What do these situations have in common? Explain..

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What do these situations have in common? Explain.

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: Cycle: Period: A function that repeats a pattern of outputs (y-values) at regular intervals One complete pattern Horizontal length of a cycle – distance along x-axis

One cycle: Period: or One cycle

Determine whether function is periodic. If so identify one cycle and determine the period. Not Periodic Period:One cycle Period:One cycle

Maximum Minimum Midline Midline: Amplitude: Horizontal line midway between maximum and minimum values Half the difference between maximum and minimum

One cycle: Period: Midline: Amplitude: What is the period, the amplitude and the equation of the midline for each sound wave displayed below. One cycle: Period: Midline: Amplitude: Pg. 832 #7-25 odd, 35, 36

The Sine Function Today’s Objective: I can graph the sine function.

xy 0

Domain: Range: Period: Amplitude: All real numbers – 1 ≤ y ≤ 1 2π2π 1 OR

Calculator [MODE]: Radians [WINDOW] Xmin = 0 Xmax = 2π Xscl = π/2 Ymin = – 2 Ymax = 2 Yscl = 0.5 Period of a Sine Curve

Calculator [MODE]: Radians [WINDOW] Xmin = 0 Xmax = 2π Xscl = π/2 Ymin = – 2 Ymax = 2 Yscl = 0.5 Amplitude of a Sine Curve

Amplitude = Period = Write an equation for the graph. Find amplitude and period for each equation. 3.. Amplitude = Period =

1.Find amplitude and period. 2.Plot 5 points: Midline points Beginning, End Middle Amplitude points Max Min 3. Sketch curve. Sketching a Sine Curve Graph (2 cycles) Amplitude = Period = 5 points: midline – max– midline – min – midline

1.Find amplitude and period. 2.Plot 5 points 3.Sketch curve. Sketching a Sine Curve Graph (2 cycles) Amplitude = Period = Pg. 856 #13-35 odd 5 points: midline – max– midline – min – midline