Trigonometry Trigonometric Identities 3

Question 1

Which of the following is the correct half-angle formula for sin(θ/2)?

Accepted Answer

±√((1 − cos θ)/2)

Answer

The half-angle identity is sin(θ/2) = ±√((1 − cos θ)/2), with the sign determined by the quadrant of θ/2.

Question 2

Simplify: tan θ · cos θ

Accepted Answer

sin θ

Answer

tan θ = sin θ/cos θ, so tan θ · cos θ = (sin θ/cos θ) · cos θ = sin θ.

Question 3

Which identity represents the product-to-sum formula for sin A · cos B?

Accepted Answer

(1/2)[sin(A+B) + sin(A−B)]

Answer

The product-to-sum formula gives sin A cos B = (1/2)[sin(A+B) + sin(A−B)].

Question 4

What is sin(3π/2) + cos(π)?

Accepted Answer

−2

Answer

sin(3π/2) = −1 and cos(π) = −1, so their sum is −1 + (−1) = −2.

Question 5

If sin x = cos x, which identity confirms the solution x = π/4 + nπ?

Accepted Answer

Dividing both sides by cos x gives tan x = 1

Answer

Dividing sin x = cos x by cos x yields tan x = 1, which holds when x = π/4 + nπ.

Trigonometry Practice Test