You may know that #Cos 0 = 1# and #cos pi = -1#
If you keep adding #2 pi# to the angle, the value doesn't change
So, #cos pi + 2 pi = cos 3 * pi# is also = - 1. Similarly, #cos 5 * pi, cos 7 * pi, cos 9 * pi# etc. in general #cos (2 * n + 1) * pi#, where n is an integer like 1, 2, 3, etc, are -1