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Chapter 4 Trigonometric Functions 4.6 MATHPOWERTM 12, WESTERN EDITION 4.6.1 The Reciprocal Functions The graphs of y = tanq and the reciprocal trigonometric functions are periodic functions, but they differ from the sinusoidal functions y = sinq and y = cosq in that they have restrictions on their domains. Recall the reciprocal functions: 1 cscx sin x 1 secx cos x 1 tan x cot x The transformations that will be applied to the reciprocal functions follow the same rules as those of the primary ratios. y = acsc b(x + c) + d 4.6.2 Graphing the Tangent Function Asymptotes: Period: Domain: Range: 4.6.3 Graphing the Cotangent Function 1. Draw vertical asymptotes. 2. Plot the points at y = 1 and -1. 3. Sketch the cotangent function. 4.6.4 Graphing the Cotangent Function [cont’d] Asymptotes: Period: Domain: Range: 4.6.5 Graphing the Cosecant Function 1. Draw the vertical asymptotes. 2. Plot the points at y = 1 and -1. 3. Sketch the cosecant function. 4.6.6 Graphing the Cosecant Function [cont’d] Asymptotes: Period: Domain: Range: 4.6.7 The Cosecant Function y = csc x Asymptotes: Domain: Range: Period: 4.6.8 Graphing the Secant Function 1. Draw the vertical asymptotes. 2. Plot the points at y = 1 and -1. 3. Sketch the secant function. 4.6.9 Graphing the Secant Function [cont’d] Asymptotes: Period: Domain: Range: 4.6.10 Suggested Questions: Page 232 1-11 odd, 12-15 (graphing calculator), 16, 17 4.6.11