Chapter 12.9, Problem 13PPS

To determine

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

Answer to Problem 13PPS

  $\frac{\pi }{6}={30}^{\circ },\frac{11\pi }{6}={330}^{\circ }$

Explanation of Solution

Given: $\mathrm{Arccos}\left(\frac{\sqrt{3}}{2}\right)$

Calculation: Let $\mathrm{Arccos}\left(\frac{\sqrt{3}}{2}\right)=x$ ;

  $\begin{array}{l}\mathrm{Arccos}\left(\frac{\sqrt{3}}{2}\right)=x\\ \Rightarrow \left(\frac{\sqrt{3}}{2}\right)=\cos x\\ \Rightarrow \cos x=\left(\frac{\sqrt{3}}{2}\right)\\ \Rightarrow x=\frac{\pi }{6},\frac{11\pi }{6}\\ \Rightarrow x=\frac{{180}^{\circ }}{6},\frac{11\times {180}^{\circ }}{6}\\ \Rightarrow x={30}^{\circ },{330}^{\circ }\end{array}$

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