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Math Help - Help understanding x,y,z equations

  1. #1
    Jun 2012

    Angry Help understanding x,y,z equations

    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...
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  2. #2
    MHF Contributor Reckoner's Avatar
    May 2008
    Baltimore, MD (USA)

    Re: Help understanding x,y,z equations

    These are a slightly modified form of spherical coordinates. Take a look.
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  3. #3
    MHF Contributor

    Apr 2005

    Re: Help understanding x,y,z equations

    But however "sci fi" or strange they are, you should be able to read the equations and do what they say.

    You are told that
    y = r * cos(phi), x = r * sin(phi) * sin(theta), z = -r * sin(phi) * cos (theta)
    and that r = 5, theta=4, phi=6
    so that y= 5 cos(6)= 4.8, x= 5 sin(6)sin(4)= 0.0364, and z= -5 sin(6)cos(4)=-0.5214.

    Why x, y, and z are given by those functions of r, phi, and theta depends upon what those numbers represent geometrically and you don't tell us that.
    (You say "phi is the angle that is between y and z.
    theta is(probably) between y and z." but that can't be right. First that would mean phi and theta are the same. Second, y and z, and x, are numbers, not directions so there is NO angle between them.)
    Last edited by HallsofIvy; June 17th 2012 at 07:04 PM.
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