What are the cylindrical coordinates of the point whose spherical coordinates are (4, 2, 1π/6) ?
1 Answer
Assuming the usual spherical coordinate system,
Explanation:
There are several different conventions as to the order of the angles in spherical coordinates. See http://mathworld.wolfram.com/SphericalCoordinates.html for more info.
I will assume that the order of coordinates wanted here is radial, azimuthal, polar, which matches that link, also has the advantage of being a right-handed coordinate system, and is the system most often seen.
Relation of spherical to Cartesian coordinates:
Spherical radius:
Spherical azimuth:
Spherical polar angle:
Cylindrical coordinates are less confused, and the standard definition is shown here: http://mathworld.wolfram.com/SphericalCoordinates.html.
Cylindrical radius:
Cylindrical azimuth:
Height:
From these, we may relate the cylindrical coordinates to the spherical ones:
So in this case,