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Brief Users Guide for the   TI-84 &TI-83 Plus

Content:  This document covers basic math, special expression, graphing, complex numbers, list arithmetic, tables, special functions, calculus, matrices,
sequences, dot product,angle between two vectors, cross product, triple scalar-product, transferring programs and all basic operations as performed on
the TI-83 Plus calculator.

Additions: 4/2/17 
INDEX:

To facilitate lookup, the instructions are divided into the following categories:

         I.   Basic Information - What's my operating system version?, how much RAM do my programs 
             take, is my calc upgradeable?, adjusting brightness of display, friendly values using TRACE.
       
II.  Basic Math – Math operations, how to change settings, and how to obtain certain symbols.
       III.  Special Expressions – Absolute Value, Greatest Integer, logs of different bases, etc.
       IV.  Graphing and Evaluating Functions – Graphing, finding roots, graphing inequalities with and without the
              Inequalz App., finding intersections of graphs,  graphing inequalities, marking points on a graph, using [TABLE]
              to find points for graphing a parabola by hand, using the Solver, CALC, or TABLE to find roots or evaluate a
              function
etc, using TABLE to graph an equation by hand,  solving equations with roots >2 with Solver,
        V.  Special Functions – Greatest Integer, Absolute Value, Piecewise Functions, Trig Functions, hyperbolic
              functions, graphing parametric equations, etc.  .
        VI.  Calculus – Finding the derivative at a certain point, finding the integral,
       VII.  Matrices – Determinant, Transpose, Row Operations, system of equations, source for program for rref and ref.
      VIII.  Sequences - Finding several terms of a sequence,
finding a specific term of a sequence
              summing sequences, cumulative sum of sequence, series
        IX.  Complex Numbers - Solving a polynomial with complex coefficients,  program for finding complex coefficients,
         X.  Combining and Connecting Operations - Doing expressions with several terms,
        XI.   Arithmetic and other operations with lists - clearing lists, arithmetic with lists, logic with lists,
       XII.   
Special Techniques - Graphing equations of the form x=y² +3x +2,
      
XIII.  Transferring Programs and Data – Transferring data or programs from one calculator to  
              another, entering TI-84 programs on a computer, transferring a program from a computer to a TI-84 calculator, transferring a
              program from a TI-84 to a computer,
      XIV.  Applications - Making conversions using the Conversion Application, Inequality Application see section IV.
        XV. Vectors - Multiply by a scalar, Dot Product, Angle between two vectors, Triple Scalar-Product, Cross-Product program,
      XVI. Problems - trigonometry, calculator hangs up,

RELEASE DATE:  10/5/03         DATE LAST REVISED:  7/4/14
© 2003 Frank Kizer  NOTE:  See copy restrictions and printing hints at the end of this document.  
Important Note:  The TI-84 Silver Edition and the TI-84 calculators with newer operating systems have
  different keystrokes for some statistical operations and have additional functions for other operations.
  To familiarize yourself with these changes, click here .

 General Operating Instructions:   All keys have at least two functions and some have three.  The default function for a key is the white print on
the key.  When 2nd is pressed the key function is as indicated in yellow print (gray or blue on some later models) on the panel immediately above
the key.  When ALPHA is pressed, the function is the white (green on TI-84) label immediately above the key and, in most cases, near the right
end of the key.  When APPS is pressed, the names of applications that are installed on your calculator displayed.

Things the TI-83 Plus and TI-84 will not do:  Students should be aware that TI-83 Plus, and TI-84 calculators will not manipulate variables.  
That is, they will not simplify expressions, factor expression such as quadratic equations, and they will not do multiplications of variables
such as in the FOIL method.  Furthermore,  they will not do indefinite integrals or find the anti-derivative of an expression with variables. 
They will, however, find the area under a curve between limits that the user specifies and they will find the value of the derivative of a function
at a specific point.

 I.  BASIC INFORMATION
 
1.  Turning the calculator ON and OFF.
        a)  To turn on: Press the ON key.
         b)  To turn off:  Press 2nd; then OFF (the second function for the ON key.)

 2.  Adjusting the contrast of the screen.
         a) To make the screen display darker: Press the 2nd key; then press the up arrow     
             key.
         b) To make the screen display lighter: Press the 2nd key; then press the down
             arrow key.

  3.  Finding your operating system version number.
        a)  Press 2nd; then MEM.  The memory management screen will be displayed at the top of the screen.
        b)  Press ENTER and a screen will be displayed with the version number of the OS.  It may be
             anything from 1.12 to 1.19. 
   4.  Finding our how much free RAM I have.
        a)  Press 2nd; then MEM. Scroll to 2: Mem Mgmt/Del...and press ENTER.
        b)  The FREE RAM and ARC MEM (archive memory) will be displayed.
        c)  To find out how your memory is used, for example how much memory a program uses,
             from the above screen, highlight 1:All and press ENTER.
   5.  Is my calculator upgradeable?  TI-83 Plus and later are upgradeable.  The TI-82 and TI-83 (not
        Plus) are not upgradeable.

6)  Friendly Values on Graphs Using TRACE:
       Many times when you use the TRACE function, you will get an x-value such as 2.784532.  If you change the x-min and x-max in the WINDOW function to be multiples of 4.7 and the y-min and y-max to multiples of 3.1, the displayed values will be "friendlier."  That is, they will be integers or numbers with one or two decimal places.  You can always set the values by hand, but the easiest method is to use the ZDecimal function of ZOOM.  Just press ZOOM; then 4, for ZDecimal. 
      It may be that the display is now partially off the screen.  If you want the entire graph on the screen, use the Zoom Out function. To do that, press ZOOM, 3, ENTER.   Incidentally, 4 seems to be the default setting for the zoom factors.  So, if your graph is now too small, set the factors to 2 if they’re not already set at 2.  To do that press ZOOM, cursor to MEMORY, press 4, and set both factors to 2. 
      If you’re trying to find the value at a specific point, a zero for example, and the cursor still does not fall on the x-axis, you could try different strategies such as ZBox, but I usually prefer to use the zero function.  To do that, press 2nd, CALC, 2.  That will set you up for finding a zero.  Remember that any time you want to get back to the standard window just press ZOOM, 6.

II. BASIC MATH

SPECIAL NOTE FOR TI-84 USERS:
   
When using the TI-84 for such operations as fractions it is useful to go to the MATHPRINT mode. To do that
     press MODE, scroll down to MATHPRINT, highlight MATHPRINT and press ENTER.


1
. Clearing the Calculator Screen.
         a) To clear the calculator screen: Press the CLEAR key.
         b)  Note that CLEAR may also take you to another screen if you are using one of
              the screens that does not permit data entry.

2.  To move to another screen:
         a)  Press 2nd, QUIT.
         b)  You can also use CLEAR if you’re not using a screen on which entries are made.  Some
              examples of screens where entries are made are the following: Y=, List, or PRGM.

3. Correcting errors or changing characters.   
         a) To replace a character at the cursor position, just press the new
             character.
         b) To insert a character in the position of the cursor, press  2nd, press
             the INS key, and then press the key for the desired character.
         c) To delete a character in the position of the cursor, press the
DEL key.

