1. 5.4 Graphs of the Sine and Cosine Functions

2. The Graph of y = sin x y x

3. (0, 0)

4. Characteristics of the Sine Function
1. The domain is the set of all real numbers.
2. The range consists of all real numbers from -1 to 1, inclusive.
3. The sine function is an odd function (symmetric with respect to the origin). 4. 5.

5. Characteristics of the Sine Function6.

6. Use the graph of
to sketch the graph of

7. (0,0)

8. (0,0)

10. The Graph of y = cos x y x

11. (0, 1)

12. Characteristics of the Cosine Function
1. The domain is the set of all real numbers.
2. The range consists of all real numbers from -1 to 1, inclusive.
3. The cosine function is an even function (symmetric with respect to the y-axis). 4. 5.

13. Characteristics of the Cosine Function6.

14. The graphs of the sine and cosine functions are called sinusoidal graphs.

15. Theorem

20. Find an equation for the graph.

21. Amplitude = 4
Period =T =2

22. Amplitude = 4
Period =T =2