Chapter 14.3, Problem 1CYU

To determine

To calculate: $\text{cos}{165}^{\circ }.$

Answer to Problem 1CYU

  $\frac{-(\sqrt{3}+1)}{2\sqrt{2}}.$

Explanation of Solution

Given information:

The given expression is $\text{cos}{165}^{\circ }.$

Formula used:

  $\cos ({180}^{\circ }-\text{θ})=-\cos \text{θ},\cos {15}^{\circ }=\frac{\sqrt{3}+1}{2\sqrt{2}}\text{.}$

Calculation:

  $\begin{array}{l}\text{cos(}{165}^{\circ })=\text{cos(}{180}^{\circ }-{15}^{\circ })\\ =\text{cos}{15}^{\circ }\\ =\frac{-(\sqrt{3}+1)}{2\sqrt{2}}.\\ =\frac{1-\sqrt{3}}{2\sqrt{2}}.\end{array}$