Chapter 12.9, Problem 19PPS

To determine

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

Answer to Problem 19PPS

  $\frac{1}{\sqrt{3}}$

Explanation of Solution

Given: $\tan \left[\mathrm{Arcsin}\left(\frac{-1}{2}\right)\right]$

Calculation: Let

  $\begin{array}{l}\mathrm{Arcsin}\left(-\frac{1}{2}\right)=x\\ \Rightarrow -\frac{1}{2}=\sin x\\ \Rightarrow \sin x=-\frac{1}{2}\\ \Rightarrow x=\frac{7\pi }{6}\\ \tan \left[\mathrm{Arcsin}\left(-\frac{1}{2}\right)\right]\\ =\tan x\\ =\tan \frac{7\pi }{6}\\ =\frac{1}{\sqrt{3}}\end{array}$

Thus, obtained value is equal to the given expression.