Home / Math / Analytical Geometry / Polar Coordinates

Polar Coordinates

Polar coordinate is a method of presentation of points in the plane with use of Ordered Pair. This polar coordinate system comprises of an origin, pole, a Ray of specific angle and a polar axis. The polar axis is any line which initiates from the origin and extends to the indefinite Point in any of the prescribed direction. The Position of the point can be determined by the position and distance from the origin and by its angle. If the rotation of polar axis is anticlockwise then the angle generated will be positive. If it is clockwise the angle generated will be negative.
These are useful in solving circular Symmetry. Besides Cartesian coordinate system the polar coordinate is another way to find the position of the point. Polar Coordinates help us to know about the following aspects:
How to plot a point when its polar coordinate is given.
How polar coordinates can be converted in Cartesian coordinates.
Again conversion of Cartesian into polar coordinate.
Identifying the angle whether they are positive or negative.
Whether equation is satisfying the curve or not.
The polar coordinate system is a two dimensional coordinate system which is ascertained by distance from any fixed point and from the angle in the fixed direction. The fixed point in the graph is a pole; the distance which is measured from the pole is its radius. The equation which is defined in the form of algebraic curve given in the polar coordinates is polar equation. As the polar coordinate system has the circular nature so many curves can be explained by it. The polar rose, Archimedean spiral, Lemniscate, Limacon and cardioid are among its best renowned curves. 

Topics Covered in Polar Coordinates

Locus and Polar Coordinates

Locus for a Point can be defined as a curve or a path that results from the condition (s) that is satisfied by the point for an Algebraic Relation governed by some fixed rule. This statement is valid only for those points which are lying in the plane and not in the outer region of the plane, i.e., the equation of loci cannot be found for those points lying...Read More

Applications of Polar Coordinates

The Polar Coordinates are defined as two-dimensional co-ordinate system, used to locate arbitrary Point positions lying on the circumference of a single two-dimensional plane like a Circle and situated at a particular distance from a fixed point.
Their use in this context is where the phenomenon being considered is essentially related to the direction ...Read More

Transformation from Rectangular to Polar Coordinates

A plane can be defined as a point having zero-dimensions or a line having one-dimension or a space which encompasses three-dimensions. Any Point taken on this plane can be represented in two different ways that are:

  1. Rectangular coordinates and
  2. Polar coordinates.
The Rectangular coordinates are present in the form of P...Read More

Equation of a Locus

Locus for a Point can be defined as a curve or a path that results from the condition (s) that is satisfied by the point for an Algebraic Relation governed by some fixed rule. This statement is valid only for those points which are lying in the plane and not in the outer region of the plane, i.e., the equation of loci cannot be found for those points lying in the ext...Read More

Polar Coordinates to Cartesian

Coordinates are of two types; one is Cartesian coordinates and second is Polar Coordinates. We can convert polar coordinates to Cartesian coordinates and from Cartesian coordinates to polar coordinates.
Basically we use graph to mark these coordinates. Cartesian coordinates consist of two points, position on x- axis and Position of y- axis. These coordina...Read More

Graphing Polar Coordinates

Polar coordinate system is defined in terms of distance from a fixed Point and an angle when viewed from a particular direction. Let the distance of a point P(X, Y) from origin (an arbitrary fixed point) be denoted by ‘H’ and origin is denoted by the symbol 'O'. Consider the angle between the radial line from point 'P' to 'O' and given line “θ = 0” (a kind of ...Read More

Polar Coordinates Integration

Polar Coordinates Integration Calculus can be used to calculate the length of the arc defined by in Polar Coordinates form (r and Ó¨) for any curve r (Ó¨). Let “L” represent the length of the arc along the curve between to ends P and Q. Where, these points correspond to“Ó¨= a” and “Ó¨= b” such that their difference lies between 0 and 2∏.
 

 
Length of ...Read More

Further Read

Math Topics
    Facebook Facebook Facebook Share
Copyright 2008-2012. All Rights Reserved.