# Plotting a 3-d surface in spherical co-ordinates

1. Jul 23, 2010

1. The problem statement, all variables and given/known data
The following is an equation of a 3-d surface in spherical co-ordinates.
r = f(theta,phi) = sin(theta)
Plot it on 3-d space.
2. Relevant equations
r = $$\sqrt{x^2 + y^2 + z^2 }$$
theta = arccos (z/ $$\sqrt{x^2 + y^2 + z^2 }$$)

3. The attempt at a solution
I converted the equation of the surface into cartesian co-ordinates , and got the following equation of a 3-d surface

(x^2 + y^2 + z^2)^2 = (x^2 + y^2)
is the above equation in cartesian co-ordinates right ?
and is it a right approach to plot it?

I think the plot is as shown in image given below ,

[PLAIN]http://img689.imageshack.us/img689/7079/capturevug.jpg [Broken]

Last edited by a moderator: May 4, 2017
2. Jul 24, 2010

### ehild

The surface has axial symmetry around the z axis. What is the projection of the surface to the y=0 plane? You get the 3D surface by rotating this curve around z. What kind of curve is this?

ehild

Last edited: Jul 24, 2010
3. Jul 27, 2010