# What is spherical polar coordinate system?

Jul 9, 2015

We can describe any point in 3 dimensional space using a radius $r$ and two angles $\theta$ and $\phi$ as:

$\left(r \cos \theta \cos \phi , r \sin \theta \cos \phi , r \sin \phi\right)$

#### Explanation:

We can describe any point in the X-Y plane as $\left(r \cos \theta , r \sin \theta\right)$, where $r$ is the radius and $\theta$ is an angle from the $x$ axis.

Then rotate into the Z dimension by rotating by angle $\phi$ about a line in the X-Y plane through the origin perpendicular to the radius.

That results in a point $\left(r \cos \theta \cos \phi , r \sin \theta \cos \phi , r \sin \phi\right)$

This point lies on the sphere of radius $r$