MPT Trigonometry 3 — Questions and Answers
Question 1: What is the amplitude of y = -3cos(x)?
- -3
- 3 (Correct answer)
- 1/3
- 6
Correct answer: 3
Amplitude is the absolute value of the leading coefficient: |-3| = 3.
Question 2: If sin(θ) = -√3/2 and θ is in the third quadrant, what is θ?
- π/3
- 2π/3
- 4π/3 (Correct answer)
- 5π/3
Correct answer: 4π/3
sin(60°) = √3/2, and in the third quadrant: π + π/3 = 4π/3.
Question 3: Simplify: (1 - cos²θ) / sin(θ) for sin(θ) ≠ 0.
- cos(θ)
- sin(θ) (Correct answer)
- tan(θ)
- 1
Correct answer: sin(θ)
1 - cos²θ = sin²θ by the Pythagorean identity, so sin²θ/sinθ = sinθ.
Question 4: What is the reference angle for 210°?
- 30° (Correct answer)
- 60°
- 45°
- 70°
Correct answer: 30°
210° is in the third quadrant; 210° - 180° = 30° is the reference angle.
Question 5: What is the range of the function y = arcsin(x)?
- [-π, π]
- [0, π]
- [-π/2, π/2] (Correct answer)
- (-∞, ∞)
Correct answer: [-π/2, π/2]
The range of arcsin (inverse sine) is [-π/2, π/2] by definition.
Question 6: Using the Law of Cosines, if a=5, b=7, and C=60°, what is c²?
- 39 (Correct answer)
- 49
- 74
- 29
Correct answer: 39
c² = 25 + 49 - 2(5)(7)cos(60°) = 74 - 70(0.5) = 74 - 35 = 39.
Question 7: What is the exact value of cos(π/6)?
- 1/2
- √2/2
- √3/2 (Correct answer)
- √3/3
Correct answer: √3/2
cos(π/6) = cos(30°) = √3/2.
MPT Trigonometry 3
What is the amplitude of y = -3cos(x)?