Polar Co-ordinates

What is Polar Co-ordinates?

Besides Cartesian co-ordinate system we have several other methods for locating position of a point on a plane. Of all these system we shall make here a brief discussion on Polar Co-ordinates only. Polar Co-ordinates are widely used in higher mathematics as well as in other branches of science. 


In polar co-ordinate system the position of a point on the reference plane is uniquely determined referred to a fixed point on the plane and a half line drawn through the fixed point. The fixed point is called the Pole or Origin and the half line drawn through the pole is called the Initial Line.

Polar Co-ordinates

Let OX  be the initial line drawn through the pole O on the plane of reference. Take any point P on the plane and join OP . 

If OP = r and ∠XOP = θ then the real numbers r and θ are together called the Polar Co-ordinates of P and denoted by (r, θ); here OP. If OP = r and Polar Co-ordinates of P and denoted by (r, θ); here OP = r is called the Radius Vector and ∠XOP = θ, the Vectorial Angle of P. the angle θ is measured by the method of measurement of trigonometrical angle i.e., θ is taken to be positive when it is measured in the anti-clockwise sense from the initial line and negative when it is measured in the clockwise sense from the initial line.

By convection, to represent the polar co-ordinate of a point we first write the radius vector (r) and then the vectorial angle (θ) and they are put together in braces putting a comma between them. 


Note: 

(i) for given values of r and θ we shall get one and only one point on the reference plane; conversely, for a given point on the plane r possesses a definite finite value but θ can have infinite number of value (viz ., θ, 2π + θ, 4π + θ,…….etc.). 


(ii) The polar Co-ordinates of the pole are assumed to be (0, 0). 


(iii) If the sense of radius vector is taken into account then the value of r may be negative. Thus, if the direction from O to P is taken as positive then the direction from P to O will be negative. Hence, if the points P, O, P’ are collinear such that OP = OP’ = r and ∠XOP = θ then the polar co-ordinates of P and P' are (r, θ) and (-r, θ) respectively. 

However, in practice, it is convenient to take both the radius vector (r) and the vectorial angle (θ) as positive. 


(iv) Remembering the rules regarding the signs of r and θ we can represent the polar co-ordinate of P in following different ways: 

(r, θ); (-r, π + θ); [r, -(2π - θ)]; [-r, -(π - θ)].

 Co-ordinate Geometry 





11 and 12 Grade Math 

From Polar Co-ordinates to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Line-Segment, Ray and Line | Definition of in Line-segment | Symbol

    Jun 14, 24 10:30 AM

    Line-Segment, Ray and Line
    Definition of in Line-segment, ray and line geometry: A line segment is a fixed part of a line. It has two end points. It is named by the end points. In the figure given below end points are A and B…

    Read More

  2. Definition of Points, Lines and Shapes in Geometry | Types & Examples

    Jun 14, 24 09:45 AM

    How Many Points are There?
    Definition of points, lines and shapes in geometry: Point: A point is the fundamental element of geometry. If we put the tip of a pencil on a paper and press it lightly,

    Read More

  3. Subtracting Integers | Subtraction of Integers |Fundamental Operations

    Jun 13, 24 04:32 PM

    Subtraction of Integers
    Subtracting integers is the second operations on integers, among the four fundamental operations on integers. Change the sign of the integer to be subtracted and then add.

    Read More

  4. 6th Grade Worksheet on Whole Numbers |Answer|6th Grade Math Worksheets

    Jun 13, 24 04:17 PM

    6th Grade Worksheet on Whole Numbers
    In 6th Grade Worksheet on Whole Numbers contains various types of questions on whole numbers, successor and predecessor of a number, number line, addition of whole numbers, subtraction of whole number…

    Read More

  5. 6th Grade Integers Worksheet | Word Problems | True / False | Answers

    Jun 13, 24 03:50 PM

    6th Grade Integers Worksheet
    In 6th grade integers worksheet contains various types of questions on integers, absolute value of an integer, addition of integer, properties of integer, subtraction of integer, properties of subtrac…

    Read More