Chapter 9.4, Problem 8E

Solution

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

  $\theta =\frac{\pi }{6}$ or $\theta ={30}^{\circ }$ .

Given:

  ${\sin }^{-1}\frac{1}{2}$ .

Calculation:

When $-\frac{\pi }{2}\le \theta \le \frac{\pi }{2}$ , or $-{90}^{\circ }\le \theta \le {90}^{\circ }$ , the angle whose sine is $\frac{1}{2}$ is,

  $\begin{array}{c}\theta ={\sin }^{-1}\frac{1}{2}\\ =\frac{\pi }{6}\end{array}$

Or,

  $\begin{array}{c}\theta ={\sin }^{-1}\frac{1}{2}\\ ={30}^{\circ }\end{array}$