Question

Suppose θ is an angle in the 2nd quadrant and sin(θ)=1/2 What is the value of cos(θ)

a. 1/2


b. −3√/2


c. −3/5



d. −3√/3



e. -1/2

Answer 1

B. -√(3)/2

Explanation:

Given:

• θ is an angle in the 2nd quadrant
• sin(θ) = 1/2

We know that in the 2nd quadrant, sinθ is positive and cosθ is negative.

The Pythagorean identity states that sin²(θ) + cos²(θ) = 1.

Substituting sin(θ) = 1/2, we get:

(½)² + cos²(θ) = 1

cos²(θ) = ¾

cos(θ) = -√(3)/2

Therefore, the value of cos(θ) is -√(3)/2.