Q 4 - Calculus

Question

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

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

Step-by-Step Solution

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 1: 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.

Step 2: 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$z=z_0$