 4. Changing the MODE:
      (Use the MODE for such things as changing from degrees to radians, displaying numbers as
       powers of ten, using split screen, enabling complex number calculations and other       
       similar things.)
         a) Press the MODE key.
         b) Use the arrow keys to move the cursor to the desired item.
         c) Press ENTER to highlight the selected item.
         d) Press CLEAR or 2nd, QUIT to return to the home screen,

 5. Performing numerical calculations:
       a) On the graphing calculator screen, the multiplication symbol will appear    
       as * and the division symbol will appear as /.
      b) Parentheses can be used to denote multiplication or as grouping symbols to  
         clarify the order of operations.
       c) To enter an exponent use the ^ key for any exponent.  You can also use the x2
           to raise a number to the second power. Other functions are available by pressing MATH.
       d) Use the (-) key for negative numbers and the - key for subtraction.

 6. Raising a number to a power:
      a) Enter the number.
      b) Press the ^ key. For the TI-84, the exponent will be entered to the raised exponent position. When
          you have finished with the exponent, press the right arrow key to return to the normal position and
          press ENTER to display the results.
      c) Enter the number for the power.
      d) Press ENTER.
      e) For an exponent of 2 only, you can use the x2 key after entering the
         number that you want to raise to the second power.
      f) Alternate method for raising to the third power only:  Enter your number,
         press MATH; then 3; then ENTER. (Note that using ^ is more efficient.)

 7. Finding the root of a number:
      a)  For square root, press 2nd; then the square root symbol (x2 key). For the TI-84 press the right arrow key
           to move the cursor from under the root sign; the press ENTER to display the results.
      b) For other roots, enter the number for the root index.
      c) Press the MATH key.
      d) Press 5 to paste the unspecified root symbol to the screen.   
      e) Enter the number you want to find the root of.
      f)  Press ENTER. For the TI-84, press the right arrow key to move the cursor from under the radical sign
          before pressing ENTER.
      g)  As an alternate method for cube root only, you can also choose to press 
           MATH, enter 4 to select item 4, and enter your number. Finally, press ENTER.

 8.  Operations with fractions TI-84 OS 2.55 and Newer: (See TI-83 Plus in next item.)
     
In addition to the above capability, the TI-84 with recent operating systems has additional capability
      to deal with fractions.
      Adding Fractions.
     
Let's add 1/3 and 1/4
      a) Press ALPHA, F1 (the Y= key),1 (or ENTER) and an outline for entering the fractions appears.
      b) Press 1, right arrow, 3, right arrow.
      c) Press +; then ALPHA, F1 (the Y= key),1 (or ENTER) and the outline for the second fraction appears.
      d) Press 1, right arrow, 4, right arrow.
      e) If you want the answer in decimal form, press ENTER.  If you want it in fraction form press MATH,
          ENTER, ENTER.
      f) If the results of the operation greater than 1 and you want the answer as a mixed number, after you get the answer
         as an improper fraction do the following: Press 2nd, Ans; then ALPHA, F1, 3, ENTER.
      Add a Fraction and a Mixed Number:
      Let's add 4 1/3 +5/6.
      a) Press ALPHA, F1 (the Y= key),3 and an outline for entering the mixed number appears.
      b) Press 4, right arrow, 1, right arrow,3, right arrow.
      c) Press +; then ALPHA, F1 (the Y= key),1 (or ENTER) and the outline for the fraction appears.
      d) Press 5, right arrow, 4, right arrow.
      e) If you want the answer in decimal form, press ENTER.  If you want it as an improper fraction, press MATH, ENTER,
          ENTER.
      f) If you want the result is greater than 1 and you want the answer as a mixed number, after obtaining the improper fraction form,
         press , press 2nd, Ans; then ALPHA, F1, 3, ENTER.

9.  Operations with fractions: (TI-83 Plus and older TI-84).
         a)  Use the divide symbol between the numerator and denominator. Ex: ¼ is 
              entered as 1÷4.
         b)  Use the correct operator symbol (divide, multiply, add, subtract) between
              fractions.
         c)  Pressing ENTER will give you the answer in decimal format.  To get the answer
             as a fraction, skip step c) and continue as below.
         d)  Press MATH to select Frac; then ENTER.
               NOTE:  You can convert decimals to fractions using step d), but the decimal
              must have 12 decimal places.  Example:  To convert the decimal equivalent of
             1/3 to a fraction, you must enter this number, .333333333333.  Otherwise the
             calculator will just return the decimal you entered.

       

 III.  SPECIAL EXPRESSIONS:
 1. To enter the symbols, =, , >, <, , and ≤ :
         a) Press the 2nd ; then the TEST key.
         b) Enter the item number for the desired symbol.

  2. To find the absolute value of a number:
       a)   Press MATH and move the cursor to NUM.
       b)  Press 1 to paste Abs( to the home screen. 
       c)  Enter your number.
       d)  Press ENTER.

  3. Finding the greatest integer function of a number.
         a) Press the MATH key.
         b) Use right arrow to move the highlight to NUM.
         c) Press 5 to select int(.
         d) Enter your number.
         e) Press ENTER. (Note that this also works for negative numbers.)
        

  4.  Logs to different bases:
      
Of course, logs to base 10, LOG, and to base e, LN, are functions on the keyboard. But what about the most
       common log with computers, often designated as lg?  What we must do is divide the available logarithm by the
       logarithm of  the base wanted. The algebraic expression in general terms is as follows: the equation is as follows:
       logbx =logax/logab
       Using the natural log, ln, and lg for log to base 2, we have the following:
        lg x =ln x/ln 2
        Since 0.69314 is a good approximation to ln 2, we can change that to the following:
         lg x =ln x/0.69314 and truncate any numbers greater than zero.        

IV.  GRAPHING & EVALUATING FUNCTIONS:
 
 (NOTE:  Always make sure that the Plot functions are not highlighted before graphing anything other
   than statistical information.)
 1. Graphing a function.
        
First, clear all equations from the Y= entries.  Do this by positioning the cursor on any entry and pressing ENTER.
         a) Press the Y= key. All equations must be in the slope-intercept form, y=mx+b, before entry.
         b) Enter the function(s) using the [X,T,Θ,n] key to enter the variable, for example X.
         c) Press GRAPH to graph the function.  (If you don’t see your graph, press
            TRACE and use the arrows to find the maximum or minimum value of your 
            function.  Press ENTER.)
         d) To leave the screen without graphing: press 2nd, QUIT.
         e) Press CLEAR while the cursor is on the same line as the function to erase the
             function.
         f)  To deselect a function, move the cursor to the equal sign and press ENTER.

  2.  To obtain the standard size viewing window:
           a) Press the Zoom key.
           b) Press 6 to execute Z Standard.

  3.   To change the viewing window to a custom size:
           a) Press the WINDOW key.
           b) Use the cursor keys to move the cursor to the value to be changed.
           c) Enter the new value.
           d) Press Graph to see the new graph, or press 2nd, QUIT to return to the calculations 
               screen.
           e) ZSquare keeps the y-scale the same and adjust the x-scale so that one unit 
              on the x-axis equals one unit on the y-axis.
          f)  ZDecimal makes each movement of the cursor equivalent to one-tenth of a
             unit.
         g) ZInteger makes each movement of the cursor equivalent to one unit.

  4.  Evaluating a function without using the graph screen.
         a) Press 2nd, Y-VARS.
         b) Press ENTER.
         c) Select the name of a function, e.g., Y1.
         d) Enter an x-value as YI (3) or a list of x-values in the form Y1 ({2,3,4,5}).  (In the
             last form, make sure the interior grouping symbols are braces rather than
             parentheses.)
         e) Press Enter.
         f)  As an alternative to this, see "Finding the value of a function at a given value of x," below.

