7.4 Periodic Graphs & Phase Shifts Objectives:

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7.4 Periodic Graphs & Phase Shifts Objectives: State the period, amplitude, vertical shift, & phase shift given the function rule or graph of a sine or cosine function. Use graphs to determine whether an equation could possibly be an identity. Periodic Graphs & Phase Shifts 7.4

Example #1 Describe the graph of the function and sketch it on the interval [−2π, 2π].

Phase Shifts Phase shifts are another name for horizontal translations. A negative phase shift translates the graph left, a positive phase shift translates it right.

Example #2a Describe the graph of each function.

Example #2b Describe the graph of each function.

Example #3 State the amplitude, period, and phase shift.

Combined Transformations

Example #4 Describe the graph and sketch it.

Example #5 Describe the graph and sketch it.

Example #6 Find a sine and cosine function whose graph looks like the graph shown.