-screen modes, 9-3 split-screen modes from a program, 9-6 tables Shade(, 8-9, A-26 Shadexi(, 13-36, A-26 split-screen modes G-T (graph-table) Horiz (horizontal) ZOOM (zoom menu), 6-10 Sequential (graphing order mode), 1-12, A-26 service infornmtion, B-12 setting display contrast, 1-3 graph styles, 3-9 graph styles from a program, modes, 1-9 - 9-6 to list names, clearing elements from lists, 12-12 creating list names, 12-12 detaching fornmlas from list names, 12-16 displaying, 12-10 edit-elements context, 12-18 - S (continued) star list editor - - S (continued) (eonthmed) statistieal editing elements of fornmlagenerated lists, 12-16 editing list elements, 12-13 enter-names context, 12-19 entering list names, 12-11 formula-generated list names, 12-15 remoxqng lists, 12-12 restoring list names L1-L& 12-12, 12-21 switching eontexts, 12-17 x_ew-elements eontext, 12-18 x_ew-names eontext, 12-19 STAT PLOTS metal, 12-34 stat tests and confidence intel_rals ANOVA( (one-way analysis of variance), 13-25 x2-Test (ehi-squm'e test), 13-22 LinRegTTest (linear regression t test), 13-24 1-PropZlnt (one-proportion z confidence interval), 13-20 1-PropZTest (one-proportion z test), 13-14 2-PropZlnt (two-proportion z eonfidence interval), 13-21 2-PropZTest (two-proportion z test), 13-15 2-SampFTest 13-23 (two-sample 2-SampTInt (two-sample t eonfidenee interval), 2-SampTTest 13-13 F-Test), 13-19 (two-sample t test), 2-SampZlnt (two-sample z eonfidenee interval), 2-SampZTest (two-sample 13-12 13-18 z test), Tlnterval (one-sample t eonfidenee inte_x_al), 13-17 T-Test (one-sample t test), 13-11 Zlnterval (one-sample z eonfidenee inte_x_al), 13-16 Z-Test (one-sample z test), 13-10 Stats input option, 13-6, 13-7 STAT TESTS menu, 13-9 statistieal distribution functions. See distribution functions plotting, - 12-31 Boxplot (regular box plot), 12-33 defining, 12-34 from a program, 12-37 Histogram, 12-32 ModBoxplot (modified box plot), 12-32 NormProbPIot (normal probability plot), 12-33 Scatter, 12-31 tracing, 12-36 turning on/off stat plots, 3-7, 12-35 x_e,slng window, 12-36 xyLine, 12-31 statistieal vm'iables table, 12-29 stdDev( (standard dexdation), 11-18, A-28 Stop, 16-15, A-28 Store (-)), 1-14, A-28 StoreGDB, 8-19, A-28 StorePic, 8-17, A-29 storing graph databases (GDBs), 8-19 graph pictures, 8-17 vmiable values, 1-14 String_Equ( (string-to-equation conversions), 15-8, A-29 strings, 15-3 to 15-9 concatenation (÷), 15-6, A-38 converting, 15-7, 15-8 defined, 15-3 displaying contents, 15-5 entering, functions 15-3 in CATALOG, 15-6 indicator ("), 15-3 length (length(), 15-8, A-13 storing, 15-5 vmiables, 15-4 student-t distribution probability (tcdf0, 13-31, A-29 probability density function (tpdf0, 13-30, A-30 sub((substring), 15-9, A-29 subroutines, 16-15, 16-22 subtraction (-), 2-3, A-38 sum((sumnmtion), 11-18, A-29 system variables, A-49 Index-13 -T- - T (continued) TABLE SETUP screen, 7-3 tables, 7-1 to 7-6 description, 7-5 variables, 7-3 to 7-5 time value tangent (tan(), 2-3, A-29 Tangent( (draw line), 8-8, A-29 tangent lines, drawi_lg, 8-8 tan h( (hyperbolic tangent), 15-10, A-29 tanh'l( (hyperbolic aretangent), 15-10, A-29 ATbl (table step variable), 7-3 TblStart (table start variable), 7-3 tcdf( (student-t distribution probability), 13-31, A-29 teelmieal support, B-12 TEST (relational menu), 2-25 TEST LOGIC (Boolean menu), 2-26 Text( instruction, 8-12, 9-6, A-29 placing on a graph, 8-12 Then, 16-9, A-11 thick (_.) graph style, 3-9 TI-82 link differences, 19-9 transmitting to/from, 19-2-t, 19-8, 19-9 TI-83 16-20 Link. See linking menu map, A-39 TI-GRAPH LINK, 19-3 Time axes format, 6-8, A-30 time value of money (TVM) calculating, 12-t-6 C/Y vm'iable (nmnber of compounding periods 12`1-12`1 formulas, A-54 FV vm'iable (furore I% variable (annual 12.t-12.t Index-14 value), interest (eontinued) N vm'iable (number of payment periods), 14-12-t PMT vm'iable (payment amount), 14-14 tan((tangent), 2-3, A-29 tan'l((aretangent), 2-3, A-29 features, 17, 18 keyboard, 2, 3 key code diagram, of money - PV variable (present value), 12`1-12`1 PlY vm'iable (number of payment periods per yem'), 12`1-12-1 tvm_FV (future value), 