1. MATHPOWER TM 12, WESTERN EDITION 4.6 4.6.1 Chapter 4 Trigonometric Functions

2. The graphs of y = tan  and the reciprocal trigonometric functions are periodic functions, but they differ from the sinusoidal functions y = sin  and y = cos  in that they have restrictions on their domains. The Reciprocal Functions Recall the reciprocal functions: 4.6.2 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

3. 4.6.3 Graphing the Tangent Function Asymptotes: Domain: Range: Period: all real numbers 

4. 1. Draw vertical asymptotes. 2. Plot the points at y = 1 and 3. Sketch the cotangent function. Graphing the Cotangent Function 4.6.4

5. 4.6.5 Graphing the Cotangent Function [cont’d] Asymptotes: Domain: Range: Period: all real numbers 

6. 4.6.6 Graphing the Cosecant Function 1. Draw the vertical asymptotes. 2. Plot the points at y = 1 and 3. Sketch the cosecant function.

7. Graphing the Cosecant Function [cont’d] Asymptotes: Domain: Range: Period: -1 ≥ y ≥ 1  4.6.7

8. 4.6.8 The Cosecant Function Graph y = 2csc x. y = csc x y = 2csc x Asymptotes: Domain: Range: Period: -2 ≥ y ≥ 2  For y = 2csc x: Graph y = csc 2x. For y = csc2 x: Asymptotes: Domain: Range:-1 ≥ y ≥ 1 Period:

9. 4.6.9 Graphing the Secant Function 1. Draw the vertical asymptotes. 2. Plot the points at y = 1 and 3. Sketch the secant function.

10. Graphing the Secant Function [cont’d] Asymptotes: Domain: Range: Period: -1 ≥ y ≥ 1  4.6.10

11. 4.6.11 Suggested Questions: Page 232 1-11 odd, 12-15 (graphing calculator), 16, 17