# Transforming from cartesian to cylindrical and spherical

1. Sep 13, 2015

### yango_17

1. The problem statement, all variables and given/known data
Translate the following equations from the given coordinate system into equations in each of the other two systems. Also, identify the surfaces so described by providing appropriate sketches.

2. Relevant equations

3. The attempt at a solution
For my solutions, I obtained z=2r^2 for the cylindrical equation and for the spherical equation I got:
(ρcosφ)^2 = 2(ρsinφcosθ)^2 + 2(ρsinφsinθ)^2. For my sketch I drew an infinite cylinder:

I was wondering whether my conversions were correct, as when I transform the same equation from cartesian to spherical and from cylindrical to spherical I seem to obtain different equations.

2. Sep 13, 2015

### Staff: Mentor

That's not a cylinder -- it's a cone. (Mathematically, cones have two parts.)

What was your equation in Cartesian form?

3. Sep 13, 2015

### yango_17

Sorry I meant cone hahah. My original equation in cartesian form was z^2=2x^2+2y^2

4. Sep 13, 2015

### Staff: Mentor

Then your cylindrical equation should be $z^2 = 2r^2$, not $z = 2r^2$ as you showed earlier.

5. Sep 13, 2015

### yango_17

Does the spherical equation look correct?

6. Sep 13, 2015

### Staff: Mentor

I'll take a look at it in a little while (it's dinner time...)

7. Sep 13, 2015

### yango_17

Much appreciated (:

8. Sep 13, 2015

### Staff: Mentor

This is correct, as far as you went, but the right side could be simplified considerably.

9. Sep 13, 2015

### yango_17

How would you go about simplifying it?

10. Sep 13, 2015

### Staff: Mentor

Expand the terms on the right side.