Plotting a 3-d surface in spherical co-ordinates

[ask_LXXXVI]

Homework Statement

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.

Homework Equations

r = \sqrt{x^2 + y^2 + z^2 }
theta = arccos (z/ \sqrt{x^2 + y^2 + z^2 })

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 ,
but how to arrive at the plot given below I am unable to think.Please help

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

 

[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

 

[ask_LXXXVI]

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.


ehild

Thanks for helping me in visualising how to plot the curve.

What kind of curve is this?


ehild

It is the radiation pattern of a Hertz Dipole Antenna.For more you can readhttp://books.google.co.in/books?id=...R K shevgaonkar&pg=PA379#v=onepage&q&f=false"from google books