There are conversions between Cartesian and spherical coordinates based on trigonometric functions. Both spherical coordinates and cylindrical coordinates are extensions of the two dimensional polar coordinate system. Spherical coordinates are the natural coordinates for physical situations where there is spherical symmetry. In such a situation, one can describe waves using spherical harmonics.
Unlike Cartesian coordinates, spherical coordinates include some redundancy in naming points, especially ones on the zaxis. For instance, (1, 0°, 0°), (1, 0°, 45°), and (1, 180°, 270°) all describe the same point. Spherical coordinates emphasize distance from the origin. One application is ergodynamic design, where <math>r</math> is the arm length of a stationary person and the angles describe the direction of the arm as it reaches out.
Conversion from spherical to Cartesian coordinates
Conversion from Cartesian to spherical coordinates
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