Question

Let $b$be a constant. Prove that the equation of the plane $y=b$is $r=bcsc\theta$in cylindrical coordinates.

Short answer

Conversion of equation is done using$x=r\cos \theta ,y=r\sin \theta ,z=z$.

Step-by-step solution

Given Information

Equation of plane in rectangular coordinates is given by $y=b$($b$is constant)

Simplification

We know that

$x=r\cos \theta ,y=r\sin \theta ,z=z$

For the transformation, use $y=r\sin \theta$in $y=b$

$r\sin \theta =b$

$r=\frac{b}{\sin \theta }$

$\Rightarrow r=b\csc \theta$