The wording of the following problem confuses me:
Find the Fourier sine series for $f(x)=x$, on $0\leq x<L$. To which value does the series converge at $x=\frac32 L$?
Can someone clarify what is meant by "the Fourier sine series"? From what I know, Fourier series are defined for functions with a domain $[-\pi, \pi]$. To get to this, we let $$ \theta = \left(\frac{2x}{L}-1\right)\pi $$ However, now the function $f(\theta)$ is not even in $\theta$ so the cosine terms won't dissapear.
Can someone clarify the situation for me?