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Help understanding x,y,z equations

  1. Jun 17, 2012 #1
    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

    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. jcsd
  3. Jun 17, 2012 #2
    [itex]\phi[/itex] 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 [itex]\theta[/itex].

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