Hello all

I have the function

$\displaystyle s(x)= sin(x)cos^2(x)$

and i need to show that it is a $\displaystyle 2\pi$-periodic trigonometric function,

My first idea was simply something along the lines of $\displaystyle sin(x)cos^2(x)=sin(2\pi x)cos^2(2\pi x)$

Furthermore i need to determine the fourrier coefficients for all $\displaystyle n \in Z$

$\displaystyle 1/2pi \int_{-\pi}^{\pi} s(x)e^{-inx} dx$

Any helps or hints is very much appreciated