$ x(t)=10cos(4\pi n + 2\pi)\! $
In order to find the period of the signal below, we need to find the smallest value of K that will make N an integer.
$ N = \frac{2\pi}{\omega_0} K \! $
$ N = \frac{2\pi}{2\pi} K \! $
$ N = \frac{2\pi}{2\pi} K \! $
$ N = K\! $
So the smallest value that K can have is 1.
$ K = 1\! $