  5.  To change or erase a function:
         a) Press the Y= key.
         b) Use the arrow keys to move the cursor to the desired location and make
             changes by inserting, deleting, or changing the desired characters.
         c) To erase a function, with the cursor on the same line as the function, press the
             CLEAR key.

  6. To use the trace function:
         a) Press the Trace key.
          b) Use the right and left arrow keys to move the cursor along the graph. The
              coordinates of the cursor location are shown at the bottom of the screen.
         c) If more than one graph is on the screen, you can press the up or down arrows
            to jump from one graph to another.

  7.  Finding the maximum and minimum points.
         a) Enter the function and graph.
         b) Press the 2nd, CALC.
         c) Press 3 for minimum or 4 for maximum.
         d) Move the cursor to the left of the point and press ENTER.
         e) Move the cursor to the right of the point and press ENTER
         f)   Move the cursor slightly between those two points and press ENTER again.
         g) The maxima or minima will appear at the bottom of the screen.

  8.  Finding the value of a function at a given value of x.
         a) Enter the function and the graph.
         b) Press the Calc key.
         c) Press 1 to select value.
         d) Enter the x-value and press ENTER. The y-value will appear at the bottom of the screen

  9.  To zoom in using a box.
          a) Enter the function and graph.
          b) Press the ZOOM key.
          c) Press 1 to select ZBox.
          d) Move the cursor above and to the left of the location you want enlarged and
              press Enter.
          e) Move the cursor below and to the right of the location you want enlarged and
              press Enter.
          f) The box is then enlarged to fill the screen.

10.  Finding the intersection point of two graphs.
          a) Enter two functions on separate "Y=" lines and press GRAPH. Equations must be in
             slope-intercept form.
          b) Press 2nd,  CALC.
          c) Press 5 to select intersect.
          d) 
Move the cursor to a little away from the intersection and press ENTER to mark the first graph
               line and move the cursor to the next graph line.
         
e Move the cursor to a little away from the intersection and press ENTER to mark the second graph
               line and set the cursor to guess the intersection.
          e)
Move the cursor approximately to the intersection and press ENTER.
          f) The coordinates for the point of intersection will appear at the bottom of the screen.

 11.  Solving an equation in one variable. (Also known as finding the roots or x-axis intercepts.)
          a) Enter the function and graph.
          b) Press 2nd, CALC.
          c) Press 2 to select zero.
          d) Move the cursor to the left of the intercept and press ENTER.
          e)  Move the cursor to the right of the intercept and press ENTER.
          e) Move the cursor approximately the intercept and press ENTER.
          f)  The coordinates for the root wilI appear at the bottom of the screen.
           NOTE:  This can also be done using the Solver.  See the last item in this section for that procedure.

12.  Finding coordinates to graph a parabola by hand.
          a)  Enter the graph in your calculator as described above.
          b)  Next locate the vertex by pressing [2nd],[CALC], and pressing either 3 or 4, depending on
               whether the vertex is a minimum or maximum for the parabola.
          c)  Move the cursor slightly to the left of the vertex and press [ENTER].
          d)  Move the cursor slightly to the right of the vertex and press [ENTER].
          e)  Finally, move the cursor approximately to the vertex and press [ENTER].  The x- and y-values
               for the vertex will appear at the bottom of the screen.
           f)  Press [2nd],[TABLE].   (Be sure that your independent variable is set for Ask.  If not press
               [2nd], [TBLSET] and highlight "Ask" (opposite Indpnt.)
           g)  Enter two more values for "x" in the table and the corresponding values for "y" will appear.
           h)  Use these coordinates and the symmetry property of a parabola to graph the parabola on a
                sheet of paper. (NOTE:  If the vertex is at an integer value, you can find the vertex from the
                table.)

13. Graphing Inequalities.
           
I will first describe the method for TI-83 Plus calculators that don't have the Inequalz application and
            the method for the TI-84 and TI-83 plus calculators that have the application.
           a)  Write each equation in the y =mx + b format and enter them into  the "Y=" positions.   
               (Remember  that you may need to change the direction of the inequality sign if you have to
               multiply or divide by -1 during the rearranging of the equation.)
           b)  Shading of the graph is determined by the symbol to the left of the "Y=" entry.  Using the left
                arrow, move the cursor all the way to the left of the Y= symbol.
           c)  Pressing ENTER in that position will display different symbols.  For < or <, press ENTER
                until the upright triangle is displayed.  For > or >, press ENTER until the upside down
                triangle is displayed.
           d)  After you have the correct symbol displayed, press ENTER to graph the inequality.
            TI-84 and others with the Inequalz App:
                  
Assume you want to enter the inequality Y
≤ -x+6.
             
a)  Press APPS, scrowl down to the Inequaliz entry (it’s down past he foreign language entries), and press
                   ENTER.  When the Inequality Graphing screen appears, press ENTER to go to the graphing screen.
              b)  If the cursor isn’t already on the = sign, move it there and press ALPHA, F3 ( the ZOOM key) to enter
                   the ≤ symbol.  
             c)  Now move the cursor off the symbol and enter  –x +6, the right side of the inequality.  Press GRAPH
                  and the graph with the applicable area shaded will be displayed.
                  If you want to solve a system of linear equations, click on the line TI-83 Plus Lin Prog and you will find
                  the complete method in that document.  You can use the index to make finding the procedure easier.

14.  Marking points on a graph.
           A few students who capture screens like to have marks on graphs.  Although some would
           consider this more trouble than it's worth, I'll include it for those brave souls who feel they must
           have them. Although marks can be put directly on the graphing screen, that method uses the
           dot as a mark and it cannot be seen when imposed on the line of a graph.  So, I will describe the
           method of entering marks from the home screen where you can select a + or a box..
            a)  First, if you are a little picky about having the marks line up exactly on the graph, you  
                should press ZOOM, 4 to select ZDECIMAL.  Then graph your function and see if it the x-
                and y-values that you are interested in appear on the screen.  If not, press ZOOM, cursor
                over to MEMORY and press 4.  Then make the X- and Y-Fact integers larger than 1.  Then
                press ZOOM, 3 to change the x- and y-scales.
            b)  Go to the home screen to start the procedure.  The syntax is Pt-On(x,y,mark.  So, press 
                 2nd,  DRAW and cursor over to POINTS.
            c)  Press ENTER and Pt-On( will appear on the home screen. 
            d)  Enter the x-coordinate, y-coordinate, and the mark number. For the mark, 1=a dot, 2 = a
                 box and 3 = a cross.  I will use 3.  Let's say we graph X2 and we want to mark coordinates
                 (2,4).  Then your entry will be Pt-On(2,4,3.  (The mark will be a +.)
            e)  To mark additional points, press 2nd, ENTRY and change the x-, y-coordinates to those for
                 the next point.  Continue this for additional points.
            f)  To erase all points, press 2nd, DRAW, ENTER. 

