1. Lesson 8-2 Sine and Cosine Curves https://encrypted- tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q u308QRANh_v4UHWiw

2. Objective:

3. Objective: To find equations of different sine and cosine curves and to apply these equations.

4. Recall from earlier work that the graph of y = cf(x) can be obtained by vertically stretching or shrinking the graph of y = f(x).

5. This is illustrated by the sine graph below:

6. blue: y = sin x red: y = 2 sin x

7. This is illustrated by the sine graph below: blue: y = sin x red: y = 2 sin x

8. This is illustrated by the sine graph below: blue: y = sin x red: y = 2 sin x Notice: y = 2 sin x has an amplitude of 2

9. This is illustrated by the cosine graph below:

10. blue: y = -1/2 cos x red: y = cos x

11. This is illustrated by the cosine graph below: blue: y = -1/2 cos x red: y = cos x

12. This is illustrated by the cosine graph below: blue: y = -1/2 cos x red: y = cos x Notice: y = -1/2 cos x has an amplitude of 1/2

13. We also learned in our earlier days that the graph of y = f(cx) can be obtained by shrinking or stretching the graph horizontally.

14. This is illustrated by the sine graph below:

15. blue: y = sin x red: y = sin 2x

16. This is illustrated by the sine graph below: blue: y = sin x red: y = sin 2x

17. This is illustrated by the cosine graph below:

18. blue: y = cos x red: y = cos 1/3x

19. This is illustrated by the cosine graph below: blue: y = cos x red: y = cos 1/3x

20. This is illustrated by the cosine graph below: blue: y = cos x red: y = cos 1/3x Remember: The fundamental period for either the sine or cosine function is 2π.

21. In general, we can determine useful information about the graphs of y = A sin Bx and y = A cos Bx by analyzing the factors the factors A and B.

23. Give the amplitude and period of the function:

25. Sketch at least one cycle of its graph.

27. Assignment: Pg. 304 - 305 C.E.  1-7 all W.E.  2-10 even, 11-16 all