
Cartesian to Spherical
Hi,
I need to convert these coordinates from cartesian to spherical.
(3,4,12)
and these coordinates from spherical to cartesian
(5, $\displaystyle \frac{\pi}{4}$, $\displaystyle \frac{\pi}{6}$)
I've done a bunch of searches, but none of the websites I found were very clear. Could someone explain this to me?

You should know that
$\displaystyle x = r\sin{\theta}\cos{\phi}$
$\displaystyle y = r\sin{\theta}\sin{\phi}$
$\displaystyle z = r\cos{\theta}$.
Going the other way:
$\displaystyle r = \sqrt{x^2 + y^2 + z^2}$
$\displaystyle \theta = \arccos{\frac{z}{x^2 + y^2 + z^2}}$
Finding $\displaystyle \phi$ is more difficult as it depends on the values of $\displaystyle x$ and $\displaystyle y$.
Namely:
$\displaystyle \phi = \arctan{\frac{y}{x}}$ for $\displaystyle x > 0$
$\displaystyle \phi = \pi + \arctan{\frac{y}{x}}$ for $\displaystyle y \geq 0, x < 0$
$\displaystyle \phi = \pi + \arctan{\frac{y}{x}}$ for $\displaystyle y < 0, x < 0$
$\displaystyle \phi = \frac{\pi}{2}$ for $\displaystyle y > 0, x = 0$
$\displaystyle \phi = \frac{\pi}{2}$ for $\displaystyle y < 0, x = 0$
$\displaystyle \phi = $ undefined for $\displaystyle y = 0, x = 0$.
These values come from elementary trigonometry.