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.
Unlike Cartesian coordinates, spherical coordinates include some redundancy in naming points, especially ones on the z-axis. For instance, (1,0,0), (1,0,45), and (-1,180,270) all describe the same point. Spherical coordinates emphasize length from the origin; one application is ergodynamic design where r is the arm length of a stationary person and the angles describe reaching in various directions.