6 4 Amplitude and Period of Sine and
- Slides: 6
6. 4 Amplitude and Period of Sine and Cosine Functions Objectives: Find the amplitude and period for sine and cosine functions. Write equations of sine and cosine functions given the amplitude and period.
Joke of the day! What did the grape say when it was squeezed? Nothing. It just gave out a little wine.
Amp. of sine and cosine functions: Ex. 1) •
Period of sine and cosine functions: Ex. 2) Ex. 3) •
Ex. 4) Ex. 5) • A pendulum swings a total distance of 0. 30 meter. The center point is zero. It completes a cycle every 2 seconds. a. ) Assuming that the pendulum is at the center point and heading right at t=0, find an equation for the motion of the pendulum. b. ) Determine the distance from center at 1 sec. , 1. 5 sec. , 1. 75 sec. , and 2 sec.
Frequency: The number of cycles per unit of time. Period = 1/frequency frequency= 1/period *period is reciprocal of frequency and vice-versa. Ex. 6) The Sears Tower in Chicago sways back and forth at a vibration frequency of about 0. 1 hertz (unit of frequency). On average, it sways 6 inches from true center. Write an equation of the sine function that represents this behavior.
