To define a spherical coordinate system, one must choose two orthogonal directions, the zenith and the azimuth reference, and an origin point in space. It can also be extended to higher-dimensional spaces and is then referred to as a hyperspherical coordinate system. The spherical coordinate system generalises the two-dimensional polar coordinate system. Elevation angle of zero is at the horizon. The inclination angle is often replaced by the elevation angle measured from the reference plane. The spherical coordinate systems used in mathematics normally use radians rather than degrees and measure the azimuthal angle counter-clockwise rather than clockwise. There are a number of different celestial coordinate systems based on different fundamental planes and with different terms for the various coordinates. In a geographical coordinate system positions are measured in latitude, longitude and height or altitude. Other conventions are also used, so great care needs to be taken to check which one is being used.Ī number of different spherical coordinate systems following other conventions are used outside mathematics. In both systems ρ is often used instead of r. In one system frequently encountered in physics (r, θ, φ) gives the radial distance, polar angle, and azimuthal angle, whereas in another system used in many mathematics books (r, θ, φ) gives the radial distance, azimuthal angle, and polar angle. The use of symbols and the order of the coordinates differs between sources. The polar angle may be called co-latitude, zenith angle, normal angle, or inclination angle. The radial distance is also called the radius or radial coordinate. In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. The angles (`theta` and `phi`) are returned in decimal degrees. The length (`rho`) of the vector is in the units entered. This formula lets the user enter three Cartesian coordinates (X, Y and Z) This algorithm converts the spherical coordinates. However, these can be automatically converted to compatible units via the pull-down menu. Spherical Coordinates (ρ,θ,?): The calculator returns the magnitude of the vector (ρ) as a real number, and the azimuth angle from the x-axis (?) and the polar angle from the z-axis (θ) as degrees. The Cartesian to Spherical Coordinates calculator computes the spherical coordinates Vector in 3D for a vector given its Cartesian coordinates.
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