Graphing Trigonometric Functions Worksheets
Practice exact trigonometric values and identities with angle units and domains stated.
Before you begin
Use radians, the unit circle and exact special-angle values.
Worked example
For y = 3 sin(1x), give the amplitude and period, then sketch one period using five key points. Angles are radians.
- Amplitude is the absolute value of the coefficient.
- Period is 2π divided by the positive coefficient of x.
- Divide the period into four equal intervals; the sine values are 0, 1, 0, −1, 0.
Answer: Amplitude 3; period 2π/1. Key points: (0, 0), (π/2, 3), (π/1, 0), (3π/2, −3), (2π/1, 0).
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
For y = 2 sin(2x), give the amplitude and period, then sketch one period using five key points. Angles are radians.
2
For y = 1 sin(2x), give the amplitude and period, then sketch one period using five key points. Angles are radians.
3
For y = 3 sin(1x), give the amplitude and period, then sketch one period using five key points. Angles are radians.
4
For y = 4 sin(1x), give the amplitude and period, then sketch one period using five key points. Angles are radians.
5
For y = 1 sin(1x), give the amplitude and period, then sketch one period using five key points. Angles are radians.
6
For y = 3 sin(2x), give the amplitude and period, then sketch one period using five key points. Angles are radians.
Answer Key
1. Amplitude 2; period 2π/2. Key points: (0, 0), (π/4, 2), (π/2, 0), (3π/4, −2), (2π/2, 0).2. Amplitude 1; period 2π/2. Key points: (0, 0), (π/4, 1), (π/2, 0), (3π/4, −1), (2π/2, 0).3. Amplitude 3; period 2π/1. Key points: (0, 0), (π/2, 3), (π/1, 0), (3π/2, −3), (2π/1, 0).4. Amplitude 4; period 2π/1. Key points: (0, 0), (π/2, 4), (π/1, 0), (3π/2, −4), (2π/1, 0).5. Amplitude 1; period 2π/1. Key points: (0, 0), (π/2, 1), (π/1, 0), (3π/2, −1), (2π/1, 0).6. Amplitude 3; period 2π/2. Key points: (0, 0), (π/4, 3), (π/2, 0), (3π/4, −3), (2π/2, 0).