Fourier Transform--Sine

$\displaystyle {\mathcal F}[\sin(2\pi k_0x)]$	$\textstyle =$	$\displaystyle \int_{-\infty}^\infty e^{-2\pi ikx}\left({e^{2\pi ik_0x}-e^{-2\pi ik_0x}\over 2i}\right)\,dx$
	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}i\int_{-\infty}^\infty [-e^{-2\pi i(k-k_0)x}+e^{-2\pi i(k+k_0)x}]\,dt$
	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}i[\delta(k+k_0)-\delta(k-k_0)],$