Chapter 9.4, Problem 2GP

Solution

To find: the value of the given expression both in degrees and radians.

  $\theta =\frac{\pi }{3}$ or $\theta ={60}^{\circ }$ .

Given:

  ${\cos }^{-1}\frac{1}{2}$ .

Calculation:

When $0\le \theta \le \pi$ , or $0^{\circ }\le \theta \le {180}^{\circ }$ , the angle whose cosine is $\frac{1}{2}$ is,

  $\begin{array}{c}\theta ={\cos }^{-1}\frac{1}{2}\\ =\frac{\pi }{3}\end{array}$

Or,

  $\begin{array}{c}\theta ={\cos }^{-1}\frac{1}{2}\\ ={60}^{\circ }\end{array}$