Mathematical Analysis

Vector and Other Analyses

What is a polar coordinate system?

In effect, a polar coordinate system “wraps” a two-dimensional (Euclidean) coordinate system onto the surface of a sphere (for more information about coordinate systems, see “Geometry and Trigonometry”). A polar coordinate system examines a point in space defined in terms of its position and distance on a sphere with a unit radius. The center of the sphere is considered the origin; the first two coordinates are the longitude and latitude on the sphere; the third coordinate defines the distance of the point from the center of the sphere—the values of latitude, longitude, and height. In polar coordinates—it’s easy to see on a globe of our own planet—latitude ranges from +90 to -90, longitude ranges from -180 to +180, and height ranges from zero to infinity. Height can also be negative: The North Pole is at coordinates of (+90, —, +r) (the “—” means there is no longitude), the South Pole is at coordinates of (-90, —, -r), and a point on the equator is at coordinates (0, 0, r).



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