Right I'm currently revising this stuff too so ill give it a go...
Is it supposed to be expressed in real form or complex?
Heres the complex form:
And heres the real form:
Heres what it all means...
BUT... This is for when the function is periodic... But yours is periodic (i.e. . So you must change the integral limit accordingly.
If the function is odd the a_k = 0 and if its is even then b_k = 0. So as the sine function is odd... a_k = 0!
Is this enough to start you off?