Hi!

Im asked to write sine AND cosine series of $\displaystyle sin(x) ; x \in <0,\pi)$

*what does that mean? i thought the fourier series can exist for the sine part being 0 OR the cosine being 0 OR both sine and cosine being included in the formula.. how do i do then one SINE and another COSINE serie of the same function?

*Im confused with the condition: first of all it doesn't look like a periodic function to me, but im supposed to do a fourier transform on it...

if i imagine it's a periodic function(somehow) then:

*how does the function look like? is it the positive parts of sine one next to the other, thus with period = $\displaystyle \pi$ ... or is it the complete sine with a constant 0 put in between the positive parts thus the period would be $\displaystyle 2\pi$?

*Also, how do i know what the function looks like on x < 0 ? (considering it is periodic, is the function even or odd or none of these?

Thanks!