15.  Finding roots of equations by several methods:
      
There are three commonly used methods for finding roots: Using the CALC function of the grapher, using
       TABLE, or using Solver.  I generally prefer the CALC method, but in deference to those who want to use
       other methods, I will describe all three.  Since this is a brief guide, I will not cover every single detail of
       all methods.
           Using the CALC method:
           
a)  Press Y= and enter your equation, say x² -8x +15
            b)  Press 2ND, CALC, 2 and the graph will be displayed with the prompt to set the Left Bound.
            c)  Move the cursor to slightly to the left of the point where the graph crosses the x-axis and press
                 ENTER.
            d)  Move the cursor to slightly beyond the x-intercept and press ENTER. 
            e)  At the "Guess?" prompt move the cursor to approximately where the graph crosses the x-axis
                 and press ENTER.  (Actually you don't really have to move it this last step.)  The answer 3 will
                 appear for the first root.  Go through the same steps for the second root.
             f)  Suppose you get a decimal answer that you think might be a fraction, and you want to convert
                 it to a fraction.  Press 2ND, QUIT to leave the grapher, press X (on the X, T, 0, n button.).  Now,
                 press MATH, 1, ENTER and the fractional equivalent will be displayed if the answer is a rational
                 number.
           Using TABLE:
           
 a)  Press Y= and enter your equation, say x² -8x +15.
             b)  Press 2ND< TABLE and scroll down the list of y-values in the tables to see if there is a zero.
                  The corresponding x-value is a root. 
             c)  If the answer is not an integer you may not find zeros, depending on the answer and how you
                  have the TABLSET configured.  You can get fractional values by pressing 2ND TBLSET
                  and changing the ΔTbl to a decimal.  Generally, if this happens I would change to one of the
                  other methods.
           Using the Solver:
        
   a)  From the home screen, press MATH, 0 (that's zero) and the Equation Solver will be displayed.
            b)  Enter your equation opposite eqn:0=.  If that is not displayed, press the up-arrow; then enter
                 the equation.
            c)  Press ENTER and the present value of x and the bounds will be displayed.  Change the bound
                 if you wish; then position the cursor opposite x=.
            d)  Press ALPHA, SOLVE (the ENTER button) and the smalller will be displayed after a short time.
            e)  Now, to find the other root, change the left bound to slightly above 3, say  3.001and enter 4.
            f)  Press ALPHA, SOLVE and the second root will be displayed. 
 

16. Using TABLE to Graph an Equation by Hand:   
        
a)  Press Y= and clear all equations from the Y= positions, then enter an your equation, say
              x² -8x +15, opposite Y1=.            
         b)  Press 2ND, TABLE and scroll up or down  the list of x-values in the tables to find
              numbers that are convenient for the size of your graph paper.  X-values 1, 2, and 3
              with corresponding y values 8, 3, and 0 would normally be satisfactory for this particular
               equation.
          c)  Use the x- and y-values to locate points on your graph and draw the graph in the usual
              manner. 
         d)  If the numbers are too far apart in value, you can change their spacing by changing the     
              ΔTbl setting.  To do that, press 2ND TBLSET  and changing the ΔTbl to the
              separation you want.  Then press TBLSET to go back to the tables.
          e)  If you want to use specific values of “X,” press 2ND, TBLSET, move the cursor down to
                “Ask” opposite “Indpnt” and press ENTER. Now press 2ND, TABLE to go back to the
                tables.  You can now enter the x-value(s) of your choice and the corresponding y-value  
                will be displayed in the y-column.
           Easier Method:  The following method is easier and just as good for linear equations:
           First use a) and b) above to graph the equation.
           c)  Press Trace and move the cursor in the range of the values of "x" that you want to find values for.
           d)  Enter a value for "x"  that you want to find a y-value for.  The x- and y-values will appear on the screen.
            f)  Repeat this process starting with "Press Trace" for each set of values that you want.

17.  Evaluating a Function at a specific variable value:
       There are four ways to do this:
          Using the Home Screen:
         
Assume that we have the function y=x²+3x +2 and we want to evaluate this function at x=-2.
            a)  From the home screen, enter -2; then press X (the X,T,0,n button), STO, ALPHA, :(the colon is made
                 with the decimal key.
            b)  Enter your equation, say x² -8x +15, immediately after the semicolon so that you have -2
→X:x²+3x+2. 
            c)  Press ENTER and the answer will be displayed.  
            d)  If you want to do additional values, press 2ND, ENTRY.  Change the -2 to whatever you want and press
                 ENTER.
            e)  If you want the answer in fractions, after step b), press MATH ENTER to get -2
→X:x²+3x+2►Frac.
           Using the CALC method:
           
a)  Press Y= and enter your equation, say x² -8x +15
            b)  Press 2ND, CALC, ENTER and the graph will be displayed.
            c)  After the graph is drawn, enter -2 opposite the X= entry and press ENTER.  The answer will be displayed.
           Using the TABLE: 
            
Once you get the TABLESET configured, this is one of the easiest methods, especially if you want
              to evaluate the function at several values such as doing a curve by hand.
             a)  Press 2ND, TABLESET, move the cursor to "ASK" opposite Indpnt and press ENTER.
             b)  Press 2ND, TABLE and enter whatever values you want in the x-column.  The corresponding
                  values of y will appear in the Y-column.
            Using the Solver:
            
a)  From the home screen, press MATH, 0 (that's zero) and the Equation Solver will be displayed.
             b)  Enter your equation opposite eqn:0=.  If that is not displayed, press the up-arrow; then enter
                 the equation.  After you have entered the equation above, you will need to enter a dummy variable,
                 say D, so that the entry looks like this: eqn:0=x²+3x +2 -D.  Enter the "D" by pressing ALPHA,
                 D (the key for x-1 ).
             c)  Press ENTER  and the present value of x and the bounds will be displayed.  Change the value of x to
                  x=-2.  Change the bounds  if you wish; then move the cursor to D, the variable you want to find the value for.
             d)  Press ALPHA, SOLVE and the answer will be displayed as the value for D after a short time.  With this
                  problem, the answer will be D=35 for x=-2.

18.   Using the Solver for Polynomials of degree >2:
          
Let's take as the example x^4+10^3+35x²+50x +24
        
    a)  From the home screen, press MATH, 0 (that's zero) and the Equation Solver will be displayed.
             b)  Enter your equation opposite eqn:0=.  If that is not displayed, press the up-arrow; then enter
                  the equation.
             c)  Press ENTER and the present value of x and the bounds will be displayed.  Change the bound
                  if you wish.  Let's use {-24,0}.  Then position the cursor opposite x= and enter -24.
             d)  Press ALPHA, SOLVE (the ENTER button) and the smaller of the roots will be displayed after a short time.
                  The answer we get will be -3.9999999... which is -4.
             e)  Now change the bounds to {-3.8, 0} and the number opposite x= to -3.8. 
                  Press ALPHA SOLVE and you'll get -.99999999... which is 1.
             f)  You can either continue this process or use synthetic division to find the second degree equation and solve
                 that in the usual manner.

 V. SPECIAL FUNCTIONS
 1.  Changing from radian measure to the degree mode:
          a) Press the MODE key.
          b) Move the cursor to either radian or degree to match the units of your angle.
          c) Press Enter.
          d) Press CLEAR or 2nd, QUIT to return to the calculator screen.

  2. Graphing piecewise functions or  functions on an interval:
         
 a) To graph a function on the interval x < a, enter the function in parentheses, followed by
             (x<a).  For example, to graph x² -2 on the interval x<1, enter this:  (x²-2)(x<1)
          b) To graph a function on the interval x > a, enter the function in parentheses, followed by (x>a).
          c) To graph a function of the interval a<x<b, enter the function in parentheses, followed by
             (x>a)(x<b).

3.  Graphing trigonometric functions:
          a)  You must have the calculator set to radians to graph a trig function.  See the MODE section if
               you don't know how to do that.
          b)  Press "Y=" and then press the button for the function you want to graph.
          c)  Enter the argument of the function, e.g., X, and press GRAPH.

