TMUA Trigonometry 2 — Questions and Answers
Question 1: Which of the following is equal to sin(π - x)?
- sin(x) (Correct answer)
- -sin(x)
- cos(x)
- -cos(x)
Correct answer: sin(x)
By the identity sin(π - x) = sin(x), the answer is sin(x).
Question 2: If cos(θ) = 3/5 and θ is in the fourth quadrant, what is sin(θ)?
- -4/5 (Correct answer)
- 4/5
- -3/4
- 3/4
Correct answer: -4/5
Using sin²θ + cos²θ = 1 gives |sin θ| = 4/5, and since θ is in Q4, sin θ = -4/5.
Question 3: What is the period of the function f(x) = tan(3x)?
- π/3 (Correct answer)
- π
- 3π
- 2π/3
Correct answer: π/3
The period of tan(kx) is π/k, so for k = 3 the period is π/3.
Question 4: Simplify: (1 - cos²x) / sin(x), for sin(x) ≠ 0.
- sin(x) (Correct answer)
- cos(x)
- tan(x)
- 1
Correct answer: sin(x)
Since 1 - cos²x = sin²x, dividing by sin(x) gives sin(x).
Question 5: What is the exact value of cos(150°)?
- -√3/2 (Correct answer)
- √3/2
- -1/2
- 1/2
Correct answer: -√3/2
cos(150°) = cos(180° - 30°) = -cos(30°) = -√3/2.
Question 6: If sin(α) = 1/3, what is sin(2α)?
- 4√2/9 (Correct answer)
- 2/9
- 2√2/3
- 1/9
Correct answer: 4√2/9
sin(2α) = 2sin(α)cos(α); cos(α) = √(1 - 1/9) = 2√2/3, so sin(2α) = 2·(1/3)·(2√2/3) = 4√2/9.
Question 7: What is the range of f(x) = 3sin(x) + 1?
- [-2, 4] (Correct answer)
- [-3, 3]
- [1, 4]
- [-1, 3]
Correct answer: [-2, 4]
Since sin(x) ∈ [-1, 1], multiplying by 3 gives [-3, 3], then adding 1 gives [-2, 4].
TMUA Trigonometry 2
Which of the following is equal to sin(π - x)?