Question

The angle θ is located in Quadrant II, and cos(θ) = -1/2. What is the value of sin(θ)?

A. 1/2
B. -√3/2
C. -1/2
D. √3/2

Answer 1

The value of sin(θ) is √3/2 when θ is located in Quadrant II and cos(θ) = -1/2.

Step-by-step explanation:

To find the value of sin(θ) when the angle θ is located in Quadrant II, and cos(θ) = -1/2, we use the Pythagorean identity sin2(θ) + cos2(θ) = 1. Since we know that cos(θ) is negative in Quadrant II and given that cos(θ) = -1/2, we can solve for sin(θ) as follows:

• cos2(θ) = (1/2)2 = 1/4
• sin2(θ) = 1 - cos2(θ) = 1 - 1/4 = 3/4
• sin(θ) = ±√(3/4) = ±√3/2

Since θ is in Quadrant II, where sin(θ) is positive, the value of sin(θ) must be √3/2, without the negative sign. Therefore, the correct answer is D. √3/2.