Graphing Trig Functions Worksheet 4

Practice exact trigonometric values and identities with angle units and domains stated.

medium: Practice the same exercise types with a fresh numbered set.

14 problems · 25-30 minutes · Skills: trigonometry, graphing, functions

About This Worksheet

This medium-level worksheet contains 14 problems designed for 11th Grade students practicing graphing trig functions. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

Use radians, the unit circle and exact special-angle values.

Practice exact trigonometric values and identities with angle units and domains stated.
Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: For y = 3 sin(1x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

Solution Steps:

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).

Tip: Check your result using the method in the example before moving to the next question.

Paper Include separate answer key in PDF

For y = 3 sin(2x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 1 sin(2x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 2 sin(2x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 3 sin(3x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 1 sin(1x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 3 sin(1x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 4 sin(3x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 2 sin(1x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 2 sin(3x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 4 sin(2x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 1 sin(3x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 4 sin(1x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 2 sin(3x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

For y = 4 sin(1x), give the amplitude and period, then sketch one period using five key points. Angles are radians.

Answer Key

1. Amplitude 3; period 2π/2. Key points: (0, 0), (π/4, 3), (π/2, 0), (3π/4, −3), (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 2; period 2π/2. Key points: (0, 0), (π/4, 2), (π/2, 0), (3π/4, −2), (2π/2, 0).4. Amplitude 3; period 2π/3. Key points: (0, 0), (π/6, 3), (π/3, 0), (3π/6, −3), (2π/3, 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/1. Key points: (0, 0), (π/2, 3), (π/1, 0), (3π/2, −3), (2π/1, 0).7. Amplitude 4; period 2π/3. Key points: (0, 0), (π/6, 4), (π/3, 0), (3π/6, −4), (2π/3, 0).8. Amplitude 2; period 2π/1. Key points: (0, 0), (π/2, 2), (π/1, 0), (3π/2, −2), (2π/1, 0).9. Amplitude 2; period 2π/3. Key points: (0, 0), (π/6, 2), (π/3, 0), (3π/6, −2), (2π/3, 0).10. Amplitude 4; period 2π/2. Key points: (0, 0), (π/4, 4), (π/2, 0), (3π/4, −4), (2π/2, 0).11. Amplitude 1; period 2π/3. Key points: (0, 0), (π/6, 1), (π/3, 0), (3π/6, −1), (2π/3, 0).12. Amplitude 4; period 2π/1. Key points: (0, 0), (π/2, 4), (π/1, 0), (3π/2, −4), (2π/1, 0).13. Amplitude 2; period 2π/3. Key points: (0, 0), (π/6, 2), (π/3, 0), (3π/6, −2), (2π/3, 0).14. Amplitude 4; period 2π/1. Key points: (0, 0), (π/2, 4), (π/1, 0), (3π/2, −4), (2π/1, 0).

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What skills does this trigonometry worksheet cover?

This worksheet focuses on trigonometry, graphing, functions. It is designed for 11th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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This worksheet contains 14 problems. It typically takes 25-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.