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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

What is the amplitude of y=5sin⁡xy=5\sin x?

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: Amplitude is the absolute value of the coefficient of sine.
  3. Check the angle and sign: The correct answer is 5.

Amplitude is the absolute value of the coefficient of sine.

2. QuestionMultiple choice

What is the period of y=cos⁡(3x)y=\cos(3x)?

Please select an answer first.

Correct answer: B

The correct answer is 2π3\frac{2\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: The period is 2π/|3|=2π/3.
  3. Check the angle and sign: The correct answer is 2π3\frac{2\pi}{3}.

The period is 2π/|3|=2π/3.

3. QuestionMultiple choice

What is the midline of y=2sin⁡x−4y=2\sin x-4?

Please select an answer first.

Correct answer: C

The correct answer is y=−4y=-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: The vertical shift k=-4 is the midline.
  3. Check the angle and sign: The correct answer is y=−4y=-4.

The vertical shift k=-4 is the midline.

4. QuestionMultiple choice

Which equation shifts y=sin⁡xy=\sin x right by π2\frac{\pi}{2}?

Please select an answer first.

Correct answer: D

The correct answer is y=sin⁡(x−π2)y=\sin\left(x-\frac{\pi}{2}\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: Replacing x with x-π/2 shifts the graph right by π/2.
  3. Check the angle and sign: The correct answer is y=sin⁡(x−π2)y=\sin\left(x-\frac{\pi}{2}\right).

Replacing x with x-π/2 shifts the graph right by π/2.

5. QuestionMultiple choice

What is the range of y=−3cos⁡x+2y=-3\cos x+2?

Please select an answer first.

Correct answer: A

The correct answer is [−1,5][-1,5].

  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: Since -1≤cos x≤1, -3cos x+2 ranges from -1 to 5.
  3. Check the angle and sign: The correct answer is [−1,5][-1,5].

Since -1≤cos x≤1, -3cos x+2 ranges from -1 to 5.

6. QuestionMultiple choice

How many complete cycles does y=sin⁡(4x)y=\sin(4x) complete on [0,2π][0,2\pi]?

Please select an answer first.

Correct answer: B

The correct answer is 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: Its period is π/2, so 2π divided by π/2 gives 4 cycles.
  3. Check the angle and sign: The correct answer is 4.

Its period is π/2, so 2π divided by π/2 gives 4 cycles.

7. QuestionMultiple choice

What is the maximum value of y=4cos⁡x−1y=4\cos x-1?

Please select an answer first.

Correct answer: C

The correct answer is 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 reaches 1, so the maximum is 4(1)-1=3.
  3. Check the angle and sign: The correct answer is 3.

Cosine reaches 1, so the maximum is 4(1)-1=3.

8. QuestionMultiple choice

Where are the vertical asymptotes of y=tan⁡xy=\tan x in [0,2π)[0,2\pi)?

Please select an answer first.

Correct answer: D

The correct answer is x=π2,3π2x=\frac{\pi}{2},\frac{3\pi}{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: Tangent is undefined where cosine is zero.
  3. Check the angle and sign: The correct answer is x=π2,3π2x=\frac{\pi}{2},\frac{3\pi}{2}.

Tangent is undefined where cosine is zero.

9. QuestionMultiple choice

Which equation has amplitude 2, period 2π, and midline y=3?

Please select an answer first.

Correct answer: A

The correct answer is y=2sin⁡x+3y=2\sin x+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: The coefficient 2 gives amplitude, the x coefficient 1 gives period 2π, and +3 gives the midline.
  3. Check the angle and sign: The correct answer is y=2sin⁡x+3y=2\sin x+3.

The coefficient 2 gives amplitude, the x coefficient 1 gives period 2π, and +3 gives the midline.

10. QuestionMultiple choice

What is the phase shift of y=cos⁡(x+π4)y=\cos\left(x+\frac{\pi}{4}\right)?

Please select an answer first.

Correct answer: B

The correct answer is Left π4\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: The form cos(x+c) shifts left by c.
  3. Check the angle and sign: The correct answer is Left π4\frac{\pi}{4}.

The form cos(x+c) shifts left by c.

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