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5 August, 11:05

How are polar and rectangular planes related?

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  1. 5 August, 11:27
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    Polar coordinates (r,ϑ) and Cartesian coordinates (x, y) are related as follows:

    Cartesian - > Polar

    x = r cos (ϑ)

    y = r sin (ϑ)

    Polar - > Cartesian

    r^2 = x^2 + y^2

    ϑ = arctan (y/x)

    The polar coo's can be extended to cylindrical by introduction a dimension z - which is perpendicular to the polar plane, it follows that:

    z = z

    in between the systems (r,ϑ, z) and (x, y, z)

    The polar coordinates are particularly useful when a problem has circular or cylindrical symmetry, i. e. it is usually "easier" to perform calculations on a circle (for example) using the polar coordinates.
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