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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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5. 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

What is the arc length of a circle with radius 6 and central angle π3\frac{\pi}{3}?

Please select an answer first.

Correct answer: A

The correct answer is 2π.

  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 s=rθ: 6(π/3)=2π.
  3. Check the angle and sign: The correct answer is 2π.

Use s=rθ: 6(π/3)=2π.

2. QuestionMultiple choice

What is the area of a sector with radius 4 and angle π2\frac{\pi}{2}?

Please select an answer first.

Correct answer: B

The correct answer is 4π.

  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 A=1/2 r^2 θ=1/2(16)(π/2)=4π.
  3. Check the angle and sign: The correct answer is 4π.

Use A=1/2 r^2 θ=1/2(16)(π/2)=4π.

3. QuestionMultiple choice

A wheel turns through 3π3\pi radians in 2 seconds. What is its angular speed?

Please select an answer first.

Correct answer: C

The correct answer is 3π2\frac{3\pi}{2} radians per second.

  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: Angular speed is angle divided by time: 3π/2.
  3. Check the angle and sign: The correct answer is 3π2\frac{3\pi}{2} radians per second.

Angular speed is angle divided by time: 3π/2.

4. QuestionMultiple choice

Which model describes a quantity that repeats every 24 hours?

Please select an answer first.

Correct answer: D

The correct answer is A periodic trigonometric model.

  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 sinusoidal model can represent regular repeated cycles.
  3. Check the angle and sign: The correct answer is A periodic trigonometric model.

A sinusoidal model can represent regular repeated cycles.

5. QuestionMultiple choice

Convert the polar point (4,π2)(4,\frac{\pi}{2}) to rectangular coordinates.

Please select an answer first.

Correct answer: A

The correct answer is (0,4)(0,4).

  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: Use x=r cosθ and y=r sinθ: x=0 and y=4.
  3. Check the angle and sign: The correct answer is (0,4)(0,4).

Use x=r cosθ and y=r sinθ: x=0 and y=4.

6. QuestionMultiple choice

Convert the rectangular point (3,3)(3,3) to polar form with positive r.

Please select an answer first.

Correct answer: B

The correct answer is (32,π4)(3\sqrt{2},\frac{\pi}{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: r=√(3^2+3^2)=3√2 and the angle is π/4.
  3. Check the angle and sign: The correct answer is (32,π4)(3\sqrt{2},\frac{\pi}{4}).

r=√(3^2+3^2)=3√2 and the angle is π/4.

7. QuestionMultiple choice

What is the period of a pendulum model h(t)=2cos⁡(π4t)+5h(t)=2\cos(\frac{\pi}{4}t)+5?

Please select an answer first.

Correct answer: C

The correct answer is 8 seconds.

  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 period is 2π/(π/4)=8 seconds.
  3. Check the angle and sign: The correct answer is 8 seconds.

The period is 2π/(π/4)=8 seconds.

8. QuestionMultiple choice

What is the midline of T(t)=70+12sin⁡(π6t)T(t)=70+12\sin(\frac{\pi}{6}t)?

Please select an answer first.

Correct answer: D

The correct answer is 70.

  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 constant term is the midline around which the temperature oscillates.
  3. Check the angle and sign: The correct answer is 70.

The constant term is the midline around which the temperature oscillates.

9. QuestionMultiple choice

If a sinusoidal model has maximum 18 and minimum 6, what is its amplitude?

Please select an answer first.

Correct answer: A

The correct answer is 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: Amplitude is half the range: (18-6)/2=6.
  3. Check the angle and sign: The correct answer is 6.

Amplitude is half the range: (18-6)/2=6.

10. QuestionMultiple choice

What is the angular frequency of y=sin⁡(5t)y=\sin(5t)?

Please select an answer first.

Correct answer: B

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: In y=sin(ωt), the coefficient ω is the angular frequency.
  3. Check the angle and sign: The correct answer is 5.

In y=sin(ωt), the coefficient ω is the angular frequency.

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