# Thread: Identify the surface whose equation is given in spherical coordinates

1. ## Identify the surface whose equation is given in spherical coordinates

Sorry I don't know how to write a nice looking equation on here so, this is the question:

rho^2 (sin^(2) (phi) * sin^(2) (theta) + cos^(2) (phi)) = 9

What surface is this?

2. Originally Posted by Susaluda
Sorry I don't know how to write a nice looking equation on here so, this is the question:

rho^2 (sin^(2) (phi) * sin^(2) (theta) + cos^(2) (phi)) = 9

What surface is this?
Just to clarify, this is:

$\displaystyle \rho^2 \big(\sin^2 (\phi) \sin^2(\theta) + \cos^2(\phi)\big) = 9$

3. Yes, that's right.

4. Originally Posted by Susaluda
Yes, that's right.
Are you away that, to convert from spherical to cartesian coordinates, you use the following:

$\displaystyle x = \rho \cos(\phi) \sin(\theta)$

$\displaystyle y = \rho \sin(\phi) \sin(\theta)$

$\displaystyle z = \rho \cos(\theta)$

5. Originally Posted by Mush
Just to clarify, this is:

$\displaystyle \rho^2 \big(\sin^2 (\phi) \sin^2(\theta) + \cos^2(\phi)\big) = 9$
Well, if we consider spherical polar coords (US version)

$\displaystyle x = \rho \cos \theta \sin \phi,\;\; y = \rho \sin \theta \sin \phi,\;\; z = \rho \cos \phi$

then I believe it's a cylinder $\displaystyle y^2 +z^2 = 9$

6. Wow, yeah, ok I don't know how I didn't realize that :P Thanks to both of you!

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### show rectangular equation for a surface whose spherical equation is p=

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