Fourier transforms of sin x and cos x

Using the convention $\hat f(k)=\int_{-\infty}^{\infty}f(x)e^{-ikx}\,dx$, compute the Fourier transforms of $\cos x$ and $\sin x$.

$\widehat{\cos}(k)=\pi[\delta(k-1)+\delta(k+1)]$ and $\widehat{\sin}(k)=-i\pi[\delta(k-1)-\delta(k+1)]$. Neither function is integrable, so the answer is a distribution: write them via Euler's formula and use $\widehat{e^{iax}}(k)=2\pi\delta(k-a)$.