 4.  Hyperbolic Functions:
        The hyperbolic functions are available on the TI-84, but only from the catalog.  Find cosh as follows:
        a)  Press 2ND,  CATALOG and the catalog listing will appear.
        b)  Press  C; then scroll down to cosh(, and press ENTER.  Note that the catalog automatically selects
             the ALPHA mode, so do not press ALPHA before pressing C.
        c)  Enter the value of the argument and press ENTER.  You may either close the parentheses or not
             as you choose.
         d)  You may enter more than one value for the argument by entering the values as a list. For example,
              cosh({.5, .7, .9}); then ENTER.  You must close the braces, but you have the option of closing the
              parentheses.
              Note that the other hyperbolic functions are listed in alphabetic order in the CATALOG.
         e)  The hyperbolic functions can also be graphed by pressing Y= and going through the steps above to
              enter the desired function opposite Y1, for example.  Enter "X" as the argument and press GRAPH to
              display the graph of the function.

5.  Graphing Parametric Equations:
    
Suppose that an object has been launched with an initial velocity of 50 m/s at an angle of 30 degrees.  Graph the trajectory
     and determine the maximum height and range. 
     a)  Press MODE and highlight PAR in the fourth line and press ENTER.
     b)  Press Y= to go to the graphing screen and enter 50cos(30)T opposite X1T and 50sin(30)T-1/2*9.8T² opposite Y1T.
     c) Press WINDOW and set Tmin = 0, Tmax = 6, Tstep = .1, Xmin=0, Xmax=250, Ymin=-2, and Ymax=250.  Set the scales at 10 or
         whatever value you wish. Press Graph to graph the trajectory. The setting of Tmax is not critical, but if it is too long, the graph may
         take a long time to complete, and if it is too short, the graph will not be extended to the x-axis.
     d)  Press TRACE and move the cursor to the maximum as indicated by the y-values at the bottom of the screen.  Do the same for
          the point where the graph crosses the x-axis to get the range.
     f)  You can find the velocity and the component velocities at any point as follows:  Press 2ND, CALC, press the number for the component
          ( dy/dx, dy/dt, dx/dt) you want.  Now, move the cursor to the point on graph where you want the value and press ENTER.             

VI.  CALCULUS
1.   Finding the numerical derivative of a function:
          a) Press the Math key.
          b) Press 8 to select nDeriv(.
          c)  Press 2nd, Y-VARS; select the variable you want and press ENTER.
          d)  Enter the name of the independent variable, probably X.
          
e)  Enter the value of the point where you want the derivative evaluated. For example if you want
               the derivative for Y1 evaluated at 3, you would have this: nDeriv(Y1, x,3). 
           f)  Press ENTER and the value will be displayed.

  2.  Determining the value of the derivative from points on a graph.
          a) Enter the function and graph.
          b) Press 2nd, CALC.
          c) Press 6 to choose dy/dx.
          d) Move the cursor to the desired point and press ENTER. The value of the
              numerical derivative will appear at the bottom of the screen.

  3.  Drawing a tangent line at a point.
          a) Enter the function and graph.
          b) Press 2nd, DRAW.
          c)  Press 5 to select Tangent(.
          d)  Move the cursor to the point of tangency desired and press ENTER.
          e)    To clear the tangent line, press 2nd, DRAW and then  ENTER.

  4.  Calculating the value of a definite integral:
       
Be sure to have the calculator in radian mode.
         a) Press the MATH key.
          b) Press 9 to select fnInt(.
          c) You will now enter an expression in the form Y,X,a,b inside the parentheses.
              In that expression, Y is the expression you are integrating; for example Y1, X is the
              variable of integration, usually X; a is lower limit and b is the upper limit.   
          d) For the expression to be integrated, you can either choose a variable entered
              into the Y= screen, or you can enter the expression itself.  As an example,
              you might have  fnInt(Y1,X,1,2 with your expression entered into Y1, or you
              might have fnInt( x2,x,1,2 where you have entered the expression x2 yourself.
              Notice that you must enter Y1 from the Y-VARS menu if you use that
             method.
          e) Press the ENTER key to see the value of the definite integral.
          Note that with the newer TI-84 set in MATHPRINT mode the format for the definite integral is displayed.  The appropriate
          components--function, limits, etc.--are filled in using to cursor arrows to navigate to the different parts.  When all is completely
          filled in, press ENTER to get the answer. 

  5.  Alternate procedure for finding the value of a definite integral.
          a) Press the ZOOM key.
          b) Press 4 to select ZDecimal.  (You don’t have to do this step, but it will be
              easier to set your limits if you do.)
          c) Press the Y= key.
          d) Enter the function you are integrating.
          e) Press the GRAPH key.
          f) Press 2nd, CALC.
          g) Press 7 to select the integral.
          h) Move the cursor to the lower limit of integration and press the ENTER key.
      
   i) Move the cursor to the upper limit of integration and press the ENTER key.
 
         j) The integrated region will be shaded, and the value of the definite integral will
            appear at the bottom of the screen.   (NOTE:  Be careful about curves that go below the x-axis.)
          k)  To clear the shaded area, press 2ND, DRAW, ENTER.

 VII.  MATRICES:
1)  Entering a matrix:
         a)  Press 2nd, MATRIX, move the cursor to EDIT.
         b)  Move the cursor to the matrix number you want to edit or enter numbers into
                   and press ENTER.
         c)  Enter the number of rows and press ENTER; then enter the number of
                   columns and press ENTER.
         d)  Enter each value of the matrix and press ENTER after each value.
         e)  Press 2nd, QUIT to go to the home screen.       

 2)  Multiplying two matrices [A] * [B]:
         a)  Enter the data into matrices [A] and [B] and press 2nd, QUIT to go to the
                   home screen.
         b)  Press 2nd, MATRIX, select the matrix you want as the first in the product, [A],
                  and press ENTER.
         c)  Press the multiply symbol.
         d)  Press 2nd, MATRIX, select the matrix you want as the second in the product,
                  [B], and press ENTER.
         e)  Press ENTER to perform the multiplication step.
         f)  Remember that the numbers of columns in [A] must equal the number of
                  rows in [B] or you will get a dimension error.
 3)  Doing other matrix math:
         a)  Press 2nd, MATRIX and cursor over to MATH.  There you will see a list of
              operations that you can do.  To do find the determinant, use Det.  To find
              the transpose, use T. 
         b)  After you select the operation you want, press ENTER.
         c)  Press 2nd, MATRIX, select the matrix you want to operate on, and press
              ENTER.
         d)  Press ENTER again to get your answer.    

 NOTE:  You can do any of the elementary row operations.  They are very useful for doing the arithmetic for Gauss or Gauss-Jordan elimination, but a little time is required to get the hang of doing row operations. So, since most students don’t take the time to use those functions, I’m not going to include them.  Instead, I’ll give you my Website as a reference for doing those operations if you want to do them.  First go to my Website:  http://www.grafcalcwhiz.com
Go to the listing “TI FAQs” in the navigation bar on the left.  Click on the link “More Detailed Page 1”. That will take you to a long page of 40 FAQs.  Cursor down to the answers and then down to answer (21). That will give you the procedure for doing the row operations.  Alternately, to find item 21,  you can use Find under the Edit menu and enter (21) in the dialog box.  Then click Next to find the answer.    

