I'm working on Fourier Series problems, and my first step is to always draw and visualize the functions I am faced with. If f(x) = -1 when -$\pi$ < x < $\pi$ and f(x) = 1 when 0 < x < $\pi$. What happens with the region from 0 to $\pi$? How f(x) can be defined?
And now that we are all here. When trying to find $a_0$, $a_n$ and $b_n$, do I need to calculate each twice? One for when f(x) = 1 and once when f(x) = -1? If yes, do I need to sum them up? My professor always gave us f(x) = 0 and f(x) = 1, so it was obvious what to do.