How to transform $x > 0, x < y$ to cylindrical coordinates?

Question

I have the following set

$$A=\{ (x,y,z) : x > 0, x < y, 1 < x^2 + y^2 < 3, 1 < z < 5 \}$$

I know how to transform $x^2 + y^2$ and $z$ to cylindrical coordinates:

$$1 < x^2 + y^2 < 3 \implies 1 < r < \sqrt{3}$$

$1 < z < 5$ just stays the same.

But what about $x > 0$ and $x < y$?

Answer 1

Okay so since $x > 0$, $x < y$ means:

and $\theta \in [0, 2 \pi[$ is the rotation counterclockwise, then since the blue area corresponds to $[\frac{\pi}{4}, \frac{\pi}{2}]$, then $[\frac{\pi}{4}, \frac{\pi}{2}[$ is the range of $\theta$ given the restrictions $x > 0$ and $x < y$.