Suppose I want to write the function $x \sin(t)$ as the series over the interval $x \in (0,\pi)$
$x\sin(t) = \sum_{n=1}^{\infty}(a_n \cos(t) + b_n \sin(t) )\sin(nx)$
Then would the coefficients $a_n$ and $b_n$ be just simply
$a_n =\frac{1}{\pi \cos(t)} \int_{0}^{\pi}x\sin(nx) \;\mathrm{d}x = \frac{\tan(t)}{\pi} \int_{0}^{\pi}x\sin(nx) \;\mathrm{d}x $
$b_n =\frac{1}{\pi \sin(t)} \int_{0}^{\pi}x\sin(t)\sin(nx) \;\mathrm{d}x = \frac{1}{\pi} \int_{0}^{\pi}x\sin(nx) \;\mathrm{d}x$
Could i just treat the trig functions as parameters?
Thanks
EDIT: The bounty is supposed to read "not enough attention". I may have misselcted the wrong item when I set the bounty