Given $A = \{(s,t) \in \mathbb{R}^2; s \geq 0, t \geq 0, s^2 + t^2 \leq 1\}$.
This region is the first quadrant of a circle centered at $0$ with radius $r=1$.
I want to determine the bounds of $s$ and $t$. My approach:
$s^2 + t^2 \leq 1 \implies s^2 \leq 1 - t^2 \implies s \leq \sqrt{1 - t^2}$
$\implies 0 \leq s \leq \sqrt{1 - t^2}$.
However, I don't know how to find the upper bound of $t$. Is it also given by $t \leq \sqrt{1 - s^2}$? I am not sure but it confuses me that both bounds depend on the other variable.