# Help understanding x,y,z equations

1. Jun 17, 2012

### noatom

I have a point at 0,0,0(the origin).

And I have an object that will move around that point.
The following data is given for that object:
r = 5
theta=4
phi=6

phi is the angle that is between y and z.
theta is(probably) between y and z.

To find the object coordinates(x,y,z),the following equations are given:

y = r * cos(phi)
x = r * sin(phi) * sin(theta)
z = -r * sin(phi) * cos (theta)

we use -r on z because theta is measured counterclockwise from -z.

As you can see the equations above make an object stay at some certain coordinates away from the origin. Everything is solved,the only problem is that I don't understand it.
I understand how we get y,but the x and z are sci fi for me,I mean why does x use sin on both phi and theta and z uses sin and cos?

Take it easy on me,I suck at math,and in the last 3 days I've been trying to understand those equations.If you know why everything is like that,please explain with as many details as you can,so I can finally understand and sleep...

2. Jun 17, 2012

### Muphrid

$\phi$ is the angle between the object's position and the y-axis. We decompose the position vector into a part parallel to the y-axis and a part perpendicular, which must then lie in the zx-plane.

Considering just that last part--the part of the position vector that lies in the zx-plane--and find the angle that makes with the -z-axis. This is the angle $\theta$.

Everything in this procedure is just about drawing right triangles, see?