# Trigonometry of a sphere

1. Jun 11, 2009

### frogtag

Can someone just check my maths to see if this is correct.

Hopefully, this should give the coordinates for a point on a sphere?

x = radius x cos(vert angle) x sin(hoz angle)
y = radius x cos(hoz angle)
z = radius x sin(vert angle) x sin(hoz angle)

2. Jun 11, 2009

### mgb_phys

3. Jun 11, 2009

### HallsofIvy

Staff Emeritus
In polar coordinates, $x= \rho cos(\theta) sin(\theta)$, $y= \rho sin(\theta) sin(\phi)$, $z= \rho cos(\phi)$. There $\theta$ is what I think you are calling the "horizontal angle"- the angle between the positive x-axis and the line from (0,0,0) to the point (x,y,0)- also sometimes called the "longitude". $\phi$ is the "co-latitude", the angle between the z-axis and the line from (0,0,0) to (x,y,z). $\rho$ is the straight line distance between (0,0,0) and (x,y,z).

For a sphere of radius R, this is $x= R cos(\theta) sin(\theta)$, $y= R sin(\theta) sin(\phi)$, $z= R cos(\phi)$.