Chapter 7.9, Problem 16P

Let $f(x)={\sin }^{2}x,0<x<\pi .$ Sketch (or computer plot) the even function $f_c$ of period $2\pi$, the odd function $f$, of period $2\pi$, and the function $f_p$ of period $\pi$, each of which is equal to $f(x)$ on $(0,\pi ).$ Expand each of these functions in an appropriate Fourier series.