Using the TI-83+ ™
Setting up the calculator.
Graphing the sine and
cosine functions.
Graphing the tangent
Graphing the reciprocal
trig functions.
Setting Up the Calculator
Press the Mode key.
Select the appropriate
Press Window key.
Choose your x-min value
and x-max value.
Use the “pi” or “π” key when
Set your x-scale by using ¼
of the length of the period.
Graphing Sine and Cosine Curves
in the form: y= a sin(bx)
y =a cos(bx)
Choosing the Ymin and Ymax values depends on
the amplitude. Find the amplitude, l a l.
It is recommended to select a Ymin at least one
value lower than your amplitude (plus the phase
shift) and to select a Ymax at least one value higher
than that value. Select an appropriate y-scl based
on the size of your amplitude. A “1” value will
probably be sufficient.
Leave Xres = 1.
Viewing the Graph
Press the y= key.
Check to be sure the
“Plot 1” key is not
Enter the equation
under Y1=.
Press the graph key.
SAMPLE GRAPH: y= 3 sin(2x)
For y = 3 sin (2x), the
amplitude = 3 and the
period is (2π)/2 or π.
Setting The Window:
In order to graph 2 full
cycles, set the Xmin at –π
and the Xmax at π.
Since the period is π, the
Xscl should be ¼ of π, or
Since the amplitude is 3,
set the Ymin = -4, the
Ymax = 4, and Yscl=1.
Enter the equation in Y1=
Graphing the tangent curve in
the form of y = a tan (bx)
The window setting for x min and x max
should be set according to the number of
cycles desired. Again, the x scl should be set
to ¼ of the period. Recall the period of the
tangent function is π/ lbl
Since the tangent function has no upper and
lower limit, choose a reasonable y min and y
max value for the window setting. Be sure to
include values at least from a to –a.
SAMPLE GRAPH: y = 2 tan x
For y = 2 tan x, a = 2
and the period is π/1,
or π.
Setting the window:
Since the period is π,
the Xmin should be set
at –π, the Xmax is π,
and the Xscl should be
set to π/4.
Since a =2, set the
Ymin to -5, Ymax to 5,
and the Yscl to 1.
Enter the equation in
In order to graph the
reciprocal trig functions,
use the reciprocal key
x-1 with either the sin,
cos, or tan key.
SAMPLE PROBLEM: y = 2sec x
Since the secant is the reciprocal of cosine, consider
the graph of y = 2 cos x when setting the Xmin,
Xmax and Xscl on the window. Since the period is
2π, set the xscl:
Xmax = 2π
Xscl =π/2
Since the secant has no limit, set the Ymin lower
than –l a l and Ymax higher than la l.
Xmin= -2π
Ymin=- 6 and Ymax = 6.
Enter the equation in Y1=.
The graph of y = 2 sec x
The graph of y = 2 sec x
is shown here. Do you
see the asymptotes?
Are there any x or yintercepts?
Now, try these! Graph at least
two cycles.
y = 3 csc 4x.
y = 5 cot 2x.
y = 2 cos ¼x.
y = -4 sin πx
y = ½ tan x.
y = -3 sec x/2
1) y= 3csc(4x)
2) y=5cot (2x)
3) y= 2 cos ¼x 4) y=-4sinπx
5) y= ½ tan x
6) y= - 3sec x/2

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