Graphs of Sine and Cosine

1. Graphs of Sine and Cosine Essential Questions • How do we recognize and graph periodic and trigonometric functions? Holt McDougal Algebra 2 Holt Algebra 2

2. Periodic functions are functions that repeat exactly in regular intervals called cycles. The length of the cycle is called its period. Examine the graph of the periodic function and nonperiodic function below. Notice that a cycle may begin at any point on the graph of a function.

3. Identifying Periodic Functions Identify whether each function is periodic. If the function is periodic, give the period. 1. The pattern repeats exactly, so the function is periodic. Identify the period by using the start and finish of one cycle. This function is periodic with a period of .

4. Identifying Periodic Functions Identify whether each function is periodic. If the function is periodic, give the period. Although there is some symmetry, the pattern does not repeat exactly. 2. This function is not periodic.

5. Identifying Periodic Functions Identify whether each function is periodic. If the function is periodic, give the period. 3. 4. periodic; 3 not periodic

6. Equation of a Sine Function Amplitude Period Complete Cycle

7. Equation of a Sine Function Draw one cycle of the function’s graph. Amplitude Period

8. Equation of a Sine Function Draw one cycle of the function’s graph. Amplitude Period

9. Equation of a Sine Function Draw one cycle of the function’s graph. Amplitude Period

10. Equation of a Cosine Function Amplitude Period Complete Cycle

11. Equation of a Cosine Function Draw one cycle of the function’s graph. Amplitude Period

12. Equation of a Cosine Function Draw one cycle of the function’s graph. Amplitude Period

13. Equation of a Cosine Function Draw one cycle of the function’s graph. Amplitude Period

14. Lesson 11.1 Practice A