Free ACT Math: Trigonometry Questions and Answers 2

Question 1

In a right triangle, the opposite side is 7 and the hypotenuse is 25. What is tan θ?

Accepted Answer

7/24

Answer

First find adjacent side: adj = √(25² − 7²) = √(625 − 49) = √576 = 24. tan θ = opposite/adjacent = 7/24.

Question 2

What is the exact value of cos(60°)?

Accepted Answer

1/2

Answer

From the 30-60-90 triangle: cos(60°) = adjacent/hypotenuse = 1/2. This is one of the standard values to memorize for the ACT.

Question 3

An angle measures 5π/6 radians. What is this in degrees?

Accepted Answer

150°

Answer

Multiply by 180°/π: (5π/6) × (180/π) = 5 × 30 = 150°.

Question 4

If cos θ = −√3/2 and 180° < θ < 270°, what is θ?

Accepted Answer

210°

Answer

cos θ = −√3/2 corresponds to reference angle 30°. In Quadrant III (180° < θ < 270°): θ = 180° + 30° = 210°.

Question 5

Which identity is correct?

Accepted Answer

sin²θ + cos²θ = 1

Answer

The Pythagorean identity sin²θ + cos²θ = 1 is fundamental in trigonometry. The related identities are: tan²θ + 1 = sec²θ and cot²θ + 1 = csc²θ.

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