12-1-7,A-31 tyro_l% (interest rate), 14-7, A-31 tvm_N (# payment periods), 12-1-7, A-31 tvm_Pmt (payment A-31 amount), 14-6, tvm_PV (present Vahle), 12`1 - 7, A-31 TVM Solver, 12-1-2-1 vm'iables, 12-1-14 Tlnterval (one-sample t eonfidenee interval), 13-17, A-30 tpdf( (student-t distribution probability density funetion), 13-30, A-30 TRACE eursor, 3-18 entering numbers during, 3-19, 5-6, 6-9 expression display, 3-12`1,3-18 Trace instruction in a program, A-30 4-8, 3-19, transmitting error conditions, 19-6 from a TI-82 to a TI-83, 19-9 items to another unit, 19-6 lists to a TI-82, 19-2-1,19-8 stopping, 19- 6 to an additional TI-83, 19-7 T (transpose matrix), 10-12, A-34 transpose matrix (T), 10-12, A-34 trigonometric functions, 2-3 T-Test (one-sample t test), 13-11, per year), 12`1-12`1 rate), A-30 - T (continued) - complex, tvm_PV (present value), 114-7, A-31 two-proportion z confidence inte_a_al (2-PropZlnt), 13-21, A-20 two-proportion z test (2-PropZTest), 13-15, A-20 two-sample F-Test formula, A-52 two-sample t test formula, A-53 two-vm'iable statistics (2-Var Stats), 12-25, A-31 uv/uvAxes uw/uwAxes - 6-3 (axes format), (axes format), 6-8, A-31 6-8, A-31 -V- function, 7-5 vm'ianee of a list (variance(), A-31 VARS menu 11-18, GDB, 1-21 Picture, 1-21 Statistics, 1-21 String, 1-21 Table, 1-21 Window, 1-21 Zoom, 1-21 Vertical (draw line), &6, A-31 _dewing window, 3-11 (axes format), 6-3 6-8 W 1-Var Stats (one-variable 12-25, A-31 statistics), 2-Var Stats (two-variable 12-25, A-31 statistics), value operation 1-11t real, 1-13 recalling values, 1-15 solver editor, 2-9 statistical, 12-29 string, 15-].L 15-5 test aim inte_xral output, 13-28 types, 1-13 user and system, 1-13, A J-t9 VARS and Y-VARS menus, 1-21 variance( (variance of a list), 11-18, A-31 vw/uvAxes v sequence values, graph databases, 1-13 graph pictures, 1-13 independent/dependent, list, 1-13, 11-3 matrix, 1-13, 10-3 points, 8-1J4 stat plots, 3-7, 12-35 tvm_FV (future vane), lj4 - 7, A-31 tyro_l% (interest rate), 114-7, A-31 tvm_N (# payment periods), 114-7, A-31 tvm_Pmt (payment amount), 114-6, A-31 u sequence function, user variables, A-49 1-13 displaying and storing equation solver, 2-10 functions, 3- 7 grid, 3-1J4 labels, 3-1J4 pixels, 8-16 U - vmialAes turlling Ol1and off axes, 3-1J4 calculator, 1-2 coordinates, 3-14 expressions, 3-1J4 - - V (continued) on a graph, 3-25 w sequence function, warranty inforlnation, 6-3 B-13 Web (axes format), web plots, sequence While, 16-11,A-32 window variables 6-8, A-31 graphing, 6-11 function graphing, 3-11 parametric graphing, ]4-5 polar graphNg, 5-]4 sequence graphing, 6- 7 Index-15 -X- - Z (continued) - XFact zoom factor, 3-2J4 x-intercept of a root, 3-26 ZoomSto (store zoom _lndow), A-33 xor (Boolean) exclusive 2-26, A-32 x m root (_), 2-6 ZPrevious (use previous 3-23, A-33 or operator, Z-Test (one-sample ZTrig (trigonometric A-3J4 -y- 3-2J4 function graphing, 3-5 parametric graphing, J4-J4 polar graphing, 5-3 sequence graphing, 624 Y-VARS menu Function, 1-21 Parametric, 1-21 Polar, 1-21 On/Off, 1-21 AY window variable, 3-12 -Z- ZBox, 3-20, A-32 ZDecimal, 3-21, A-32 zero operation on a graph, 3-26 Zlnteger, 3-22, A-32 Zlnterval (one-sample z confidence intm_al), 13-16, A-32 zoom, 3-20 to 3-214 cursor, 3-20 factors, 3-2J4 function graphing, 3-20 parametric graphing, J4-8 polar graphing, 5-6 sequence graphing, 6-10 ZoomFit (zoom to fit function), A-33 3-22, Zoom In (zoom in), 3-21, A-32 ZOOM menu, 3-20 ZOOM MEMORY menu, 3-23 Zoom Out (zoom out), 3-21, A-32 ZoomRcl (recall stored window), 3-23, A-33 ZoomStat Index-16 (statistics zoom), window), ZSquare (set square pixels), 3-21, A-33 ZStandard (use standard window), 3-22, A-33 xyLine ([__) plot type, 12-31 AX window variable, 3-12 YFact zoom factor, Y= editor 3-23, 3-22, A-33 z test), 13-10, A-3]-_ window), 3-22, _ T1=83 TEXAS INSTRUMENTS J STAT PLOT TBLSET A-LOCK FORMAT QUiT INS LiNK LiST CALC TEST A ANGLE E{ DRAW FINANCE D SIN E COS I EE J { K -1 -1 C DISTR F TAN -1 TABLE G 1T N } L e IvI e x S L4 T L5 U L6 V _ W RCL X L1 Y L2 Z L3 ® ME[V] f_ i : ANS ? OFF CATALOG _ ENTRY SOLVE

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