Answer
- $\frac{\sqrt 2}{2}$
Work Step by Step
To find exact value of $\cos 225^{\circ}$, let's find its reference angle first. As $ 225^{\circ}$ terminates in quadrant III,
The reference angle = $ 225^{\circ} - 180^{\circ} $ = $45^{\circ}$
As $ 225^{\circ}$ terminates in quadrant III, its $\cos$ will be negative. Therefore by reference angle theorem-
$\cos 225^{\circ}$ = - $\cos45^{\circ}$
= - $\frac{\sqrt 2}{2}$