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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

In a right triangle, if opposite=6 and hypotenuse=10, what is sin⁡θ\sin\theta?

Please select an answer first.

Correct answer: A

The correct answer is 35\frac{3}{5}.

  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 opposite over hypotenuse: 6/10=3/5.
  3. Check the angle and sign: The correct answer is 35\frac{3}{5}.

Sine is opposite over hypotenuse: 6/10=3/5.

2. QuestionMultiple choice

Which law is most directly used when two angles and one side are known?

Please select an answer first.

Correct answer: B

The correct answer is The Law of Sines.

  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 Law of Sines relates side lengths to the sines of their opposite angles.
  3. Check the angle and sign: The correct answer is The Law of Sines.

The Law of Sines relates side lengths to the sines of their opposite angles.

3. QuestionMultiple choice

What is the Law of Cosines for side c?

Please select an answer first.

Correct answer: C

The correct answer is c2=a2+b2−2abcos⁡Cc^2=a^2+b^2-2ab\cos C.

  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 Law of Cosines generalizes the Pythagorean Theorem for any included angle.
  3. Check the angle and sign: The correct answer is c2=a2+b2−2abcos⁡Cc^2=a^2+b^2-2ab\cos C.

The Law of Cosines generalizes the Pythagorean Theorem for any included angle.

4. QuestionMultiple choice

What is the area of a triangle with sides a and b and included angle C?

Please select an answer first.

Correct answer: D

The correct answer is 12absin⁡C\frac{1}{2}ab\sin C.

  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 included-angle area formula is one-half ab sine C.
  3. Check the angle and sign: The correct answer is 12absin⁡C\frac{1}{2}ab\sin C.

The included-angle area formula is one-half ab sine C.

5. QuestionMultiple choice

If sin⁡θ=12\sin\theta=\frac{1}{2} and theta is acute, what is theta?

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 acute angle with sine 1/2 is π/6.
  3. Check the angle and sign: The correct answer is π6\frac{\pi}{6}.

The acute angle with sine 1/2 is π/6.

6. QuestionMultiple choice

A 10-foot ladder makes a 60-degree angle with the ground. How high does it reach?

Please select an answer first.

Correct answer: B

The correct answer is 535\sqrt{3} feet.

  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 height is 10sin60°=10(√3/2)=5√3.
  3. Check the angle and sign: The correct answer is 535\sqrt{3} feet.

The height is 10sin60°=10(√3/2)=5√3.

7. QuestionMultiple choice

What is the angle of elevation if height=12 and horizontal distance=5?

Please select an answer first.

Correct answer: C

The correct answer is arctan⁡(125)\arctan\left(\frac{12}{5}\right).

  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 opposite over adjacent, so θ=arctan(12/5).
  3. Check the angle and sign: The correct answer is arctan⁡(125)\arctan\left(\frac{12}{5}\right).

Tangent is opposite over adjacent, so θ=arctan(12/5).

8. QuestionMultiple choice

If a triangle has sides 5, 5, and 6, what is the angle opposite the side of length 6?

Please select an answer first.

Correct answer: D

The correct answer is Approximately 73.7 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: Use cos C=(5^2+5^2-6^2)/(2·5·5)=14/25, so C≈73.7°.
  3. Check the angle and sign: The correct answer is Approximately 73.7 degrees.

Use cos C=(5^2+5^2-6^2)/(2·5·5)=14/25, so C≈73.7°.

9. QuestionMultiple choice

What is the magnitude of vector ⟨3,4⟩\langle 3,4\rangle?

Please select an answer first.

Correct answer: A

The correct answer is 5.

  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 magnitude is √(3^2+4^2)=5.
  3. Check the angle and sign: The correct answer is 5.

The magnitude is √(3^2+4^2)=5.

10. QuestionMultiple choice

What is the dot product of ⟨2,1⟩\langle 2,1\rangle and ⟨3,4⟩\langle 3,4\rangle?

Please select an answer first.

Correct answer: B

The correct answer is 10.

  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: Compute 2(3)+1(4)=10.
  3. Check the angle and sign: The correct answer is 10.

Compute 2(3)+1(4)=10.

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