Laplace II: Steps, Impulses & Convolution · Medium problem

Compute the convolution $(\sin t * \cos t)\!\left(\dfrac{\pi}{2}\right)=\displaystyle\int_0^{\pi/2}\sin\tau\,\cos\!\left(\dfrac{\pi}{2}-\tau\right)d\tau$ by finding $\sin t*\cos t$ with the convolution theorem.