Question

What are the graphs of the constant functions$r=r_0$

$\theta ={\theta }_0$, and$z=z_0$ in the cylindrical coordinate system?

Short answer

In the equation$\theta ={\theta }_0$representing the plane parallel to$xz-$plane.

and the equation $z=z_0$representing the plane parallel to$xy-$plane

Step-by-step solution

Given information

The goal is to understand the graphs of constant functions $r=r_0,\theta ={\theta }_0$$z=z_0$in cylindrical coordinates.

The graphs of $r=r_0$represent plane equations parallel to the $yz$-plane in the cylindrical coordinate system.

Determine whether the given equations are represented a coordinate system or not

The plane$xz$- parallel to the -plane is represented by the equation$\theta ={\theta }_0$

The plane$xy-$parallel to the -plane is represented by the equation$z=z_0$