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Spherical coordinates?

  1. Apr 22, 2012 #1
    ∅θ,θI've come across two distinct 'versions' of the spherical coordinates. Could someone tell me which is correct or if both are fine.

    Version 1:

    A spherical coordinate is (rho,θ,∅)

    x=rhocos(θ)sin(∅) ; y=rhosin(θ)sin(∅) ; z=rhocos(θ)

    Version 2:

    A spherical coordinate is (r,∅,θ)

    x=rhocos(∅)sin(θ) ; y=rhosin(θ)sin(∅) ; z=rhocos(θ)
    (r could be rho as well)

    Now what's the difference between both or which is the false one?
  2. jcsd
  3. Apr 22, 2012 #2


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    Staff: Mentor

    Isn't it just a matter of symbols used for coordinates? Symbols don't matter, it is the idea that matters - and the idea is identical in both cases.
  4. Apr 22, 2012 #3

    I like Serena

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    Homework Helper

    This wiki page mentions the different conventions:

    The symbols θ, φ represent the angles for colatitude (angle from the positive z-axis) and longitude.
    But depending on the source the symbols are swapped around.

    In particular there appears to be a difference between US math books and US physics books.
    The "rest of the world" mostly appears to follow the same convention as used in US physics books.

    There is an international standard ISO 31-11, that says to use θ for colatitude and φ for longitude (US physics convention).
    The coordinates are listed as (r,θ,φ), making it a right-handed coordinate system.

    In practice it means that whenever you're dealing with spherical coordinates you have to check how the symbols are defined.
    Last edited: Apr 22, 2012
  5. Apr 22, 2012 #4
    Thanks Guys.
  6. Apr 22, 2012 #5


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    Science Advisor

    The first one looks wrong. z=rcos(θ) means x and y both must have sin(θ) as part of their definition. x=rsin(θ)cos(z) y=rsin(θ)sin(z).
  7. Apr 23, 2012 #6

    You have to make sure that the first variable in x and y are the same, and that the second in x and y is also used in z. It also depends on which side the angle is on that you are using. My physics teacher said to remember that "cos" is the side that is "cozy" with the angle.
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