Spherical Coordinate System Facts For Kids
A spherical coordinate system specifies a point in three-dimensional space using a distance (radius) and two angles (polar and azimuthal) to determine its location.
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Photos of Spherical Coordinate System
The mathematics convention. Spherical coordinates (r, θ, φ) as typically used: radial distance r, azimuthal angle θ, and polar angle φ. + The meanings of θ and φ have been swapped—compared to the physics convention. The 'south'-direction x-axis is depicted but the 'north'-direction x-axis is not. (As in physics, ρ (rho) is often used instead of r to avoid confusion with the value r in cylindrical and 2D polar coordinates.)
In the mathematics convention: A globe showing a unit sphere, with tuple coordinates of point P (red): its radial distance r (red, not labeled); its azimuthal angle θ (not labeled); and its polar angle of inclination φ (not labeled). The radial distance upward along the zenith–axis from the point of origin to the surface of the sphere is assigned the value unity, or 1. + In this image, r appears to equal 4/6, or .67, (of unity); i.e., four of the six 'nested shells' to the surface. The azimuth angle θ appears to equal positive 90°, as rotated counterclockwise from the azimuth-reference x–axis; and the inclination φ appears to equal 30°, as rotated from the zenith–axis. (Note the 'full' rotation, or inclination, from the zenith–axis to the y–axis is 90°).
The output pattern of the industrial loudspeaker shown here uses spherical polar plots taken at six frequencies
Unit vectors in spherical coordinates