Question

Find the value of cos theta if sin θ = 1/2, where 0 degrees ≤ θ < 90 degrees.

A. -1/2
B. 3/2
C. √3/2
D. 2/√3

Answer 1

To find the value of cos θ for sin θ = 1/2 in the first quadrant, use the Pythagorean identity to solve for cos θ and find that cos θ = √3/2.

Step-by-step explanation:

To find the value of cos θ given that sin θ = 1/2 and the angle is within the range of 0 degrees to 90 degrees, we can use the Pythagorean identity. This identity states that sin^2 θ + cos^2 θ = 1.

Since sin θ is given as 1/2, we can substitute this into the identity:

1. (1/2)^2 + cos^2 θ = 1
2. (1/4) + cos^2 θ = 1
3. cos^2 θ = 1 - (1/4)
4. cos^2 θ = 3/4
5. cos θ = ±3/√2

However, because we are looking in the first quadrant where all trigonometric values are positive, we choose the positive root. Therefore, cos θ = √3/2 which corresponds to option C.