1. Section 8-2 Sine and Cosine Curves

2. Recall… The Sine Graph

3. Recall… The Cosine Graph

4. Recall… What do these mean? Y = cf(x) Y = -f(x) Y = f(cx)

5. Stretching and Shrinking The graph of y = cf(x) can be obtained by vertically stretching or shrinking the graph of y = f(x). This is illustrated by the sine and cosine graphs on p. 301.

6. Recall… Amplitude =

7. Stretching and Shrinking The graph of y = f(cx) is obtained by horizontally stretching or shrinking the graph of y = f(x). This is illustrated by the graphs on p. 302.

8. The period (the fundamental period of the function) p of y = sin x and y = cos x is 2π. In general, we can determine useful information about the graphs of y = A sin Bx and y = A cos Bx by analyzing the factors A and B.

9. Period and Amplitude of Sine and Cosine Curves For functions y = A sin Bx and y = A cos Bx (A ≠ 0 and B > 0): Amplitude = |A|period =

10. Example Give the amplitude and period of Then sketch its graph

11. Example 1.Graph and y=3 on the same set of axes to determine the number of solutions that the equation has in the interval 0 < x < 2π. Approximate each solution to the nearest hundredth.