In my math script (signal theory) it says that two functions are orthogonal to each other when $\int_{-\infty}^{+\infty}s^\star(t)u(t)\,dt = 0$. Now I want to prove that $$\int_{-\infty}^{+\infty}\sin(w_1*t)\sin(w_2*t)\,dt = 0$$ applies when $w_1 \neq w_2$ applies. No matter what I try to do, I always get the problem that I have to solve the integral of a sine or cosine from minus infinity to plus infinity, which makes no sense. How can I solve the problem?
EDIT:
* means complex conjugation.