Given a random process $X(t) = Y \cos(\omega t)$, where $Y$ is a uniform RV on $[0,1]$, $t \geq 0$ and $\omega$ is a constant. Determine the pdf at $t = \frac{\pi}{2}$.
For any other given $t$ I could solve as usual for functions of a random variable: $$f_X(x) = f_y(h(x)) \left | \frac{d h(x)}{dx} \right| $$ where $h(x)= g^{-1}(x) = \frac{x_t}{\cos(\omega t)}$, but I can't divide by $\cos(\frac{\pi}{2})$ for obvious reasons. How do I proceed ?