Q 8 - Calculus

Question

To convert from cylindrical to rectangular coordinates: 

$x=\_\_\_\_,y=\_\_\_\_,z=\_\_\_\_$

Step-by-Step Solution

Answer

$$\begin{gathered} x=\rho \cos \theta \\ y=\rho \sin \theta \\ z=z \end{gathered}$$

Step 1:Given information

Given $\left(x,y,z\right)$ are rectangular coordinates and $\left(\rho ,\theta ,z\right)$ are cylindrical coordinates

Step 2:Simplification

$\left(\rho ,\theta ,z\right)$ are cylindrical coordinates and $\left(x,y,z\right)$ are rectangular coordinates

The relation is as below:

From the figure

$\cos \theta =\frac{x}{\rho }$

$\Rightarrow x=\rho \cos \theta$

Similarly

$\sin \theta =\frac{y}{\rho }$

$\Rightarrow y=\rho \sin \theta$

And from the figure we can observe $z=z$