Objectives 1 2 State the period amplitude if

Objectives: 1. 2. 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 #1 a � Determine the period of each function.

Example #1 b � Determine the period of each function.

Periods of Tangent Functions

Example #2 a � Determine the period of each function.

Example #2 b � 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 #3 a � Identify the amplitude and period of the function and sketch its graph.

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

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

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

Example #6 b � State the rule of the cosine function whose graph appears identical to the given graph. − 0. 5