Answer
$\dfrac{\sqrt 2}{2}$
Work Step by Step
When $P$ is the period of $f(x)$ then we have
$ f(x+p)=f(x)$
Since the function cosine is positive in the fourth quadrant and $\dfrac{7 \pi}{4}$ is also positive in the same quadrant.
Thus, the reference angle is: $\dfrac{\pi}{4}$.
Here, we have $ \cos (\dfrac{7 \pi}{4})=\cos (\dfrac{\pi}{4})$
and $\cos (\dfrac{\pi}{4})=\dfrac{\sqrt 2}{2}$
