So I'm trying to solve the problem of finding the Fourier series of this piecewise function:
$$f(x) = \begin{cases} 0 & -\pi \leq x\leq -\pi/2 \\ x & -\pi/2 \leq x\leq \pi/2 \\ 0 & \pi/2\leq x \leq \pi \end{cases} $$
Now I believe my function is odd, so I've just used the sines for the sum. The problem I've run into though is those zeroes to the side. I've calculated the sum for the $x$ part of the funtion and it worked fine. I just don't know how to incorporate those $f(x)=0$ on my series. If I try to integrate that $f(x)$ it's just $0$, so I don't know where to go from here.