7.3 Periodic Graphs & Amplitude Objectives: State the period & amplitude (if any) given the function rule or the graph of a sine, cosine, or tangent function. Use the period & amplitude (if any) to sketch the graph of a sine, cosine, or tangent function. Periodic Graphs & Amplitude 7.3

Periods of Sine & Cosine Functions Recall that the period of a function is the horizontal distance required for a complete cycle.

Example #1a Determine the period of each function.

Example #1b Determine the period of each function.

Periods of Tangent Functions

Example #2a Determine the period of each function.

Example #2b Determine the period of each function.

Amplitude and Period The amplitude of a function is half the distance between the maximum and minimum, provided it has a max & min which is not the case for the tangent function.

Example #3a Identify the amplitude and period of the function and sketch its graph.

Example #3b Identify the amplitude and period of the function and sketch its graph.

Example #4 Determine the amplitude and period, then sketch a graph over the interval [−π, π].

Example #5a Write an equation for the cosine function with the given information. Amplitude = 3 Period = 3π

Example #5b Write an equation for the cosine function with the given information. Amplitude = Period = 6

Example #6a State the rule of the cosine function whose graph appears identical to the given graph. 2

Example #6b State the rule of the cosine function whose graph appears identical to the given graph. −0.5