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 2^{nd} 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 2^{nd}; 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 2^{nd}, 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 2^{nd}, 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 2^{nd}, 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 2^{nd}, 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 x^{2}
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 x^{2}
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 (x^{2} 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 2^{nd} ; 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:
log_{b}x =log_{a}x/log_{a}b
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 2^{nd},
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 2^{nd}, 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 2^{nd}, 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 2^{nd}, 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 X^{2}
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 2^{ND}, 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 2^{ND},
TBLSET, move the cursor down to
“Ask” opposite “Indpnt” and press ENTER. Now press 2^{ND},
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 2^{nd}, 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 X_{1T} and 50sin(30)T-1/2*9.8T² opposite Y_{1T}.
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 2^{nd}, 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 2^{nd}, 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 2^{nd}, 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 2^{nd}, 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( x^{2},x,1,2
where you have entered the expression x^{2} 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 2^{nd}, 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
2^{nd}, 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 2^{nd}, QUIT to go to the home screen.
2) Multiplying two matrices [A] * [B]:
a) Enter the data into matrices [A] and [B] and press 2^{nd},
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
2^{nd}, 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 2^{nd},
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 a_{n} =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 L_{1}
by closing the parentheses, pressing
STO, 2ND, L_{1}. You should now have cumSum(seq(3N-2, N, 1,4))→L_{1}.
f) Press ENTER and the list of numbers will be stored in list L_{1}.
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, x^{2} , -, 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(p_{i}
*ln (p_{i}) (where p_{i} is each N_{i}/sum
(N_{i}) in the table below.
This table represents the equation as applied to
four different types, i, of trees found in 100 m² of forrest.
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 L_{1
}. If the lists are too long for that, you
can use the dimension statement. Example: 10→dim(L_{3})
and add a new list for each list you want to dimension.
a) Clear lists L_{1 }through L_{5
}as described under Lists above,
and enter the data in columns 1 and 2 from the table in
lists L_{1 }and L_{2 }
respectively..
b) Place the cursor on the title for L_{3} and enter the
following: 2ND, L_{2, }÷, 2ND, List, MATH, 5,
2ND, L_{2} ,).
The expression L_{2}/sum(L_{2})
should appear at the bottom of the screen opposite L_{3}=. Press
ENTER.
c) Move the cursor to the L_{4} title and do the following
keystrokes: LN, 2nd, L_{3}, ), ENTER.
d) Set the cursor on the L_{5 }title and do the following
keystrokes: 2nd, L_{3}, * L_{4}, ), 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, L_{5}, ),
ENTER. The final answer H' = 1.27985 the negative of SUM in the
table above.
Doing it all in one step:
The values for N_{i}, p_{i}, ln (p_{i}), and p_{i}*ln
(p_{i}) can be entered in lists L_{3}, L_{4} and L_{5} 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 L_{1} and those for Ni in L_{2} 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: L_{2}/sum
(L_{2})-->L_{3}:ln (L_{3})-->L_{4}:L_{3}*(L_{4
})-->L_{5}:
-sum(L_{4}). 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((L_{2}/sum
(L_{2})(ln((L_{2}/sum (L_{2})). 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 L_{1}, 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
L_{1.
}
b) Enter the proper combination of 1s and 0s for q in L_{2}.
c) Clear L_{3} if necessary, and place the cursor on the
title for L_{3} above the table.
d) Now press 2ND, L_{1},2ND, TEST, select LOGIC, and press number 1 (for "and"), 2nd, L_{2}.
e) Press ENTER. The
entries in the first row in
the tables will be evaluated and stored in L_{3}.
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 X_{1T} and T opposite Y_{1T}.
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 2^{nd},
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 L_{1}.
b) Quit the list editor by
pressing 2nd, QUIT and enter -7,x (multiply symbol), 2nd, L_{1}.
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 L_{1} and the second in L_{1}. 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, L_{1}, x
(the multiply symbol); then 2nd, L2, so that you have sum(L_{1}*L_{2}.
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(L_{1}^{2}
)sum(L_{2}^{2} ). 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, L_{1}, x^{2} ,). You
should now have Ans/√(sum(L_{1}^{2} ).
h) Now,
press 2nd, STAT, scroll to MATH and press 5 to display
sum(, 2nd, L_{2}, x^{2} ,). You
should now have Ans/√(sum(L_{1}^{2} )sum(L_{2}^{
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", L_{1}
:Input "VEC ", L_{2
}:L_{1}(2)L_{2}(3)-L_{1}(3)L_{2}((2)-->I
(--> is the STO key entry.)
:-L_{1}(1)L_{2}(3)-L_{1}(3)L_{2}((1)-->J
:L_{1}(1)L_{2}(2)-L_{2}(1)L_{1}((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 2^{nd}, MEM, press 3.
b)
Press 7 to select RESET.
c) Press 2 to select Defaults. Your calculator should now be reset.
Copy Restrictions:
You
may make single copies of this document for your own personal use and for the
use of other students, but inclusion in another document, publication or any use
for profit requires my permission. Teachers may make multiple copies of this
document for their students if they first get permission from me. Merely send
me an email (Just click on Webmaster in the navigation bar.) with a one-sentence
explanation of what you’re using the document for. I’ll give you permission in
a timely manner.
Making it Better: I
would be grateful if you would report any errors or suggestions for improvements
to me. Just click "E-mail Webmaster," site the item number, and tell me
your suggested change.
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