College Math Placement Test Trigonometry 3 — Questions and Answers
Question 1: What is the amplitude of y = −3 sin(x)?
- 3 (Correct answer)
- -3
- 1/3
- π
Correct answer: 3
Amplitude is the absolute value of the leading coefficient: |−3| = 3.
Question 2: What is the value of arcsin(−1)?
- −π/2 (Correct answer)
- π/2
- π
- −π
Correct answer: −π/2
arcsin(−1) = −π/2 because sin(−π/2) = −1 and −π/2 is in [−π/2, π/2].
Question 3: Simplify: (1 − cos²θ) / sin θ
- sin θ (Correct answer)
- cos θ
- tan θ
- 1
Correct answer: sin θ
1 − cos²θ = sin²θ, so sin²θ / sin θ = sin θ.
Question 4: What is the reference angle for 240°?
- 60° (Correct answer)
- 30°
- 120°
- 240°
Correct answer: 60°
240° is in Quadrant III; reference angle = 240° − 180° = 60°.
Question 5: What is cos(π/3)?
- 1/2 (Correct answer)
- √3/2
- √2/2
- √3/3
Correct answer: 1/2
π/3 = 60°, and cos 60° = 1/2.
Question 6: The graph of y = tan(x) has vertical asymptotes at x =
- π/2 + nπ (Correct answer)
- nπ
- π/4 + nπ
- 2nπ
Correct answer: π/2 + nπ
tan x = sin x / cos x is undefined wherever cos x = 0, i.e., x = π/2 + nπ.
Question 7: Which expression equals sin(2θ)?
- 2 sin θ cos θ (Correct answer)
- sin²θ − cos²θ
- cos²θ − sin²θ
- 2 cos²θ − 1
Correct answer: 2 sin θ cos θ
The double-angle formula is sin(2θ) = 2 sin θ cos θ.
College Math Placement Test Trigonometry 3
What is the amplitude of y = −3 sin(x)?