Convergent Fourier series of signum function

Question

I found problem that states: Find Fourier series of function $f: R\rightarrow R$ given as $f(x)=\mbox{sgn}(\sin x)*\cos x$ where $\mbox{sgn}(x)=1$ for $x>0$, $\mbox{sgn}(x)=0$ for $x=0$ and $\mbox{sgn}(x)=-1$ for $x<0$ and check if series converges or diverges. I am having trouble understanding how to find values of $\mbox{sgn}(\sin x)$ like $\mbox{sgn}(x)$ which is given above.