Chapter 14.3, Problem 2CYU

To determine

To Calculate:The value of $\cos {105}^{\circ }$ .

Answer to Problem 2CYU

  $\frac{1-\sqrt{3}}{2\sqrt{2}}$

Explanation of Solution

Given information:

The given expression is $\cos {105}^{\circ }$ .

Formula used:

  $\cos ({90}^{\circ }+\theta )=-\sin \theta ,\sin {15}^{\circ }=\frac{\sqrt{3}-1}{2\sqrt{2}}.$

Calculation:

  $\begin{array}{l}\cos {105}^{\circ }=\cos ({90}^{\circ }+{15}^{\circ })\text{.}\\ =\sin {15}^{\circ }\\ \text{=}\frac{-(\sqrt{3}-1)}{2\sqrt{2}}\\ =\frac{1-\sqrt{3}}{2\sqrt{2}}\end{array}$