When solving a Fourier Series, you can run into things that have the following structure. cos(n*pi) cos(n*2pi) sin(n*pi/2) These expressions can be rewritten in terms of powers of -1 or as well as seeing that some terms drop to zero or are always the same value. cos(n*pi) = (-1)^n cos(n*2pi) = 1 sin(n*pi/2) = (-1)^((n-1)/2) My question comes down to: What do you get or how to figure out what happens with this: sin(n*pi/3) I know that the constant that always pops out is sqrt(3)/2, but the sign and pattern of this value starting at n=1 is as follows. + + 0 - - 0 + + 0 - - 0 ...etc Is there a way to write this in powers of 1. I know that the 3n's are all equal to 0, but what about the other numbers? Another way to avoid this is to not try to find a different way of writing sin(n*pi/3) since it is acceptable to just use it as part of the function. But is there a way to write it?