Free ACT Math: Trigonometry Questions and Answers 3 — Questions and Answers
Question 1: What is the period of the function f(x) = 3 sin(2x)?
- π (Correct answer)
- 2π
- 6π
- 3π
Correct answer: π
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)?
- cos θ (Correct answer)
- sin θ
- −cos θ
- tan θ
Correct answer: cos θ
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?
- (1/2)(7)(10) sin 45° = 35√2/2 ≈ 24.75 sq units (Correct answer)
- (1/2)(7)(10) = 35 sq units
- 7 × 10 × sin 45° ≈ 49.5 sq units
- (7 + 10) × sin 45° ≈ 12 sq units
Correct answer: (1/2)(7)(10) sin 45° = 35√2/2 ≈ 24.75 sq units
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?
- 5/3 (Correct answer)
- 4/5
- 3/5
- 5/4
Correct answer: 5/3
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?
- 4 (Correct answer)
- 1
- −4
- 5
Correct answer: 4
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.
Question 6: Which angle in degrees has a reference angle of 40° and lies in Quadrant IV?
- 320° (Correct answer)
- 220°
- 140°
- 40°
Correct answer: 320°
In Quadrant IV, angles are between 270° and 360°. The reference angle is measured from the x-axis: θ = 360° − 40° = 320°.
Free ACT Math: Trigonometry Questions and Answers 3
What is the period of the function f(x) = 3 sin(2x)?