1. Warm Up Find the 5 key points for the following equation: y = 3 – 5sin (2x + π/3)

2. Graphs of the Reciprocal Functions (CSC/SEC)

3. Graphs of Reciprocal Functions Recall that the sine and cosecant functions are reciprocals of each other, as are cosine and secant. Therefore, the following is true: where the sine is 0, the cosecant has a vertical asymptote. Why? where the sine has a relative max, the cosecant has a relative min and vise-versa

4. Here is what the graph looks like… the gray is the sine and the black is the cosecant

5. EXAMPLE Graph: y = 2csc (x/2) b = ½ which makes the period = 4π x-intercepts = asymptotes Find the 5 key points for the sine, then graph the cosecant. The five key points are: (0, 0), (π, 2), (2π, 0), (3π, -2), (4π, 0) Vertical Asymptote

6. The Graph…

7. Secant is VERY similar… Therefore, the following are true: where the cosine is 0, the secant has a vertical asymptote. Why? where the cosine has a relative max, the secant has a relative min and vise-versa

8. Find the 5 key “elements” for… y = 3sec (x – π) + 2 b = 1 which makes the period = 2π x-intercepts = asymptotes Find the 5 key points for the cosine, then graph the secant. The five key points are: (π, 3), (3π/2, 2), (2π, 1), (5π/2, 2), (3π, 3) Vertical Asymptote

9. The Graph of y = 3sec (x – π) + 2