PRE CALCULUS Trigonometry 2 — Questions and Answers
Question 1: What is the exact value of sin(5π/6)?
- 1/2 (Correct answer)
- √3/2
- -1/2
- -√3/2
Correct answer: 1/2
5π/6 is in the second quadrant where sine is positive, and sin(5π/6) = sin(π - π/6) = sin(π/6) = 1/2.
Question 2: Which identity correctly expresses cos(2θ) in terms of sin(θ) only?
- 1 - 2sin²(θ) (Correct answer)
- 2cos²(θ) - 1
- cos²(θ) - sin²(θ)
- 1 + 2sin²(θ)
Correct answer: 1 - 2sin²(θ)
Using cos(2θ) = cos²θ - sin²θ and replacing cos²θ with 1 - sin²θ gives 1 - 2sin²θ.
Question 3: The graph of y = 3sin(2x) has an amplitude and period of:
- amplitude 3, period π (Correct answer)
- amplitude 6, period π
- amplitude 3, period 2π
- amplitude 2, period 3π
Correct answer: amplitude 3, period π
Amplitude = |A| = 3 and period = 2π/|B| = 2π/2 = π.
Question 4: tan(θ) is undefined when θ equals:
- π/2 + nπ for any integer n (Correct answer)
- nπ for any integer n
- π/4 + nπ for any integer n
- π/3 + nπ for any integer n
Correct answer: π/2 + nπ for any integer n
tan(θ) = sin(θ)/cos(θ) is undefined wherever cos(θ) = 0, which occurs at θ = π/2 + nπ.
Question 5: If sin(θ) = -3/5 and θ is in the third quadrant, what is cos(θ)?
- -4/5 (Correct answer)
- 4/5
- -3/4
- 3/4
Correct answer: -4/5
Using sin²θ + cos²θ = 1 gives cos²θ = 16/25, so cosθ = ±4/5; in Q3 cosine is negative, so cosθ = -4/5.
Question 6: What is the phase shift of y = sin(x - π/3)?
- π/3 to the right (Correct answer)
- π/3 to the left
- π/6 to the right
- 3π to the right
Correct answer: π/3 to the right
For y = sin(x - c), the phase shift is c units to the right; here c = π/3.
Question 7: Which of the following equals cot(θ)?
- cos(θ)/sin(θ) (Correct answer)
- sin(θ)/cos(θ)
- 1/sin(θ)
- 1/cos(θ)
Correct answer: cos(θ)/sin(θ)
Cotangent is the reciprocal of tangent, so cot(θ) = cos(θ)/sin(θ).
PRE CALCULUS Trigonometry 2
What is the exact value of sin(5π/6)?