Answer
- $\frac{\sqrt 2}{2}$
Work Step by Step
To find exact value of $\cos 135^{\circ}$, let's find its reference angle first. As $ 135^{\circ}$ terminates in quadrant II,
The reference angle = $ 180^{\circ} - 135^{\circ}$ = $45^{\circ}$
As $ 135^{\circ}$ terminates in quadrant II, its cos will be negative. Therefore by reference angle theorem-
$\cos 135^{\circ}$ = - $\cos45^{\circ}$
= - $\frac{\sqrt 2}{2}$
