Chapter 12.9, Problem 1CYU

To determine

To find the value of angle from given expression and write the angle measure in radian and degrees both.

Answer to Problem 1CYU

  $\frac{\pi }{6}={30}^{\circ },\frac{5\pi }{6}={150}^{\circ }$

Explanation of Solution

Given: ${\sin }^{-1}\left(\frac{1}{2}\right)$

Calculation: Let ${\sin }^{-1}\left(\frac{1}{2}\right)=x$ ;

  $\begin{array}{l}{\sin }^{-1}\left(\frac{1}{2}\right)=x\\ \Rightarrow \left(\frac{1}{2}\right)=\sin \left(x\right)\\ \Rightarrow \sin x=\left(\frac{1}{2}\right)\\ \Rightarrow x=\frac{\pi }{6},\frac{5\pi }{6}\\ \Rightarrow x=\frac{{180}^{\circ }}{6},\frac{5\times {180}^{\circ }}{6}\\ \Rightarrow x={30}^{\circ },{150}^{\circ }\end{array}$

Thus, obtained values are the angle measures of the given expression.