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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= ππ

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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.**

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

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1) y= 3csc(4x) ) 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

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