Answer
Exact value of $\cos \frac{7\pi}{4} = \frac{\sqrt 2}{ 2} $
Work Step by Step
To find exact value of $\cos \frac{7\pi}{4}$, let's find its reference angle first.
As $ \frac{7\pi}{4}$ terminates in quadrant IV,
The reference angle = $2\pi -\frac{7\pi}{4} $ = $\frac{\pi}{4}$
As $ \frac{7\pi}{4}$ terminates in quadrant IV, its $\cos$ will be positive. Therefore by reference angle theorem-
$\cos \frac{7\pi}{4}$ = $\cos\frac{\pi}{4}$
= $\frac{1}{\sqrt 2}$
= $\frac{\sqrt 2}{ 2}$