 4)  Doing rref and ref:
         a)  First enter your matrix as in item 1 of this section and press 2nd, QUIT to go to the home
              screen.
         b)  Press 2nd, MATRIX, and move the cursor to MATH.
         c)  Select item A for ref or B for rref as you choose and press ENTER.  Note that if you know you
              want to use item B or A(for rref or ref) just press ALPHA; then the appropriate letter.
         d)  Press 2nd, MATRIX and press the number for the matrix you want to operate on. You should now
              have displayed on the home screen rref(A, or the letter for whatever matrix you have chosen.
         e)  If you want non-integer answers to be displayed in fractions skip to the next step.  If you want them
              displayed in decimals, press ENTER and the answer will appear.
          f)  If you want the answer in fractions, and press MATH, ENTER and rref([A]
►Frac will be displayed
                  on the home screen.  Press
ENTER to display the answer.  .

5)  Solving a system of linear equations:
      Let's take the following set of simple equations:
         3x -3y = -2
         2x +y = 1
      
Entering the matrix:
         a)  Press 2nd, MATRIX, move the cursor to EDIT.
         b)  Move the cursor to the matrix (A, B, etc)  that you want to edit or enter numbers in,
                   and press ENTER.  (Alternatively, you can press the number opposite the matrix you choose.)
         c)  Enter 2 for the number of rows and press ENTER; then enter 3 for the number of
                   columns and press ENTER again.
         d)  Enter each value of the matrix and press ENTER after each value.  Enter only the coefficients of the
              variables and the constants.  Do NOT enter variables, or plus signs, but do enter a negative sign for either
              a negative or minus sign.
              Enter the numbers 3, -3, -2, 2, 1, 1 and press ENTER after each number.
         e)  When you have finished, press 2nd, QUIT to go to the home screen.    
      Solving the system of equations using the rref operation:
         f)   From the home screen, press 2nd, MATRIX, and move the cursor to MATH.
         g)  Select item B for rref and press ENTER.  Alternatively,  you can press ALPHA; then B to paste rref(
              to the home screen. 
         h)  Press 2nd, MATRIX and press the number for the matrix you want to solve, for example 1 for [A].
          i)  If you want the answer in fractions, press MATH, ENTER, ENTER, otherwise, just press ENTER and
              the answer will appear.

6)  Solving linear programming problems using the simplex method.
       You will need a program for this.  You can either copy one of my simplex programs from this
       website and enter it by hand or copy someone else's program.  STCC students may call me at
       333-5989 to arrange to have this program transferred electronically to their calculator.

VIII.  SEQUENCES AND SERIES:
        
1)  Find the first four terms of the sequence an =3n-2.
              a)  Press 2nd, LIST, cursor over to OPS and press 5.  seq( will be pasted to the home screen.
              b)  Enter 3; ALPHA; N; - ;2;, :ALPHA; N;, ; 1;, ;4  You now should have seq(3N-2, N, 1,4 on the
                   home screen.  (It is not necessary to close the parentheses in this situation.)  (Note that 
                   the second "N" is just defining the variable that you want to use.)
              c)  Press ENTER and {1  4  7  10} will be displayed.

         2)  Find the sum of the sequence above. 
              This type problem will usually be written using the summation symbol, Σ.
              a)  Press 2nd, LIST; cursor over to MATH and press 5.
              b)  Press 2nd, LIST, cursor over to OPS and press 5.  sum(seq(  will now appear on the 
                  home screen.
              c)  Enter 3; ALPHA; N; -;2;, ;ALPHA; N;, ; 1;, ;4  You now should have sum(seq(3N-2, N, 1,4 
                   displayed on the home screen. 
              d)  Press ENTER and 22 will be displayed.
             Newer TI-84 Calculators:
              a) Press 2nd, CATALOG ( the 0 key), and then "S." This will take you to the S-listings.
              b) Scroll down to "sequential Ʃ(" and press ENTER. The format for a summation will be displayedd
                  on the home screen.
              c) Fill in the blanks. You will have the summation sign formatted properly. It should contain the following
                  information: n=1 at the bottom of the summation sign, 4 at the top,and (3N-2) following the summation
                  sign.
              d)  Press ENTER and 22 will be displayed.

         3)  Find the cumulative sum of the above sequence.
              a)  Press 2nd, LIST; cursor over to OPS and press 6.
              b)  Press 2nd, LIST, cursor over to OPS and press 5. cumSum(seq(  will now appear on the
                   home screen.
              c)  Enter 3; ALPHA; N; -;ALPHA; N;, ; 1;, ;4  You now should have cumSum(seq(3N-2, N, 1,4. 
              d)  Press ENTER and {1 5 12  22} will be displayed. Note that this method gives the sum after each
                   increment of the variable N.
              e)  If you have a long list, you can store the results in list L1 by closing the parentheses, pressing
                  STO, 2ND, L1.  You should now have cumSum(seq(3N-2, N, 1,4))
→L1.
                   f)  Press ENTER and the list of numbers will be stored in list L1.  You can access the list by pressing
                        STAT, ENTER

         4)  Find the 5th term of the above sequence. 
              Although this is easily done by hand, some students like to check their results. So here's how to
              do it with your calculator.
              a)  Press 2nd, LIST, cursor over to OPS and press 5.  seq( will be pasted to the home screen.
              b)  Enter 3; ALPHA; N; -;2;ALPHA; N;, ; 5;, ;5  You now should have seq(3N-2, N, 5,5 on the
                   home screen.   (Note that the same number is entered for the beginning and end.)
              c)  Press ENTER and {13} will be displayed.
              Newer TI-84 Calculators:
              a) Press 2nd, CATALOG ( the 0 key), and then "S." This will take you to the S-listings.
              b) Scroll down to "sequential Ʃ(" and press ENTER. The format for a summation will be displayedd
                  on the home screen.
              c) Fill in the blanks as indicated in item two above, but be sure to have both the beginning and ending
                  terms set as 5.
                  sign.
              d)  Press ENTER and 13 will be displayed.

 IX.  Complex Numbers:

         1.  Finding Solutions of a Polynomial with Complex Coefficients:
        
Since the solver will not handle complex numbers, we must resort to other methods. Let's consider the equation
         (2-3i)x² +(4+i)x +(1-3i) = 0. 
         a)  Press MODE, cursor to FLOAT, move over to highlight 5, and press ENTER; then move down to the 7th line
              and highlight a+bi and press ENTER.  Press 2ND, QUIT to go back to the home screen.
         b)  Press 2, -, 3, 2ND, i (the second function of the decimal point), STO, ALPHA, A, ENTER.  This stores the
              coefficient of x² in variable "a."
         c)  Perform the same operation for the b, and c, the coefficient of x and the constant.
         d)  Now, press 2ND,
√, ALPHA, B, x2 , -, 4, ALPHA, A, ALPHA, C, ), STO, ALPHA, D.  This stores the discriminat
                   in variable d.  You can write this result down if you want it.
            e)   Press (, - (negative sign) , ALPHA,  B, +, ALPHA, D, ), ÷, (, 2, ALPHA, A, ), ENTER.  The first value for "x" will
                  be displayed.
            f)  Press 2ND, ENTRY (the ENTER key), and change the "+" sign between B and D to -. 
            g)  Press ENTER and the second value for "x" will be displayed.
                 NOTE:  You may want to change your number format back to Float.
             Here's a simple program that you can enter to do this:
             
PROGRAM: CMPXPOLY
             
"FKIZER 091207"
               :a + bi

           :Fix 5
           : Prompt A, B, C
           :
√(B² -4AC)→D
               : ClrHome
               :Disp "X1=", (-B+4AC)/(2A)
               :Disp "X2=", (-B-4AC)/2A
               :  Float   (This last step sets the calculator number format to Float.  If you don't want that, leave it out.)

