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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

Solve sin⁡x=0\sin x=0 on [0,2π][0,2\pi].

Please select an answer first.

Correct answer: A

The correct answer is x=0,π,2πx=0,\pi,2\pi.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Sine is zero on the x-axis at 0, pi, and 2pi in the closed interval.
  3. Check the result: The correct answer is x=0,π,2πx=0,\pi,2\pi.

Sine is zero on the x-axis at 0, pi, and 2pi in the closed interval.

2. QuestionMultiple choice

Solve cos⁡x=12\cos x=\frac{1}{2} on [0,2π][0,2\pi].

Please select an answer first.

Correct answer: B

The correct answer is x=π3,5π3x=\frac{\pi}{3},\frac{5\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: Cosine is 1/2 at the reference angle pi/3 in Quadrants I and IV.
  3. Check the result: The correct answer is x=π3,5π3x=\frac{\pi}{3},\frac{5\pi}{3}.

Cosine is 1/2 at the reference angle pi/3 in Quadrants I and IV.

3. QuestionMultiple choice

Solve tan⁡x=1\tan x=1 on [0,2π][0,2\pi].

Please select an answer first.

Correct answer: C

The correct answer is x=π4,5π4x=\frac{\pi}{4},\frac{5\pi}{4}.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Tangent is 1 at pi/4 and repeats every pi, giving 5pi/4.
  3. Check the result: The correct answer is x=π4,5π4x=\frac{\pi}{4},\frac{5\pi}{4}.

Tangent is 1 at pi/4 and repeats every pi, giving 5pi/4.

4. QuestionMultiple choice

Solve 2sin⁡x=32\sin x=\sqrt3 on [0,2π][0,2\pi].

Please select an answer first.

Correct answer: D

The correct answer is x=π3,2π3x=\frac{\pi}{3},\frac{2\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: Divide by 2 to get sin x=sqrt(3)/2, which occurs at pi/3 and 2pi/3.
  3. Check the result: The correct answer is x=π3,2π3x=\frac{\pi}{3},\frac{2\pi}{3}.

Divide by 2 to get sin x=sqrt(3)/2, which occurs at pi/3 and 2pi/3.

5. QuestionMultiple choice

Solve cos⁡x=−1\cos x=-1 on [0,2π][0,2\pi].

Please select an answer first.

Correct answer: A

The correct answer is x=πx=\pi.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Cosine reaches -1 at the point (-1,0), corresponding to x=pi.
  3. Check the result: The correct answer is x=πx=\pi.

Cosine reaches -1 at the point (-1,0), corresponding to x=pi.

6. QuestionMultiple choice

Solve sin⁡x=−1\sin x=-1 on [0,2π][0,2\pi].

Please select an answer first.

Correct answer: B

The correct answer is x=3π2x=\frac{3\pi}{2}.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Sine reaches -1 at the bottom of the unit circle, x=3pi/2.
  3. Check the result: The correct answer is x=3π2x=\frac{3\pi}{2}.

Sine reaches -1 at the bottom of the unit circle, x=3pi/2.

7. QuestionMultiple choice

Solve tan⁡x=0\tan x=0 on [0,2π][0,2\pi].

Please select an answer first.

Correct answer: C

The correct answer is x=0,π,2πx=0,\pi,2\pi.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Tangent is zero when sine is zero and cosine is nonzero; include 0, pi, and 2pi.
  3. Check the result: The correct answer is x=0,π,2πx=0,\pi,2\pi.

Tangent is zero when sine is zero and cosine is nonzero; include 0, pi, and 2pi.

8. QuestionMultiple choice

Solve 2cos⁡x+1=02\cos x+1=0 on [0,2π][0,2\pi].

Please select an answer first.

Correct answer: D

The correct answer is x=2π3,4π3x=\frac{2\pi}{3},\frac{4\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: Divide by 2 to get cos x=-1/2, which occurs in Quadrants II and III.
  3. Check the result: The correct answer is x=2π3,4π3x=\frac{2\pi}{3},\frac{4\pi}{3}.

Divide by 2 to get cos x=-1/2, which occurs in Quadrants II and III.

9. QuestionMultiple choice

Solve sin⁡x=12\sin x=\frac{1}{2} on [0,2π][0,2\pi].

Please select an answer first.

Correct answer: A

The correct answer is x=π6,5π6x=\frac{\pi}{6},\frac{5\pi}{6}.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Sine is 1/2 at reference angle pi/6 in Quadrants I and II.
  3. Check the result: The correct answer is x=π6,5π6x=\frac{\pi}{6},\frac{5\pi}{6}.

Sine is 1/2 at reference angle pi/6 in Quadrants I and II.

10. QuestionMultiple choice

Solve cos⁡x=−22\cos x=-\frac{\sqrt2}{2} on [0,2π][0,2\pi].

Please select an answer first.

Correct answer: B

The correct answer is x=3π4,5π4x=\frac{3\pi}{4},\frac{5\pi}{4}.

  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 negative with reference angle pi/4 in Quadrants II and III.
  3. Check the result: The correct answer is x=3π4,5π4x=\frac{3\pi}{4},\frac{5\pi}{4}.

Cosine is negative with reference angle pi/4 in Quadrants II and III.

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