1. The problem statement, all variables and given/known data f(x)= -cos(x) when -π<x<0 cos(x) when 0<x<π Decide if f is an even, odd function or either. Find the Fourier series of f. 2. Relevant equations odd function: f(x)=f(-x) even function: -f(x)=f(-x) or f(x)=-f(-x) 3. The attempt at a solution substitute -x into either cos(x) or -cos(x) => -cos(x)=-cos(-x) and cos(x)=cos(-x), therefore, f is an even function. However, I'm stuck when it comes to finding the Fourier series. I know how to solve a0, where I just need to find the integration of -cos(x)dx and cos(x)dx. To find an and bn, I need to find the integration of [-cos(x)cos(nx)dx], [cos(x)cos(nx)dx], [-cos(x)sin(nx)] and [cos(x)sin(nx)dx]. I tried to solve them using integration by parts, but it turned out to be infinitely expanding, so I guess integration by parts won't work. Is there any other way to integrate the above four functions?