Chapter 12.9, Problem 6CYU

To determine

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

Answer to Problem 6CYU

  $\frac{\sqrt{3}}{2}$

Explanation of Solution

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

Calculation: Let

  $\begin{array}{l}{\sin }^{-1}\frac{\sqrt{3}}{2}=x\\ \Rightarrow \frac{\sqrt{3}}{2}=\sin x\\ \Rightarrow \sin x=\frac{\sqrt{3}}{2}\\ \sin \left({\sin }^{-1}\frac{\sqrt{3}}{2}\right)\\ =\sin x\\ =\frac{\sqrt{3}}{2}\end{array}$

Thus, obtained value is equal to the given expression.