Question

Given that sin(θ) = 1/2 and θ lies in quadrant II, determine the value of cos(θ).

a) -√3/2
b) √3/2
c) -1/2
d) 1/2

Answer 1

The value of cos(θ) is -√3/2.

Step-by-step explanation:

To determine the value of cos(θ), we can use the Pythagorean identity, which states that sin(θ)² + cos(θ)² = 1. Since we know that sin(θ) = 1/2 and θ lies in quadrant II, we can find cos(θ) by substituting the value of sin(θ) into the identity and solving for cos(θ).

sin(θ)² + cos(θ)² = 1
1/2² + cos(θ)² = 1
1/4 + cos(θ)² = 1
cos(θ)² = 3/4
cos(θ) = ±√(3/4)
Since θ lies in quadrant II, which is negative for cosine, the answer is -√(3/4) = -√3/2 (option a).