discrete sine transform using FFT
well, you can do a little Googling and Wikipeding and find the definitions of the DST and pick one of them.  The get the definition of the DFT (the FFT is an efficient method to compute the DFT), use Euler's formula on the DST definition and see where a DFT pops out.

i might get back to this tonight and spell it out, but if you're not sure where to go next, the above (hit the links) tells you where to approach the problem.