I came across a nasty task which includes infimum of a function on a set and I am really confused about it. Main confusion is the two arguments of the function. It's not a problem for me in finding infimums and supremums of sets, but here I am just stuck.
Function: $$ f(x) = (\cos(x^2+y^2))^{\large \cos(x^2+y^2)} $$ Need to find the infimum of this function on a set $E$: $$ E=\left\{(x,y) \in \mathbb{R}^2|x^2+y^2 < \frac{\pi}{2}\right\} $$
Hint: consider the function $\tilde{f}(\varrho) = (\cos \varrho ) ^{\cos \varrho}$ defined on the interval $[0,\pi/2)$.