Table of Contents
Spherical Polar Coordinate System
A spherical coordinate system is a coordinate system for three-dimensional space using three coordinates: radial distance, azimuthal angle, and elevation angle. It is especially useful in physics and engineering because many problems in these fields can be conveniently described in terms of curved surfaces.
The radial distance (r) is the distance from the origin (0,0,0) to the point (x,y,z), measured along a straight line from the origin. The azimuthal angle (ϕ) is the angle between the positive x-axis and the line from the origin to the point (x,y,z), measured in a clockwise direction. The elevation angle (θ) is the angle between the positive y-axis and the line from the origin to the point (x,y,z), measured in a downward direction.
Spherical Coordinates To Cartesian Coordinates
Spherical coordinates are a coordinate system that uses three coordinates to specify a point in 3-dimensional space. The three coordinates are longitude (φ), latitude (θ), and altitude (h).
To convert from spherical coordinates to Cartesian coordinates, you use the following equations:
x = r cos(θ)
y = r sin(θ)
z = h
Cartesian Coordinates To Spherical Coordinates
Cartesian coordinates are a system of coordinates used in mathematics, physics and engineering that uses a set of three mutually perpendicular lines called axes to define each point in a plane. The point can then be located by its coordinates, which are the numerical values of the distances between the point and the axes.
Spherical coordinates are a system of coordinates used in mathematics and physics that uses a sphere to define points in three-dimensional space. The point can be located by its coordinates, which are the distances between the point and the points on the surface of the sphere.
Spherical Coordinates
In spherical coordinates, the position of a point is specified by the distance from the origin along the radial direction, the angle from the z-axis, and the angle from the x-axis.
The radial distance is measured in terms of the length of the radius vector, r. The angle θ is measured in radians, and the angle φ is measured in degrees.
The position of a point in spherical coordinates can be written as:
(r, θ, φ)
