Consider the equations that relate cylindrical and Cartesian coordinates in ;

a. Near which points of can we solve for r, , and z in terms of the Cartesian coordinates?

b. Explain the geometry behind your answer in (a).

I started off by saying

but then what do you do for the third equation since ? If I use H:0 then that makes everywhere, meaning that it is not in general possible to solve for r, , and z in terms of x, y, and z. That seems so odd that I assume it's wrong, and I have to think that my mistake is in H.

Any thoughts?