GRAPHING
TRIGONOMETRIC
FUNCTIONS
Using the TI-83+ ™
GRAPHING BASIC
TRIGONOMETRIC FUNCTIONS
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Setting up the calculator.
Graphing the sine and
cosine functions.
Graphing the tangent
function.
Graphing the reciprocal
trig functions.
Setting Up the Calculator
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Press the Mode key.
Select the appropriate
mode.
Press Window key.
Choose your x-min value
and x-max value.
Use the “pi” or “π” key when
appropriate.
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)
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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
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Press the y= key.
Check to be sure the
“Plot 1” key is not
highlighted.
Enter the equation
under Y1=.
Press the graph key.
SAMPLE GRAPH: y= 3 sin(2x)
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For y = 3 sin (2x), the
amplitude = 3 and the
period is (2π)/2 or π.
Setting The Window:
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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
π/4.
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)
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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:
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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
Y1=.
GRAPHING THE RECIPROCAL
FUNCTIONS
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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
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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:
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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.
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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.
1.
2.
3.
4.
5.
6.
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