graphing trigonometric functions using the ti-83+
TRANSCRIPT
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GRAPHING TRIGONOMETRIC
FUNCTIONS
Using the TI-83+ ™
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GRAPHING BASIC TRIGONOMETRIC FUNCTIONS
Setting up the calculator. Graphing the sine and
cosine functions. Graphing the tangent
function. Graphing the reciprocal
trig functions.
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Setting Up the Calculator 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.
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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.
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Viewing the Graph
Press the y= key. Check to be sure the
“Plot 1” key is not highlighted.
Enter the equation under Y1=.
Press the graph key.
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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 π/4.
Since the amplitude is 3, set the Ymin = -4, the Ymax = 4, and Yscl=1.
Enter the equation in Y1=
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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 sc l 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.
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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 Y1=.
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GRAPHING THE RECIPROCAL FUNCTIONS
In order to graph the reciprocal trig functions, use the reciprocal key x-1 with either the sin, cos, or tan key.
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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: Xmin= -2π 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. Ymin=- 6 and Ymax = 6.
Enter the equation in Y1=.
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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 y- intercepts?
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Now, try these! Graph at least two cycles.
1. y = 3 csc 4x.
2. y = 5 cot 2x.
3. y = 2 cos ¼x.
4. y = -4 sin πx
5. y = ½ tan x.
6. y = -3 sec x/2
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1) y= 3csc(4x) 2) y=5cot (2x)
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3) y= 2 cos ¼x 4) y=-4sinπx
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5) y= ½ tan x 6) y= - 3sec x/2