# Math Help - Interpret spherical coordinates geometrically

1. ## Interpret spherical coordinates geometrically

$\rho sin \phi = 1$ is given in spherical coordinates. Interpret geometrically.

How can I approach this problem? I know that

$\rho = \sqrt{x^2+y^2+z^2}$
$tan \theta = \frac{y}{x}$
$cos \phi = \frac{z}{\sqrt{x^2+y^2+z^2}}$.

I tried plugging in $\rho$ into the equation but that led me nowhere, and I don't know what to do with the $sin \phi$.

2. ## Re: Interpret spherical coordinates geometrically

Originally Posted by deezy
$\rho sin \phi = 1$

How can I approach this problem? I know that

$\rho = \sqrt{x^2+y^2+z^2}$
$tan \theta = \frac{y}{x}$
$cos \phi = \frac{z}{\sqrt{x^2+y^2+z^2}}$.

I tried plugging in $\rho$ into the equation but that led me nowhere, and I don't know what to do with the $sin \phi$.
I am not sure what you are trying to do exactly. Are you trying to write the equation is cartesian coordinates?

If so square both sides of your equation use the the pythagorean identity

$\sin^2(\phi)=1-\cos^2(\phi)$

3. ## Re: Interpret spherical coordinates geometrically

It was asking to interpret the equation geometrically.

Squaring both sides and using the identity helped, thanks!