surface in cylindrical coordinate system

Question

Question is

What is the surface in cylindrical coordinate system if angle $\theta$ is $\pi/4$?

I understand it's a plane passing through $z$ axis, but book saying it's a vertical half plane. Why it's only half plane?

Answer 1

The angle $\theta$ is measured from the $x$ axis. The set you're looking for is then formed by all points which are separated $\pi/4$ from the $x$ axis, that is a vertical plane. Perhaps this sketch will help you