First start by looking at the graph of cos(x) from 0 to 2(pi). You will note that there is only one value of x in this domain such that cos(x) = -1: x = (pi).

Now, cosine is a periodic function with a wavelength of 2(pi). So every 2(pi) there is one value of x such that cos(x) = -1.

Thus:

x = (pi) + 2(pi)*n

where n is some integer.

(A moment's thought will show you that n can be either positive or negative as well as 0.)

-Dan