Types of Coordinate Systems

The coordinate systems use values or numbers for the location of a point or a shape in the system. And the values or the numbers are called as the coordinates of the point and are related between the various systems either in the two dimensions or three dimensions. In the following article we will see in detail about the topic types of coordinate systems.
More about Types of Coordinate Systems:

There are basically two types of systems like the two dimensional coordinate systems and the three dimensional coordinate systems. The two dimensional coordinate systems are,

1. Cartesian coordinate systems

2. Polar coordinate systems

Some of the three dimensional coordinate systems are,

1. Cartesian coordinate system.

2. Spherical coordinate system.

3. Cylindrical coordinate systems.

Cartesian coordinate system:

cartesian coordinate system

A point in the cartesian coordinate system has the coordinates (x,y,z). Other three dimensional coordinates in terms of Cartesian coordinates,

Spherical coordinates: `r = sqrt (x^2+y^2+z^2)` ; `theta = arccos (z/r)` ; `phi = atan2(y,x)`

Cylindrical coordinates: `rho = sqrt (x^2+y^2)` ; ` phi = arcsin (y/rho)` ; `z = z`

Spherical coordinate system:

Spherical coordinate system

A point in the spherical coordinate system has the coordinates (r, theta, phi). The other three dimensional coordinates in terms of the spherical coordinates,

Cartesian coordinates: `x = r *sin theta*cos phi` ; `y = r *sin theta*sin phi` ; `z = r cos theta`

Cylindrical coordinates: `rho = r*sin theta` ; `phi = phi` ; `z = r*cos theta`

Cylindrical coordinate system:

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Points in the cylindrical coordinates have coordinate values (rho, phi, z). The relation between the cylindrical coordinate system and the other three dimensional coordinate systems,

Cartesian coordinates: `x = rho*cos phi` ; `y = rho*sin phi` ; `z = z`

Spherical coordinates: `r = sqrt (rho^2+z^2)` ; ` theta = arccos (z/r)` ; ` phi = phi`

Polar coordinate system:

polar coordinates

Points in the polar coordinate system has the coordinates (r,theta). The relation between the polar coordinates and the two dimensional Cartesian coordinates are,

Cartesian coordinates: `x = r* cos theta` ; `y = r* sin theta`
Example Problem on Types of Coordinate Systems:

1. Find the equivalent Cartesian coordinates for the point with the polar coordinates (6, 50).

Solution:

`x = r* cos theta`

`= 6*cos 50`

`= 6*0.64`

`= 3.8`

`y = r* sin theta`

`= 6*sin 50`

`= 4.6`

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Practice problem on types of coordinate systems:

1. Find the equivalent spherical coordinates for the location of the point (7.8, 50, 5) in the cylindrical coordinates.

Answer: (9.3, 50, 50)