Chapter 13.9, Problem 21PPS

To determine

To find the value of the given expression round to the nearest hundredth if necessary.

Answer to Problem 21PPS

  $\frac{\sqrt{3}}{2}$

Explanation of Solution

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

Calculation: Let

  $\begin{array}{l}\mathrm{Arctan}\sqrt{3}=x\\ \Rightarrow \sqrt{3}=\tan x\\ \Rightarrow \tan x=\sqrt{3}\\ \Rightarrow x=\frac{\pi }{3}\\ \sin \left(\mathrm{Arctan}\sqrt{3}\right)\\ =\sin x\\ =\tan \frac{\pi }{3}\\ =\sqrt{3}\end{array}$

Thus, obtained value is equal to the given expression.