Why Is the Expected Value of cos(t)sin(t) Zero?

[pamparana]

Hello,

Just came across this that:

E[cos(t)sin(t)] = 0

the expected value of the product of cos(t)sin(t) is 0. However, I am unable to convince myself that is the case. Can anyone help me understand why this is so?

Many thanks,

Luc

 

[g_edgar]

I suppose the probability space is $[0,2 \pi)$ with normalized Lebesgue measure? In that case, what it means is
$$\frac{1}{2\pi}\int_0^{2\pi} \sin(t) \cos(t)\,dt = 0$$