12 6 Circular and Periodic Functions Periodic Function
- Slides: 9
12. 6 Circular and Periodic Functions
Periodic Function �A periodic function has y-values that repeat at regular intervals. One complete pattern is a cycle, and the horizontal length of one cycle is a period.
Unit Circle �
Example 1 �
Example 2 Determine the period of the function.
Example 3 Determine the period of the function.
Example 4 Determine the period of the function.
Example 5 The pedals on a bicycle rotate as the bike is being ridden. The height of a bicycle pedal varies periodically as a function of the time, as shown in the figure. Notice that the pedal makes one complete rotation every two seconds. Identify the period of the function. Graph the function. Let the horizontal axis represent the time t and the vertical axis represent the height h in inches that the pedal is from the ground.
Example 6 A point on the edge of a car tire is marked with paint. As the car moves slowly, the marked point on the tire varies in distance from the surface of the road. The height in inches of the point is given by the expression h = – 8 cos t + 8, where t is the time in seconds. a. What is the maximum height above ground that the point on the tire reaches? b. What is the minimum height above ground that the point on the tire reaches? c. Identify the period of the function. d. How many rotations does the tire make per second? e. How far does the marked point travel in 30 seconds? How far does it travel in one hour?