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Trigonometry Practice Tests

These Grade 12 Math practice tests cover degree and radian measure, the unit circle, reference angles, identities, trigonometric equations, graph transformations, triangle solving, vectors, polar coordinates, and periodic applications.

Skills covered

  • Converting degrees and radians and reading exact unit-circle values
  • Using reciprocal, quotient, and Pythagorean identities to simplify expressions
  • Analyzing amplitude, period, phase shift, midline, range, and asymptotes in graphs
  • Solving right and oblique triangles with trigonometric ratios and the Laws of Sines and Cosines
  • Applying arc length, sector area, vectors, polar coordinates, and sinusoidal models

How to use these practice tests

Confirm whether the angle is in degrees or radians, identify the quadrant and sign, then choose the unit-circle value, identity, graph parameter, or triangle law that matches the problem.

For more Grade 12 Math practice, return to the Grade 12 Math category.

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Grade 12 Trigonometry Practice Tests

Practice Grade 12 Math questions about radians, degrees, the unit circle, identities, equations, trigonometric graphs, triangles, vectors, polar coordinates, and periodic models.

Choose the best answer. Check angle units, quadrant signs, identities, graph parameters, and triangle relationships before selecting an answer.

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

Which identity is always true?

Please select an answer first.

Correct answer: A

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

  1. Identify the trigonometric relationship: Determine whether the problem uses the unit circle, an identity, a graph, a triangle, an equation, or a measurement model.
  2. Apply the formula or identity: This is the fundamental Pythagorean identity.
  3. Check the angle and sign: The correct answer is sin⁡2x+cos⁡2x=1\sin^2 x+\cos^2 x=1.

This is the fundamental Pythagorean identity.

2. QuestionMultiple choice

What is sec⁡2x−tan⁡2x\sec^2 x-\tan^2 x?

Please select an answer first.

Correct answer: B

The correct answer is 1.

  1. Identify the trigonometric relationship: Determine whether the problem uses the unit circle, an identity, a graph, a triangle, an equation, or a measurement model.
  2. Apply the formula or identity: Rearrange 1+tan^2 x=sec^2 x.
  3. Check the angle and sign: The correct answer is 1.

Rearrange 1+tan^2 x=sec^2 x.

3. QuestionMultiple choice

Rewrite sin⁡xcos⁡x\frac{\sin x}{\cos x}.

Please select an answer first.

Correct answer: C

The correct answer is tan⁡x\tan x.

  1. Identify the trigonometric relationship: Determine whether the problem uses the unit circle, an identity, a graph, a triangle, an equation, or a measurement model.
  2. Apply the formula or identity: Tangent is defined as sine divided by cosine.
  3. Check the angle and sign: The correct answer is tan⁡x\tan x.

Tangent is defined as sine divided by cosine.

4. QuestionMultiple choice

Simplify 1−cos⁡2xsin⁡x\frac{1-\cos^2 x}{\sin x}, where sin⁡x≠0\sin x\ne0.

Please select an answer first.

Correct answer: D

The correct answer is sin⁡x\sin x.

  1. Identify the trigonometric relationship: Determine whether the problem uses the unit circle, an identity, a graph, a triangle, an equation, or a measurement model.
  2. Apply the formula or identity: Use 1-cos^2 x=sin^2 x, then divide by sin x.
  3. Check the angle and sign: The correct answer is sin⁡x\sin x.

Use 1-cos^2 x=sin^2 x, then divide by sin x.

5. QuestionMultiple choice

What is sin⁡(2x)\sin(2x)?

Please select an answer first.

Correct answer: A

The correct answer is 2sin⁡xcos⁡x2\sin x\cos x.

  1. Identify the trigonometric relationship: Determine whether the problem uses the unit circle, an identity, a graph, a triangle, an equation, or a measurement model.
  2. Apply the formula or identity: The double-angle identity for sine is sin(2x)=2sin x cos x.
  3. Check the angle and sign: The correct answer is 2sin⁡xcos⁡x2\sin x\cos x.

The double-angle identity for sine is sin(2x)=2sin x cos x.

6. QuestionMultiple choice

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

Please select an answer first.

Correct answer: B

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

  1. Identify the trigonometric relationship: Determine whether the problem uses the unit circle, an identity, a graph, a triangle, an equation, or a measurement model.
  2. Apply the formula or identity: Sine is zero on the x-axis at 0, π, and 2π.
  3. Check the angle and sign: The correct answer is x=0,π,2πx=0,\pi,2\pi.

Sine is zero on the x-axis at 0, π, and 2π.

7. QuestionMultiple choice

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

Please select an answer first.

Correct answer: C

The correct answer is x=π3,5π3x=\frac{\pi}{3},\frac{5\pi}{3}.

  1. Identify the trigonometric relationship: Determine whether the problem uses the unit circle, an identity, a graph, a triangle, an equation, or a measurement model.
  2. Apply the formula or identity: Cosine is 1/2 at the reference angle π/3 in Quadrants I and IV.
  3. Check the angle and sign: The correct answer is x=π3,5π3x=\frac{\pi}{3},\frac{5\pi}{3}.

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

8. QuestionMultiple choice

Which identity is equivalent to 1+cot⁡2x1+\cot^2 x?

Please select an answer first.

Correct answer: D

The correct answer is csc⁡2x\csc^2 x.

  1. Identify the trigonometric relationship: Determine whether the problem uses the unit circle, an identity, a graph, a triangle, an equation, or a measurement model.
  2. Apply the formula or identity: The reciprocal Pythagorean identity is 1+cot^2 x=csc^2 x.
  3. Check the angle and sign: The correct answer is csc⁡2x\csc^2 x.

The reciprocal Pythagorean identity is 1+cot^2 x=csc^2 x.

9. QuestionMultiple choice

What is the exact value of cos⁡(5π3)\cos\left(\frac{5\pi}{3}\right)?

Please select an answer first.

Correct answer: A

The correct answer is 12\frac{1}{2}.

  1. Identify the trigonometric relationship: Determine whether the problem uses the unit circle, an identity, a graph, a triangle, an equation, or a measurement model.
  2. Apply the formula or identity: 5π/3 has reference angle π/3 in Quadrant IV, where cosine is positive.
  3. Check the angle and sign: The correct answer is 12\frac{1}{2}.

5π/3 has reference angle π/3 in Quadrant IV, where cosine is positive.

10. QuestionMultiple choice

If tan⁡x=34\tan x=\frac{3}{4} and x is in Quadrant I, what is sec⁡x\sec x?

Please select an answer first.

Correct answer: B

The correct answer is 54\frac{5}{4}.

  1. Identify the trigonometric relationship: Determine whether the problem uses the unit circle, an identity, a graph, a triangle, an equation, or a measurement model.
  2. Apply the formula or identity: A 3-4-5 triangle gives cosine 4/5, so secant is 5/4.
  3. Check the angle and sign: The correct answer is 54\frac{5}{4}.

A 3-4-5 triangle gives cosine 4/5, so secant is 5/4.

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