# Spherical cylindrical and rectangular coordinates

## Homework Statement

Suppose that in spherical coordinates the surface S is given by the equation rho * sin(phi)= 2 * cos(theta).
Find an equation for the surface in cylindrical and rectangular coordinates. Describe the surface- what kind of surface is S?

## The Attempt at a Solution

r= rho * sin (phi)
r^2= (rho * sin(phi)^2
r^2= 4 cos ^2 (theta)
x^2 + y^2= 4 cos^2 (theta)

And now I'm drawing a blank. Can someone please help me on how to continue?- I'm clueless! Thank you!

LCKurtz
Homework Helper
Gold Member

## Homework Statement

Suppose that in spherical coordinates the surface S is given by the equation rho * sin(phi)= 2 * cos(theta).
Find an equation for the surface in cylindrical and rectangular coordinates. Describe the surface- what kind of surface is S?

## The Attempt at a Solution

r= rho * sin (phi)
r^2= (rho * sin(phi)^2
r^2= 4 cos ^2 (theta)
x^2 + y^2= 4 cos^2 (theta)

And now I'm drawing a blank. Can someone please help me on how to continue?- I'm clueless! Thank you!

You don't want to square that first equation ##r =\rho\sin\phi##. So after that first step you have ##r = 2\cos\theta##. What's the formula for ##\cos\theta##? Get it all in terms of ##x,y,z##.