Question

use the unit circle to find $cos^{-1}(\frac{1}{2})$ in degrees. remember that the domain of inverse cosine is limited to quadrants i and ii (the top half of the unit circle).

a. 60°
b. 210°
c. 135°
d. 180°

Explanation:

Step1: Recall cosine - inverse cosine relationship

The inverse - cosine function, $\cos^{-1}(x)$, gives the angle $\theta$ such that $\cos(\theta)=x$ and $\theta\in[0^{\circ},180^{\circ}]$ (quadrants I and II).

Step2: Find the angle with cosine value $\frac{1}{2}$ in the given domain

We know that $\cos(60^{\circ})=\frac{1}{2}$ and $60^{\circ}$ is in quadrant I which is within the domain of the inverse - cosine function ($0^{\circ}\leq\theta\leq180^{\circ}$).

Answer:

A. $60^{\circ}$