Periodic Functions and Trigonometry Unit Objectives: • Determine exact values for trigonometric functions: with and without a calculator • Write and graph trigonometric functions • Find amplitude, period, maximums, minimums and phase shifts for periodic functions • Model problems using trigonometric functions Today’s Objective: I can find a cycle, period and amplitude of periodic function.
What do these situations have in common? Explain Periodic Function: A function that repeats a pattern of outputs (y-values) at regular intervals Cycle: Period: One complete pattern Horizontal length of a cycle – distance along x-axis
One cycle: or Period: One cycle Period:
Determine whether function is periodic. If so identify one cycle and determine the period. Not Periodic One cycle Period: Not Periodic
Maximum Midline Minimum Midline: Horizontal line midway between maximum and minimum values Amplitude: Half the difference between maximum and minimum
What is the period, the amplitude and the equation of the midline for each sound wave displayed below. One cycle: Period: Midline: Amplitude: One cycle: Period: Midline: Pg. 832 #7 -25 odd, 35, 36 Amplitude: