1. 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

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

3. Example #1a
Determine the period of each function.

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

5. Periods of Tangent Functions

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

7. Example #2b
Determine the period of each function.

8. 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.

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

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

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

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

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

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

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