- #1

2sin54

- 109

- 1

## Homework Statement

Say I have some sort of a vector field in the cylindrical coordinate system [tex] \vec{F}(r, \Theta, z) = f(\vec{A}(r,\Theta,z),\vec{B}(r,\Theta,z)) [/tex]

How do I switch to the Cartesian coordinates? More precisely, how do I transform [tex] A_r = g(A_x,A_y,A_z), A_\Theta = h(A_x,A_y,A_z)[/tex] and so on?

## Homework Equations

https://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates

## The Attempt at a Solution

I understand that [tex]{\left(A_z\right)}_{cyl.} = {\left(A_z\right)}_{Cart.} [/tex]

and similarly for B and that

[tex] A_x = A_r\cdot\cos(\Theta), A_y = A_r\cdot\sin(\Theta [/tex].

However, what do I do with [tex] A_\Theta[/tex]?