What is the polar coordinate (ध्रुर्वीय निर्देशांक)?

The Polar Coordinate System

In our blog for the students of 9th,10th,11th,12th, NEET and IIT , this is a post dealing with one of the most complicated and a deemed-to-be very tough topic. We have made it very simple and can be useful for both RBSE and CBSE students.

Introduction to the Polar Coordinate System

When we think about plotting points in the plane, we usually think of rectangular coordinates (x,y) in the Cartesian coordinate plane. However, there are other ways of writing a coordinate pair and other types of grid systems known as Polar coordinate.

The polar coordinate system is an alternate coordinate system where the two variables are r and θ, instead of x and y.

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. Polar coordinates are points labelled (r, θ) and plotted on a polar grid. The polar grid is represented as a series of concentric circles radiating out from the pole, or the origin of the coordinate plane.

The reference point (analogous to the origin of a Cartesian system) is called the pole, and the ray from the pole in the reference direction is the polar axis. The distance from the pole is called the radial coordinate or radius, and the angle is called the angular coordinate, polar angle, or azimuth. The radial coordinate is often denoted by r or ρ, and the angular coordinate by ϕ, θ, or t.

Plotting Points Using Polar Coordinates

The polar grid is scaled as the unit circle with the positive x–axis now viewed as the polar axis and the origin as the pole. The first coordinate r is the radius or length of the directed line segment from the pole. The angle θ, measured in radians, indicates the direction of r. We move anticlockwise from the polar axis by an angle of θ and measure a directed line segment the length of r in the direction of θ. Even though we measure θ first and then r, the polar point is written with the r-coordinate first. For example, to plot the point (2,π/4),we would move π/4 units in the anticlockwise direction and then a length of 2 from the pole. This point is plotted on the grid in Figure.