Chapter 13

1. Chapter 13 Periodic Functions and Trigonometry

2. Section 13.1 Exploring Periodic Data

3. Periodic • Repeats on a regular basis • Repeats in the exact same manner • Can be predicted • Seasons of the year • Daily classes • Travel of a comet • Location of the second hand on an analog clock • Occurrence of the chorus in a song • Other examples? To be periodic Things that are periodic

4. Periodic Functions • It repeats a pattern of y – values at regular intervals • One complete pattern is called a cycle • The period of the function is the length of the x values to form one cycle. 1 Period or 1 Cycle

5. Vocabulary • A Period can be found on a graph as being when the function is at a certain y – value, moving in a certain direction, until it is back at that same y – value, moving in the same direction. • The Maximum value of a periodic function is the greatest y – value that it achieves. • The Minimum value of a periodic function is the smallest y – value that it achieves. • The Amplitude is half the distance from the minimum value to the maximum value or it is the distance from the center to one extreme. • The Frequency of a periodic function is the reciprocal of the period.

6. Cycles, Periods, and Frequencies • Identify one cycle in 2 different ways. • State the Period. • State the Frequency.

7. Cycles, Periods, and Frequencies • Identify one cycle in 2 different ways. • State the Period. • State the Frequency.

8. Cycles, Periods, and Frequencies • Identify one cycle in 2 different ways. • State the Period. • State the Frequency.

9. Periods and Trends

10. Amplitude

11. Extra Practice • Today we did page 699 #1 – 13 • If you want or need extra practice do pages 699 – 700 #16 – 19, 23 – 30