PRE CALCULUS Trigonometry 2

Question 1

What is the exact value of sin(5π/6)?

Accepted Answer

1/2

Answer

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?

Accepted Answer

1 - 2sin²(θ)

Answer

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:

Accepted Answer

amplitude 3, period π

Answer

Amplitude = |A| = 3 and period = 2π/|B| = 2π/2 = π.

Question 4

tan(θ) is undefined when θ equals:

Accepted Answer

π/2 + nπ for any integer n

Answer

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)?

Accepted Answer

-4/5

Answer

Using sin²θ + cos²θ = 1 gives cos²θ = 16/25, so cosθ = ±4/5; in Q3 cosine is negative, so cosθ = -4/5.

PRE CALCULUS Practice Test