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Chemistry LibreTexts

16.13: Coordinate Systems

  • Page ID
    107072
  • Cartesian coordinates

    Screen Shot 2019-11-01 at 12.39.33 PM.png

    2 dimensions: area element: \(dA=dx.dy\).
    3 dimensions: volume element: \(dV=dx.dy.dz\).

    Polar coordinates

    Screen Shot 2019-11-01 at 12.41.39 PM.png

    • \(x=r\cos\theta\)
    • \(y=r\sin\theta\)
    • \(r^2=x^2+y^2\)
    • \(tan \theta=y/x\)
    • \(dA=r.dr.d\theta\)

    Spherical coordinates

    Screen Shot 2019-11-01 at 12.42.10 PM.png

    • \(x=r\sin\theta\cos\phi\)
    • \(y=r\sin\theta\sin\phi\)
    • \(z=r\cos\theta\)
    • \(r^2=x^2+y^2+z^2\)
    • \(\theta=\cos^{-1}\left[\frac{z}{\sqrt{x^2+y^2+z^2}} \right]\)
    • \(\phi=\tan^{-1}\left(\frac{y}{x}\right)\)
    • \(dV=r^2\sin{\theta}dr.d\phi.d\theta\)
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