#### Answer

$\frac{\sqrt2}{2}$

#### Work Step by Step

RECALL:
In a unit circle,
$\cos{s} = x$
(Refer to Figure 13 on page 111)
The angle $\frac{7\pi}{4}$ intersects the unit circle at the point $(\frac{\sqrt2}{2}, -\frac{\sqrt2}{2})$.
This point has $x=\frac{\sqrt2}{2}$ and $y=-\frac{\sqrt2}{2}$.
Since $\cos{s}=x$, then
$\cos{\frac{7\pi}{4}} =\frac{\sqrt2}{2}$