# Spherical Coordinates

In three dimensional spaces Spherical Coordinate is used to find the location of a Point that depends on the distance ρ which is measured from the origin and two angles θ and ϕ. When we are going to define a spherical coordinate system then we have to select two orthogonal directions that is the Zenith angle and the point lies on the space. The zenith angles are those angles which are measured from horizontal to the perpendicular. Now we will see the spherical coordinate system.
A point ‘S’ in the Spherical Coordinates is defined as follows:
In the plane the radius or radial distance denotes the Euclidean distance that is measured from the origin O to S.
The angle lies between the zenith direction and the line segment OS is the inclination or it is also said to be polar angle.
The signed angle that is measured from the azimuth reference direction to the orthogonal projection of the Line Segment OS on the reference plane is the azimuth or it is also known as azimuthal angle.
If we subtract the 90 degrees to the inclination then we get the elevation angle.
The azimuth angle is arbitrary, if the inclination is zero or 180 degrees. If the value of radius is zero then both azimuth and inclination are arbitrary.
In linear Algebra, the vector from the origin O to the point S is said to be the Position vector of S.
Additionally it is necessary to find the unique Set of spherical for each point and its range is also restricted. Some conditions is also given for these angles which are:
The value of r is greater than zero,
= 00 < Ѳ < 1800; this is the standard convention of spherical coordinates.

## Spherical Coordinates Conversions

There are three types of coordinate systems, first one is Cartesian coordinate system used for two dimensional plane, second one is Cylindrical coordinate system used to find the Position of cylindrical plane and third one is Spherical Coordinate system.
Spherical coordinate system is used to calculate the position of three dimensional objects. Three c...Read More

## Spherical Coordinates Volume Element

Coordinate system can be defined as a system which may use one or more than one number or it may also use one or more than one coordinates. One of the type of it is spherical coordinate system which is defined as that system in which Position of a Point located anywhere in coordinate system can be explained by three quantities.