Let $X,Y$ be iid distributed uniformly on $[0,1]$, my task involves calculating the distribution of $(\cos(\min(X,Y)),\max(X,Y))$ I have already calculated the distribution of $(\min(X,Y),\max(X,Y))$, its density is $2\text { for } y \leq x$, where $y$ denotes $\min$, $x$ denotes $\max$.
I managed to do it myslef, later i will post my anwser.