Question

How do I convert from 3-D Cartesian coordinates to cylindrical coordinates?

Answer 1

If Cartesian coordinates are `(x,y,z)`, then its corresponding cylindrical coordinates `(r,theta,z)` can be found by

`r=sqrt{x^2+y^2}`

#theta={(tan^{-1}(y/x)" if "x>0),(pi/2" if "x=0 " and " y>0),(-pi/2" if " x=0" and "y<0),(tan^{-1}(y/x)+pi" if "x<0):}#

`z=z`

Note: It is probably much easier to find `theta` by find the angle between the positive `x`-axis and the vector `(x,y)` graphically.

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I hope that this was helpful.