Periodic Functions and Trigonometry

Exploring Periodic Data

To be periodicThings that are 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?

 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

 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.

1. Identify one cycle in 2 different ways. 2. State the Period. 3. State the Frequency.

1. Identify one cycle in 2 different ways. 2. State the Period. 3. State the Frequency.

1. Identify one cycle in 2 different ways. 2. State the Period. 3. State the Frequency.

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