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

1 Answer
Wataru
Oct 21, 2014

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.

I hope that this was helpful.

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