X. Combining and Connecting Operations:

    1) Doing expressions with several terms:
       
One of the powerful tools for use with a calculator is combining terms and connecting terms to perform
        several operations sequentially.  Let's take for example the index of Shannon which is used in ecological
        assessments.  This is the expression:
        H' = -
Σ(pi *ln (pi)   (where pi is each Ni/sum (Ni) in the table below.
      This table represents the equation as applied to four different types, i, of trees found in 100 m² of forrest. 

 i  Ni  pi  ln (pi)  pi*ln(pi)
 1  6 .3  -1.2034   -.3612
 2  4 .2  -1.6094   -.3219
 3  2 .1  -2.3026  -.2303
 4  8 .4  -0.9163  -3.665
SUM  20      -1.27985

 Solving with lists:
NOTE: 
If you get a dimension error in any of the following operations, you will need to dimension the lists.  You
can do that by just adding zeros of the same quantity as the numbers in List L1 .  If the lists are too long for that, you
can use the dimension statement.  Example:  10→dim(L3) and add a new list for each list you want to dimension. 

 
a)  Clear lists L1 through L5 as described under Lists above, and enter the data in columns 1 and 2 from the table in
         lists L1 and L2 respectively..
  b)  Place the cursor on the title for L3 and enter the following: 2ND,  L2, ÷, 2ND, List, MATH, 5, 2ND, L2 ,).
       The expression  L2/sum(L2) should appear at the bottom of the screen opposite L3=.  Press ENTER.
  c)  Move the cursor to the L4 title and do the following keystrokes: LN, 2nd, L3, ), ENTER.
  d)  Set the cursor on the L5 title and do the following keystrokes: 2nd, L3, *  L4, ), ENTER.  Check all of the
        numbers except SUM to make sure they are correct. 
   e)  To get the final sum, press 2nd, QUIT to leave the lists, then press the (-) key.
   f)  Press 2nd, LIST, MATH, 5 ( for sum), 2nd, L5, ), ENTER.  The final answer
H' = 1.27985 the negative of SUM in the
      table above.
Doing it all in one step:
The values for Ni, pi, ln (pi), and pi*ln (pi) can be entered in lists  L3, L4 and L5 with one series of expressions
 as follows:
   a)  First clear the five lists by pressing STAT, 4 to paste ClrList to the home screen.
   b)  Then enter the five lists by pressing 2ND; then the key for the list number for each list to be cleared.
        The list names should be separated by commas.
   c)  Enter the values for i in L1 and those for  Ni in L2 by pressing STAT, ENTER and entering the numbers.
   d)  Now press 2ND, QUIT to go to the home screen.
   e)  Enter the following on the home screen: L2/sum (L2)-->L3:ln (L3)-->L4:L3*(L4 )-->L5: -sum(L4).  Note that sum(
        is entered by pressing 2ND, LIST, MATH, 5 and the colons are entered by pressing ALPHA, and the decimal
        point button.
   f)  Press ENTER and all of the data in the table above will be entered in the lists except the sum and that will be
       displayed on the home screen.
  Suppose you only want the answer without the data for various steps.  Do this:
      a) After clearing the lists and entering the data as in steps a through d above, enter this formula:
      
-sum((L2/sum (L2)(ln((L2/sum (L2)).  The only entry that might not be obvious is sum(, which can be
       obtained by pressing
2ND, LIST, MATH, 5. Be careful that you have the parentheses correct.

XI.  Operations with List:
      
Arithmetic with lists is a very powerful tool for saving time, especially when doing statistics.  For a complete treatment
       of list arithmetic as applied to statistics, see the statistics guide on this same website.

       1)  Clearing a list:

            To clear a list, place the cursor on the title of the list, for example L1, and press CLEAR, then
             enter.
       2)  Doing Arithmetic with Lists:
           
The normal arithmetic operations (-,+,x,
÷, √, and square), can be done by placing the cursor on the  list title
                 and entering the desired arithmetic operation involving one or more lists.  The columns in the reference
                 lists will be operated on item by item and stored in the list where the cursor is located.  Note that you can do the sum of
                of a list at the end of the items in a list if you wish.
                

      
3)  Using the Lists to do LOGIC functions:
       NOTE:  You can use the logic functions such as "and", "or," "xor," or "not," to do things such as
                   Boolean algebra and truth tables.  Note that you must use "1" for true and "0" for false.  As
                   a simple example, suppose you wanted to do p ^ q. 
          a)  Press STAT, ENTER and enter the proper combination of 1s and 0s for p in list L1.
            
b)  Enter the proper combination of 1s and 0s for q in L2.
          c)  Clear L3 if necessary, and place the cursor on the title for L3 above the table. 
          d)  Now press 2ND, L1,2ND, TEST, select LOGIC, and press number 1 (for "and"), 2nd,  L2.
           e)   Press ENTER. The entries in the first row in the tables will be evaluated and stored in L3.
                Obviously, you can also use the other logic operations in place of "and."  Also, you can do a longer
                 logic expression by using the results in one list with a set of truth values in another list.

XII Special Techniques:
       1) Graphing equations of the form x=y² +3x +2:
           Method I:  Graph this equation using the parametric method.  If we let y = t, then x=t² +3t+2.

          
a)  Press MODE, scroll down to highlight PAR in the fourth row and press ENTER.  Press 2nd QUIT to exit
                the MODE function.
           b)  Press Y= and enter T² + 3T +2 opposite X1T and T opposite Y1T.
           c)  Press ENTER and the parametric graph will be displayed. 
            Note that TRACE is operative in this move, but that Minimum, Maximum, Zero and other functions associated
             with the function mode are not operative. 
           Method II:  For the reasons in the note above, it's probably easier just to change variables and graph using
            the function mode.
            a)  With the calculator in the normal function mode, re-write the equation as y=x²+3x +2.
            b) Enter the right part of the equation opposite Y1= and graph as usual.
            c)  All of the functions are available as usual, but you must switch the values for x and y if you are going to do any
                 graphing by hand or use the values in any other way.  .
            d)  If you want to see what the curve actually looks like, then draw the curve as follows:
                 1)  Press 2nd, DRAW, scroll down to DrawInv, and press ENTER.
                 2)  Press VARS, move the cursor to Y-VARS and press ENTER, ENTER. You should have DrawInv Y1 on the home
                      Screen. 
                 3)  Press ENTER and the function will be drawn.  Notice that none of the functions are operative.  Then general
                      trace can be used, however.

XIII. TRANSFERRING PROGRAMS AND DATA:

        1)  Transferring programs between calculators for TI-83 Plus:
             a) Turn both calculators off and plug in the unit-to-unit cable for both calculators.
             b) Turn on both calculators and press 2nd, LINK on both. Cursor over to
                  RECEIVE on the receive calculator, the calculator that you're transferring the
                  program to.
             c) Press ENTER on the receive calculator. The word "Waiting"  should appear.
             d) On the sending calculator, cursor down to Prgm and press ENTER.
              e) Cursor down to the program you want to transfer and press ENTER. The 
                  program that you selected will be marked with a square "dot."
            f) Cursor over to TRANSMIT press ENTER.
             g)  If everything is connected satisfactorily, transmission of the program should
                  start. Otherwise,  you'll get a transmit error after a few seconds.

