Chapter 12.9, Problem 17PPS

To determine

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

Answer to Problem 17PPS

  $\frac{5\pi }{6}={150}^{\circ },\frac{5\pi }{3}={300}^{\circ }$

Explanation of Solution

Given: $\mathrm{Arctan}\left(-\frac{\sqrt{3}}{3}\right)$

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

  $\begin{array}{l}\mathrm{Arctan}\left(-\frac{\sqrt{3}}{3}\right)=x\\ \Rightarrow \left(-\frac{\sqrt{3}}{3}\right)=\tan x\\ \Rightarrow \tan x=\left(-\frac{\sqrt{3}}{3}\right)\\ \Rightarrow \tan x=\left(-\frac{1}{\sqrt{3}}\right)\\ \Rightarrow x=\frac{5\pi }{6},\frac{5\pi }{3}\\ \Rightarrow x=\frac{5\times {180}^{\circ }}{6},\frac{5\times {180}^{\circ }}{3}\\ \Rightarrow x={150}^{\circ },{300}^{\circ }\end{array}$

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