Trigonometry Advanced Trigonometric Concepts 2

Question 1

What is the value of sin(75°) using the sum formula?

Accepted Answer

(√6 + √2) / 4

Answer

sin(75°) = sin(45° + 30°) = sin45·cos30 + cos45·sin30 = (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4.

Question 2

Which identity correctly expresses cos(2θ) in terms of sin(θ) only?

Accepted Answer

1 - 2sin²θ

Answer

cos(2θ) = cos²θ - sin²θ = (1 - sin²θ) - sin²θ = 1 - 2sin²θ.

Question 3

What is the period of y = 3sin(4x - π)?

Accepted Answer

π/2

Answer

The period of y = A·sin(Bx + C) is 2π/|B|, so 2π/4 = π/2.

Question 4

The expression tan(α - β) equals which of the following?

Accepted Answer

(tanα - tanβ) / (1 + tanα tanβ)

Answer

The tangent subtraction formula is tan(α - β) = (tanα - tanβ) / (1 + tanα tanβ).

Question 5

If sec θ = 2 and θ is in the first quadrant, what is tan θ?

Accepted Answer

√3

Answer

sec θ = 2 means cos θ = 1/2, so θ = 60°, and tan 60° = √3.

Trigonometry Practice Test