Trigonometry Trigonometric Identities 4

Question 1

Which of the following is equivalent to 2 sin θ cos θ?

Accepted Answer

sin(2θ)

Answer

The double-angle identity states sin(2θ) = 2 sin θ cos θ.

Question 2

Simplify: (sin θ + cos θ)² − 1

Accepted Answer

2 sin θ cos θ

Answer

Expanding gives sin²θ + 2 sin θ cos θ + cos²θ − 1 = 1 + 2 sin θ cos θ − 1 = 2 sin θ cos θ.

Question 3

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

Accepted Answer

(√6 − √2)/4

Answer

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

Question 4

Which identity allows you to rewrite sin²θ in terms of cosine?

Accepted Answer

sin²θ = (1 − cos 2θ)/2

Answer

The power-reduction identity states sin²θ = (1 − cos 2θ)/2.

Question 5

Which expression is equivalent to (tan θ + cot θ)?

Accepted Answer

1/(sin θ cos θ)

Answer

tan θ + cot θ = sin θ/cos θ + cos θ/sin θ = (sin²θ + cos²θ)/(sin θ cos θ) = 1/(sin θ cos θ).

Trigonometry Practice Test