I'm trying to show the fourier transform of a since function:

I can't figure out how to show this. I could just work through the integral of the fourier transform, but that seems difficult for me... I think I could show it more easily using the duality property. i.e, finding the fourier transform of a rectangle function, then applying the duality property to show that transform the other way around. But I can't figure out what the rectangle function should be!

Can anyone help out or give some hints? Am I on the right track? Thanks!