Periodic Functions A periodic function is a function for which there is a repeating pattern of y-values over equal intervals of x. Each complete pattern.

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Presentation transcript:

Periodic Functions A periodic function is a function for which there is a repeating pattern of y-values over equal intervals of x. Each complete pattern is called a cycle. AmplitudeOne-half of the positive difference between the maximum and the minimum y-values. PeriodThe length of the interval of x-values over which the function completes one cycle. Maximum y = 3 Minimum y = -2 One Cycle

Sine Function and the Unit Circle Comparing the unit circle and the graph of the sine function is like comparing a globe and a map.

Basic Sine Curves Frequency is the number of cycles that the graph completes in an interval of (maximum height) (Number of radians to complete one cycle)

Basic Cosine Curves Frequency is the number of cycles that the graph completes in an interval of (maximum height) (Number of radians to complete one cycle)

Comparison of Sine & Cosine

Homework Page 453:

Sketching Sine Curves

Sketching Cosine Curves

Sketching Negative Sine & Cosine Curves

Homework Sketch each function