1. Warm up  State the phase shift for. Then graph the function.  State the vertical shift and the equation of the midline for. Then graph the function. 3

2. Lesson 6-7 Graphing Other Trigonometric Functions Objective: Graph tangent, cotangent,secant and cosecant functions. Write equations of the trig functions.

3. Graph of the Tangent Function y = tan x If we were to make a chart and graph the points as we did for y=sin x an y=cosine x, we would find that there are points where tan x is undefined. (Asymptote)

4. y = tanx Period: Domain: Range: X-Intercepts: Asymptotes: Y-intercept: π All real numbers except (π/2)n, n is an odd integer All real numbers x = (π/2)n, n is an odd integer πn, n is an integer 0

5. Graph of the Cotangent Function X Cot xund efin ed 10 und efin ed 10 und efin ed

6. y = cot x Period: Domain: Range: X-Intercepts: Asymptotes: Y-intercepts: x = πn, n is an integer none π All real numbers except πn, n is an integer All real numbers (π/2)n, n is an odd integer

7. Graphs of the Reciprocal Functions y=sin x and y=csc x y=cos x and y=sec x

8. Examples  Find the value of each by referring to the graphs:  1.  2.

9. Examples  Find the values of θ for which each equation is true.  1. csc θ = -1  2. sec θ =1

10. Examples  Graph

11. Example  Write an equation for a secant function with period 3π, phase shift, and vertical shift 3.