Question

What is the exact value of $\cos 135°$ $?$

Answer 1

Find the value of $\cos 135°$:

Since, $\cos 135°=\cos (90°+45°)$

Which clearly lies in the $2^{nd}$quadrant, where $\cos$ is negative.

since $\begin{array}{rcl}& & cos(90°+\theta )=-\sin \theta \end{array}$

Thus,

$\begin{array}{rcl}\cos 135°& =& \cos (90°+45°)\\ & =& -\sin 45°\left[\sin 45°=\frac{1}{\sqrt{2}}\right]\\ & =& -\frac{1}{\sqrt{2}}\end{array}$

Hence, the value of $\cos 135°$is $\mathbf{-}\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}$.