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GRAPHING TRIGONOMETRIC FUNCTIONS Using the TI-83+ ™ GRAPHING BASIC TRIGONOMETRIC FUNCTIONS Setting up the calculator. Graphing the sine and cosine functions. Graphing the tangent function. Graphing the reciprocal trig functions. 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. 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 highlighted. 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 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) 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 Y1=. 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. 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. 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