1. The problem statement, all variables and given/known data This is a question in my classical mechanics book, and i am not very good with polar coordinates. I am suppose to fine r, phi, z in terms of x,y,z. Basically I need to derive the cylindrical polar coordinates from the Cartesian coordinates. The question specifically asks Find expressions for the unit vectors r,phi,z of cylindrical polar coordinates in terms of the Cartesian coordinates. 3. The attempt at a solution So far I have drawn a picture of cylinder and labeled everything i could. Now I know z=z, that is no problem. I know that x=r*cos[theta] and y=r*sin[theta], I also know that r=sqrt[x^2+y^2] and i know that phi=arctan[y/x]. The only way that i know how to derive these is drawing a triangle and showing it, is there any other way, like actually deriving them?