To compare and contrast: the rectangular, cylindrical and spherical coordinates systems.

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Delorenzoz · Accepted Answer

Given:  Point is represented as (r,θ,z).  Proof:  A point in cylindrical coordinate is represented by (r,θ.z).  (r,θ) are polar coordinates  z is the usual - coordinates  The rectangular (x, y, z) and the spherical coordinates (r,θ,z) are related as  x=rcos⁡θ  y=rsin⁡θ  z=z  These are used to convert from cylindrical to rectangular coordinates.  Rectangular to cylindrical coordinates:  r2=x2+y2  tan⁡θ=yx  z=z  A point in spherical coordinate is represented by (ρ,θ,φ).  The rectangular (x, y, z) and the spherical coordinates (ρ,θ,φ) are related as  x=ρsin⁡φcos⁡θ  y=ρsin⁡φsin⁡θ  z=ρcos⁡φ  These are used to convert from spherical to rectangular coordinates.  Rectangular to spherical coordinates:  ρ2=x2+y2+z2  tan⁡θ=yx  φ=cos−1(zx2+y2+z2)  Spherical to rectangular coordinates:  r=ρsin⁡φ  θ=φ  z=ρcos⁡φ  Cylindricalto spherical coordinates:  ρ2=r2+z2  θ=θ  φ=cos−1(zr2+z2)

To compare and contrast: the rectangular, cylindrical and spherical coordinates systems.

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