Chapter 12.9, Problem 16PPS

To determine

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

Answer to Problem 16PPS

  $\frac{5\pi }{6}={150}^{\circ },\frac{7\pi }{6}={210}^{\circ }$

Explanation of Solution

Given: ${\cos }^{-1}\left(-\frac{\sqrt{3}}{2}\right)$

Calculation: Let ${\cos }^{-1}\left(-\frac{\sqrt{3}}{2}\right)=x$ ;

  $\begin{array}{l}{\cos }^{-1}\left(-\frac{\sqrt{3}}{2}\right)=x\\ \Rightarrow \left(-\frac{\sqrt{3}}{2}\right)=\cos x\\ \Rightarrow \cos x=\left(-\frac{\sqrt{3}}{2}\right)\\ \Rightarrow x=\frac{5\pi }{6},\frac{7\pi }{6}\\ \Rightarrow x=\frac{5\times {180}^{\circ }}{6},\frac{7\times {180}^{\circ }}{6}\\ \Rightarrow x={150}^{\circ },{210}^{\circ }\end{array}$

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