Chapter 7.9, Problem 19P

In Problems 17 to 22 you are given $f(x)$ on an interval, say $0<x<b$.

Sketch several periods of the even function $f_c$ of period 2b, the odd function $f_c$ of period $2b_{,}$ and the function $f_p$ of period b, each of which equals $f(x)$ on $0<x<b.$ Expand each of the three functions in an appropriate Fourier series.

$f(x)=\left|\cos x\right|,0<x<\pi$.