Chapter 13.9, Problem 2BCYP

To determine

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

Answer to Problem 2BCYP

  $\frac{-1}{\sqrt{2}}$

Explanation of Solution

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

Calculation: Let

  $\begin{array}{l}\mathrm{Arccos}-\frac{\sqrt{2}}{2}=x\\ \Rightarrow -\frac{\sqrt{2}}{2}=\cos x\\ \Rightarrow \cos x=-\frac{\sqrt{2}}{2}\\ \Rightarrow \cos x=-\frac{1}{\sqrt{2}}\\ \cos \left(\mathrm{Arccos}-\frac{\sqrt{2}}{2}\right)\\ =\cos x\\ =-\frac{1}{\sqrt{2}}\end{array}$

Thus, obtained value is equal to the given expression.