![]() The polar angle may be called inclination angle, zenith angle, normal angle, or the colatitude. ![]() The radial distance from the fixed point of origin is also called the radius, or radial line, or radial coordinate. Nota bene: the physics convention is followed in this article (See both graphics re "physics convention" and re "mathematics convention"). Once the radius is fixed, the three coordinates (r, θ, φ), known as a 3- tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. (See graphic re the "physics convention".) The azimuthal angle φ is measured between the orthogonal projection of the radial line r onto the reference x-y-plane-which is orthogonal to the z-axis and passes through the fixed point of origin- and either of the fixed x-axis or y-axis, both of which are orthogonal to the z-axis and to each other. The polar angle θ is measured between the z-axis and the radial line r. In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three numbers, ( r, θ, φ): the radial distance of the radial line r connecting the point to the fixed point of origin (which is located on a fixed polar axis, or zenith direction axis, or z-axis) the polar angle θ of the radial line r and the azimuthal angle φ of the radial line r. In this image, r equals 4/6, θ equals 90°, and φ equals 30°. (As in physics, ρ ( rho) is often used instead of r to avoid confusion with the value r in cylindrical and 2D polar coordinates.) A globe showing the radial distance, polar angle and azimuthal angle of a point P with respect to a unit sphere, in the mathematics convention. The 'south'-direction x-axis is depicted but the 'north'-direction x-axis is not. + The meanings of θ and φ have been swapped-compared to the physics convention. Spherical coordinates ( r, θ, φ) as typically used: radial distance r, azimuthal angle θ, and polar angle φ. This is the convention followed in this article. Spherical coordinates ( r, θ, φ) as commonly used: ( ISO 80000-2:2019): radial distance r ( slant distance to origin), polar angle θ ( theta) (angle with respect to positive polar axis), and azimuthal angle φ ( phi) (angle of rotation from the initial meridian plane). 3-dimensional coordinate system The physics convention.
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