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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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1. Test

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

Convert π3\frac{\pi}{3} radians to degrees.

Please select an answer first.

Correct answer: A

The correct answer is 60 degrees.

  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: Multiply by 180/π: (π/3)(180/π)=60 degrees.
  3. Check the angle and sign: The correct answer is 60 degrees.

Multiply by 180/π: (π/3)(180/π)=60 degrees.

2. QuestionMultiple choice

What is sin⁡(π4)\sin\left(\frac{\pi}{4}\right)?

Please select an answer first.

Correct answer: B

The correct answer is 22\frac{\sqrt{2}}{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: The unit-circle coordinate at π/4 has y-value √2/2.
  3. Check the angle and sign: The correct answer is 22\frac{\sqrt{2}}{2}.

The unit-circle coordinate at π/4 has y-value √2/2.

3. QuestionMultiple choice

In which quadrant is θ=5π6\theta=\frac{5\pi}{6}?

Please select an answer first.

Correct answer: C

The correct answer is Quadrant II.

  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/6 is 150 degrees, which lies between 90 and 180 degrees.
  3. Check the angle and sign: The correct answer is Quadrant II.

5π/6 is 150 degrees, which lies between 90 and 180 degrees.

4. QuestionMultiple choice

What is the terminal point on the unit circle for θ=π\theta=\pi?

Please select an answer first.

Correct answer: D

The correct answer is (−1,0)(-1,0).

  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: At π radians, the unit-circle point is (-1,0).
  3. Check the angle and sign: The correct answer is (−1,0)(-1,0).

At π radians, the unit-circle point is (-1,0).

5. QuestionMultiple choice

What is the reference angle for θ=7π6\theta=\frac{7\pi}{6}?

Please select an answer first.

Correct answer: A

The correct answer is π6\frac{\pi}{6}.

  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 angle is in Quadrant III, so subtract π: 7π/6-π=π/6.
  3. Check the angle and sign: The correct answer is π6\frac{\pi}{6}.

The angle is in Quadrant III, so subtract π: 7π/6-π=π/6.

6. QuestionMultiple choice

What is cos⁡(π)\cos(\pi)?

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: The x-coordinate of the unit-circle point at π is -1.
  3. Check the angle and sign: The correct answer is -1.

The x-coordinate of the unit-circle point at π is -1.

7. QuestionMultiple choice

Which trigonometric ratio is the reciprocal of cosine?

Please select an answer first.

Correct answer: C

The correct answer is Secant.

  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: By definition, sec θ=1/cos θ.
  3. Check the angle and sign: The correct answer is Secant.

By definition, sec θ=1/cos θ.

8. QuestionMultiple choice

What is tan⁡(π4)\tan\left(\frac{\pi}{4}\right)?

Please select an answer first.

Correct answer: D

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: At π/4, sine and cosine are equal and nonzero, so tangent is 1.
  3. Check the angle and sign: The correct answer is 1.

At π/4, sine and cosine are equal and nonzero, so tangent is 1.

9. QuestionMultiple choice

A positive angle of 13π6\frac{13\pi}{6} is coterminal with which angle in [0,2π)[0,2\pi)?

Please select an answer first.

Correct answer: A

The correct answer is π6\frac{\pi}{6}.

  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: Subtract 2π: 13π/6-12π/6=π/6.
  3. Check the angle and sign: The correct answer is π6\frac{\pi}{6}.

Subtract 2π: 13π/6-12π/6=π/6.

10. QuestionMultiple choice

What is cot⁡(π4)\cot\left(\frac{\pi}{4}\right)?

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: Cotangent is cosine divided by sine, and both values are equal at π/4.
  3. Check the angle and sign: The correct answer is 1.

Cotangent is cosine divided by sine, and both values are equal at π/4.

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