2)  Writing a program on a computer for a TI-84 calculator:
          Well, there may be more than one way to do it, but here's the way I do it.  First you must have the Graph Link software for
         the TI-83 Plus calculator.  That can be downloaded free from the TI Website. Once you get that installed, just click on the icon
         and the application will open.  It's pretty  straightforward from that point.  I suggest you save the file to a folder that you will
         use to transfer the program to your calculator.  I will deal with that transfer in the next FAQ.
________________________
3)  Copying  a program from my computer to my TI-84 calculator:
          Here's the way I do it.
          a. Open TI-Connect and connect the calculator to the computer with the USB cable.
          b. Click on the TI-Device Explorer icon.
          c.  Open the folder where the program you want to copy to the calculator is stored.
          d. Drag that file to the TI-Device Explorer folder.
          e. Copying of the file will begin in a half minute or so.
_______________________________
4)  Copy a program a TI-84 calculator to a computer?
          a. Open TI-Connect and connect the calculator to the computer with the USB cable.    
              Make sure the calculator is on.
         b. Click on the TI-Device Explorer icon.
         c. After the connection to the calculator is established and the list is displayed, expand Program by  
             clicking on the + mark beside “Program.”
        d. Highlight the program that you want to copy to the computer.
        e. Click on the File menu and select Copy to PC.
        f.  The folder "My Documents" will appear with the folders listed.  Select the folder where you want to store the program and
            open it.
        g.  Copying the file will begin shortly.

XIV.  Applications:
        1.  Conversion Application:
          Finding a Conversion:
         
a)  Press APPS, scroll down to SciTools, press ENTER, and finally press any key to  
               go to the menu for the unit converter.
          b)  Press 2 for the UNIT CONVERTER.  You will notice twelve items on the menu and a
               CONSTANT function at the bottom of the screen.  Pressing Y= or WINDOW toggles 
               between constants and conversions.
         As an example, suppose you want to convert quarts to liters. 
         a)  Select 3 for volume from the CONVERSION menu and move the cursor to highlight  
             qt. If you only want the conversion, press 1, but if you want to convert, say, 4 quarts   
             to liters, press 4.  In this example, we’ll convert 4.  So, press 4.
        b)  Press ENTER and the 4E0 qt► will be displayed on the screen.
        c)  Move the cursor to highlight “L “ and press ENTER.  The conversion 3.785412E0  L  
             will be displayed on the screen. 
        Exporting a conversion:
       a)  If you want to export the conversion to the home screen for other calculations, press ZOOM for EXPT. 
       b)  Now, you must press 2nd, QUIT repeatedly until EXIT appears.  Now press Y= for EXIT and you will
            be taken to the home screen. 
      Using COPY for Constant Conversions:
      Suppose we want to convert the gravitational constant from its normal dimensions of m/s² to ft/s²
      a)  If CONSTANT is not already selected, select it by pressing Y=.
      b)  Move the cursor to highlight “g” and the value in m/s² will be displayed.
      c)  Press TRACE for COPY to display the CONVERSION menu, then press 1 for
           LENGTH. 
    d)  Highlight “m” as the unit to convert from and press ENTER, then highlight “ft” and the unit to convert to. 
          Finally, press ENTER.  The value 3.217405E1 will be displayed. 

XV. VECTORS:
    General: Vector arithmetic is done using lists.
     1. Multiplication by a scalar: Let's multiply the vector <2,3> by the scalar -5.
         a) Go to the lists by pressing STAT, ENTER and enter 2; then 3 in list L1.
         b) Quit the list editor by pressing 2nd, QUIT and enter -7,x (multiply symbol), 2nd, L1.
         c) Press ENTER to display the answer, {-14,-21}.

    2. Dot Product: Let's do the dot product of the vectors <2,3,1> and <4, -3,2>
         a) Press STAT, ENTER and enter the first vector in list L1 and the second in L1. Be aware that you will have
              three separate entries for each vector.
         b) Press 2nd, QUIT, to quit the list editor.
         c) From the home screen, press 2nd, LIST, scroll to MATH, and press 5 to display sum(.
         d) Press 2nd, L1, x (the multiply symbol); then 2nd, L2, so that you have sum(L1*L2. Close the parentheses if you
              wish.
         e) Press ENTER to display the answer, 1.
        Angle Between Vectors: To find the angle between these two vectors, divide the answer above by the following
         expression: √sum(L12 )sum(L22 ). The steps are as follows:
         f) After you have found the dot product as described above, press 2nd, Ans,÷.
         g) Now, do the following: Press 2nd,
√, 2nd, STAT, scroll to MATH and press 5 to display sum(, 2nd, L1, x2 ,). You
              should now have Ans/
√(sum(L12 ).
         h) Now, press 2nd, STAT, scroll to MATH and press 5 to display sum(, 2nd, L2, x2 ,). You
              should now have Ans/
√(sum(L12 )sum(L2 2 )). Press ENTER to get cos of the vectors.
         i) Make sure the MODE is set to DEGREE, the press 2nd, COS, 2nd, Ans to get the answer. Note that if
             that if you have the latest version of the TI-84 operating system, you may not need the outer set of
             parentheses in the denominator.

  3. Triple Scalar-Product: The triple scalar-product is just the determinant of the three vectors. Make sure you
       enter them in the proper order. The steps are as follows:
       a) Press 2nd, MATRIX to go to the matrix editor and scroll over to EDIT and press ENTER.
       b) ENTER 3 twice so that you have 3 x 3 for the size; then enter the three vectors in the proper order, for example
            u first, v second, and  w last.
       c) Press 2nd, QUIT to exit the editor; then press 2nd, MATRIX, scroll to MATH and press 1 to display det(.
       d) Press 2nd, MATRIX, ENTER so that you have det(|A|. Press ENTER to get the answer.

 4. Cross-Produce Program: There's not a good way to do the cross product with the available functions. But for
        those who need to do cross products often, I leave a simple program. When the program prompts, you must    
        enter the vectors in lisst format, e.g., {3, 4, 7}. The program follows: (The colons are inserted by the calculator.)
        :"FKIZER 070414"
        : Input "VEC 1", L1
        :Input "VEC ", L2
         
:L1(2)L2(3)-L1(3)L2((2)-->I   (--> is the STO key entry.)
        :-L1(1)L2(3)-L1(3)L2((1)-->J
        :L1(1)L2(2)-L2(1)L1((2)-->K
        :ClrHome
        :Disp "I=", I
        :Disp "J=", J
        :Disp "K=", K
         This is a very unsophisticated program, but just about anyone should be able to type it in and run it. Good luck.

 

 XVI.  PROBLEMS:

          1)  Problems with trigonometric functions:  The most common problem with trig functions is not having the MODE
              set to the dimension of the number entered.  For example, students may have entered degrees, but have their
              calculator MODE set to radians.  To correct that, see “Changing the MODE in section I.

          2)  Dim Mismatch:  This occurs when doing operations on lists that do not have the same number of entries or when doing arithmetic on
               matrices that do not have the same number of rows or columns.  To correct that, make sure you have the correct number of entries. It can
               also occur when graphing if you have one of the plots highlighted and the number of data points in the x-and y-lists do not match.  To correct
               that, just move the cursor to the plot entry, Plot1, Plot 2, etc, and press ENTER to remove the highlight from the plot entry.

          3)  If your calculator hangs up and you are unable to correct the problem, first try online or other places that provide
            help.  If you are unable to get help, you can reset the calculator.  Do that as follows:
                  a)  Press 2nd, MEM, press 3.
                  b)  Press 7 to select RESET.
                  c)  Press 2 to select Defaults.  Your calculator should now be reset.

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