Free ACT Math: Trigonometry Questions and Answers 3

Question 1

What is the period of the function f(x) = 3 sin(2x)?

Accepted Answer

π

Answer

For f(x) = A sin(Bx), the period = 2π/B. Here B = 2, so period = 2π/2 = π.

Question 2

Which of the following is equivalent to sin(90° − θ)?

Accepted Answer

cos θ

Answer

This is the co-function identity: sin(90° − θ) = cos θ. Similarly, cos(90° − θ) = sin θ.

Question 3

In triangle ABC (not right-angled), a = 7, b = 10, and C = 45°. What is the area of the triangle?

Accepted Answer

(1/2)(7)(10) sin 45° = 35√2/2 ≈ 24.75 sq units

Answer

Area of a triangle = (1/2)ab sin C = (1/2)(7)(10) sin 45° = 35 × (√2/2) = 35√2/2 ≈ 24.75 square units.

Question 4

If tan θ = 4/3, what is sec θ in the first quadrant?

Accepted Answer

5/3

Answer

Using tan θ = 4/3, we have opposite = 4, adjacent = 3, hypotenuse = √(16 + 9) = 5. cos θ = 3/5, so sec θ = 1/cos θ = 5/3.

Question 5

What is the amplitude of the function g(x) = −4 cos(x) + 1?

Accepted Answer

4

Answer

Amplitude = |A| where A is the coefficient of the trig function. For g(x) = −4 cos(x) + 1, amplitude = |−4| = 4. The vertical shift (+1) and sign (−) do not affect amplitude.

ACT Practice Test

ACT Practice Test

Free ACT Math: Trigonometry Questions and Answers 3