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Trigonometric Functions Practice Tests

These Grade 11 Math practice tests build fluency with the unit circle, degree-radian conversions, trigonometric ratios and identities, graph transformations, equations, inverse functions, and triangle applications.

Skills covered

  • Evaluating sine, cosine, tangent, and reciprocal functions on the unit circle
  • Converting between degrees and radians and identifying quadrant signs
  • Using Pythagorean, reciprocal, quotient, and symmetry identities
  • Analyzing amplitude, period, midline, shifts, range, and trig graphs
  • Solving trigonometric equations and applying right-triangle ratios, arc length, sector area, and the Laws of Sines and Cosines

How to use these practice tests

Keep angle units consistent, locate the reference angle and quadrant, select the appropriate identity or ratio, and check that the solution lies in the stated interval.

For more Grade 11 Math practice, return to the Grade 11 Math category.

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Grade 11 Trigonometric Functions Practice Tests

Practice Grade 11 Math questions about the unit circle, radians, trigonometric ratios, identities, graphs, equations, inverse functions, and triangle applications.

Choose the best answer. Use radians or degrees consistently, identify the reference angle and quadrant, and verify trig equations and triangle relationships.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Which identity is always true for real x?

Please select an answer first.

Correct answer: A

The correct answer is sin⁡2x+cos⁡2x=1\sin^2x+\cos^2x=1.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: The Pythagorean identity follows from the unit-circle equation.
  3. Check the result: The correct answer is sin⁡2x+cos⁡2x=1\sin^2x+\cos^2x=1.

The Pythagorean identity follows from the unit-circle equation.

2. QuestionMultiple choice

Which expression equals tan⁡x\tan x when cos⁡x≠0\cos x\ne0?

Please select an answer first.

Correct answer: B

The correct answer is sin⁡xcos⁡x\frac{\sin x}{\cos x}.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: By definition, tangent is sine divided by cosine.
  3. Check the result: The correct answer is sin⁡xcos⁡x\frac{\sin x}{\cos x}.

By definition, tangent is sine divided by cosine.

3. QuestionMultiple choice

Which is the reciprocal identity for secant?

Please select an answer first.

Correct answer: C

The correct answer is sec⁡x=1cos⁡x\sec x=\frac{1}{\cos x}.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Secant is the reciprocal of cosine.
  3. Check the result: The correct answer is sec⁡x=1cos⁡x\sec x=\frac{1}{\cos x}.

Secant is the reciprocal of cosine.

4. QuestionMultiple choice

If sin⁡θ=35\sin\theta=\frac{3}{5} and theta is acute, what is cos⁡θ\cos\theta?

Please select an answer first.

Correct answer: D

The correct answer is 45\frac{4}{5}.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Use sin^2 theta + cos^2 theta = 1: cos theta = sqrt(1-9/25)=4/5 for an acute angle.
  3. Check the result: The correct answer is 45\frac{4}{5}.

Use sin^2 theta + cos^2 theta = 1: cos theta = sqrt(1-9/25)=4/5 for an acute angle.

5. QuestionMultiple choice

If cos⁡θ=513\cos\theta=\frac{5}{13} and theta is acute, what is sin⁡θ\sin\theta?

Please select an answer first.

Correct answer: A

The correct answer is 1213\frac{12}{13}.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: The 5-12-13 right triangle gives sin theta = 12/13.
  3. Check the result: The correct answer is 1213\frac{12}{13}.

The 5-12-13 right triangle gives sin theta = 12/13.

6. QuestionMultiple choice

Which identity relates tangent and secant?

Please select an answer first.

Correct answer: B

The correct answer is 1+tan⁡2x=sec⁡2x1+\tan^2x=\sec^2x.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Divide the identity sin^2x+cos^2x=1 by cos^2x.
  3. Check the result: The correct answer is 1+tan⁡2x=sec⁡2x1+\tan^2x=\sec^2x.

Divide the identity sin^2x+cos^2x=1 by cos^2x.

7. QuestionMultiple choice

What is 1sec⁡θ\frac{1}{\sec\theta}?

Please select an answer first.

Correct answer: C

The correct answer is cos⁡θ\cos\theta.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Since sec theta = 1/cos theta, its reciprocal is cos theta.
  3. Check the result: The correct answer is cos⁡θ\cos\theta.

Since sec theta = 1/cos theta, its reciprocal is cos theta.

8. QuestionMultiple choice

If theta is acute and tan⁡θ=3\tan\theta=\sqrt3, what is theta?

Please select an answer first.

Correct answer: D

The correct answer is π3\frac{\pi}{3}.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: The acute angle with tangent sqrt(3) is pi/3.
  3. Check the result: The correct answer is π3\frac{\pi}{3}.

The acute angle with tangent sqrt(3) is pi/3.

9. QuestionMultiple choice

Which identity is true?

Please select an answer first.

Correct answer: A

The correct answer is sin⁡(π−x)=sin⁡x\sin(\pi-x)=\sin x.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Angles pi-x and x have the same sine because they share the same height on the unit circle.
  3. Check the result: The correct answer is sin⁡(π−x)=sin⁡x\sin(\pi-x)=\sin x.

Angles pi-x and x have the same sine because they share the same height on the unit circle.

10. QuestionMultiple choice

Which identity describes cosine as an even function?

Please select an answer first.

Correct answer: B

The correct answer is cos⁡(−x)=cos⁡x\cos(-x)=\cos x.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Cosine is even, so changing the sign of the input does not change its value.
  3. Check the result: The correct answer is cos⁡(−x)=cos⁡x\cos(-x)=\cos x.

Cosine is even, so changing the sign of the input does not change its value.

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