$ x(t)=10cos(4\pi n + 2\pi)+5sin(2\pi n + 4\pi)\! $
In order to find the period of the signal below, we need to find a value of K that will make N an integer.
$ N_1 = \frac{2\pi}{\omega_0} K \! $
$ N_1 = \frac{2\pi}{4\pi} K \! $
$ N_1 = 2K \! $
$ N_2 = \frac{2\pi}{\omega_0} K \! $
$ N_2 = \frac{2\pi}{2\pi} K \! $
$ N_2 = K \! $
Since both numbers are integers before multiplying by K, we can just let K = 1.
$ a_k = \frac{1}{N} \sum^{N-1}_{n = 0} X[n] e^{-jk\frac{2\pi}{N} n} $
