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Distance equations for different cord. systems

  1. Sep 25, 2006 #1
    I need to show that

    ds^2 = dx^ + dy^2 + dz^2

    is the same as

    ds^2 = dr^2 + r^2 (dpheta^2 + sin^2pheta*dphi^2)

    .... I know that I need to use x = r sin pheta cos phi
    y = r sin pheta sin phi
    z = r cos pheta

    I am confused but I think I have to take the derivitive of something. Do I somehow take the partial derivitives and if so of what? Can someone point me in the right direction. Thank you!
     
  2. jcsd
  3. Sep 25, 2006 #2

    AKG

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    In general, I believe if you have a function f of several variables x1, ..., xn, then:

    [tex]df = \sum _{k=1} ^n\frac{\partial f}{\partial x_k}dx_k[/tex]
     
  4. Sep 25, 2006 #3

    AKG

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    Do Not Post The Same Question Twice
     
  5. Sep 25, 2006 #4

    StatusX

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    dx=[itex]\partial x /\partial r dr + \partial x /\partial \theta d\theta + \partial x /\partial \phi d\phi[/itex], and likewise for y and z. Plug in and simplify.
     
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