Trigonometric Functions Practice Questions

Common Core (US) · Common Core Algebra 2 · 127 free MCQs with instant results and detailed explanations.

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Sample Questions from Trigonometric Functions

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Easy

What is the range of the sine function?

A. [-1, 1]

B. [0, 1]

C. (-∞, ∞)

D. [1, 2]

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Correct Answer: A

The range of the sine function is from -1 to 1, meaning it can take any value between -1 and 1 inclusive.

Easy

Which of the following angles has the same sine value as 45°?

A. 135°

B. 90°

C. 60°

D. 30°

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Correct Answer: A

The sine function is positive in both the first and second quadrants. Since sin(45°) = √2/2, sin(135°) also equals √2/2.

Easy

Which of the following represents the cosine function of angle θ?

A. Adjacent/Hypotenuse

B. Opposite/Hypotenuse

C. Adjacent/Opposite

D. Hypotenuse/Opposite

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Correct Answer: A

The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Medium

What is the period of the function f(x) = 2sin(πx)?

A. 1

B. 2

C. π

D. 2π

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Correct Answer: A

The period of the sine function is determined by the coefficient of x in the argument. Here, it is 2 (which is 2/π). Therefore, the period is 1.

Medium

If cos(θ) = 0.6, what is sin²(θ) + cos²(θ)?

A. 0.36

B. 1

C. 0.64

D. 0.8

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Correct Answer: B

According to the Pythagorean identity, sin²(θ) + cos²(θ) = 1 for all angles θ.

Medium

Which of the following represents the amplitude of the function y = 3cos(2x)?

A. 2

B. 3

C. 1

D. 6

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Correct Answer: B

The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine term. Here, it is 3.

Medium

Which of the following equations represents the cosine function shifted left by π/4 units?

A. y = cos(x + π/4)

B. y = cos(x - π/4)

C. y = cos(π/4 - x)

D. y = cos(x) + π/4

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Correct Answer: A

To shift the cosine function left by π/4, you add π/4 to x in the argument of the function, making the equation y = cos(x + π/4).

Hard

A Ferris wheel has a radius of 10 meters and completes one full rotation every 30 seconds. If a rider starts at the lowest point of the Ferris wheel, what is the height of the rider above the ground after 10 seconds?

A. 10 meters

B. 15 meters

C. 20 meters

D. 5 meters

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Correct Answer: B

After 10 seconds, the Ferris wheel has completed one-third of a rotation. The rider's height can be calculated using the formula: height = radius * sin(angle) + center height. Here, the angle is 120° (2π/3 radians), which gives a height of 15 meters above the ground.

Hard

If sin(θ) = 0.6, what is the value of cos(θ) in the first quadrant?

A. 0.8

B. 0.6

C. 0.4

D. 0.5

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Correct Answer: A

In the first quadrant, sin²(θ) + cos²(θ) = 1. Thus, cos(θ) = √(1 - sin²(θ)) = √(1 - 0.36) = √(0.64) = 0.8.

Q10

Hard

What is the amplitude of the function f(x) = 3sin(4x) + 1?

A. 3

B. 4

C. 1

D. 0

Show Answer & Explanation

Correct Answer: A

The amplitude of a sine function in the form f(x) = a*sin(bx) + c is given by the absolute value of a. Here, a = 3, so the amplitude is 3.

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Trigonometric Functions — Common Core (US) Common Core Algebra 2 Practice Questions Online

This page contains 127 practice MCQs for the chapter Trigonometric Functions in Common Core (US) Common Core Algebra 2. The questions are organized by difficulty — 27 easy, 73 medium, 27 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.