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Spherical Coordinate System

How to establish a spherical coordinate system such that each point has a unique representation?

  • Assuming you have 3 axes.
  • Pick two axis lines
    1. azimuthal line
    2. zenith line
  • The azimuthal is usually the x-axis
  • Zenith is usually the z-axis
  • The plane on which the azimuthal line lies is the azimuthal plane
  • Zenith is perpendicular to this plane
  • The azimuthal angle is the angle from the azimuthal line to the projection of a point onto the azimuthal plane.
  • The polar angle is the angle from the zenith line to the point
  • The complement of the polar angle is the elevation angle which is measured from the azimuthal plane

The symbols used to represent these things may vary. Physicists and mathematicians use the opposite symbols to represent them. But the meaning is the same. There is an azimuthal angle and a polar angle

If you don’t know which is which, the one with the shorter range is usually the polar angle. If this angle also has negatives then it might be the elevation angle instead of the polar angle