Trigonometry Trigonometric Identities 5

Question 1

Which of the following is the cofunction identity for cos θ?

Accepted Answer

cos θ = sin(π/2 − θ)

Answer

The cofunction identity states cos θ = sin(π/2 − θ), meaning cosine and sine are cofunctions of complementary angles.

Question 2

If cos(2θ) = 7/25, what is the value of cos²θ − sin²θ?

Accepted Answer

7/25

Answer

The identity cos(2θ) = cos²θ − sin²θ means cos²θ − sin²θ equals cos(2θ) directly, which is 7/25.

Question 3

Simplify: sin(θ) / (1 + cos θ)

Accepted Answer

tan(θ/2)

Answer

Using the half-angle identity, sin θ/(1 + cos θ) = tan(θ/2).

Question 4

Which expression is equivalent to cos(A − B)?

Accepted Answer

cos A cos B + sin A sin B

Answer

The cosine difference formula is cos(A − B) = cos A cos B + sin A sin B.

Question 5

What is the value of sin(15°) using the difference formula?

Accepted Answer

(√6 − √2)/4

Answer

sin(15°) = sin(45° − 30°) = sin45°cos30° − cos45°sin30° = (√2/2)(√3/2) − (√2/2)(1/2) = (√6 − √2)/4.

Trigonometry Practice Test