Table of Contents

## What are Polar Coordinates?

Polar coordinates are a system of coordinates that uses a radial distance and an angle to identify a point in two-dimensional space. In polar coordinates, the point (x, y) is represented as (r, θ), where r is the radial distance from the origin and θ is the angle measured from the positive x-axis.

### Polar Coordinates Formula

- In mathematics, polar coordinates are a coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction. The fixed point is called the pole, and the direction is called the polar axis.
- The coordinate system is defined by the equation
- where is the distance from the pole to the point, is the angle from the polar axis to the point, and is the signed distance from the origin to the point.

### Plotting Points in Polar Coordinate System

- A point in polar coordinate system is specified by its distance from the origin and the angle from the positive x-axis. The distance from the origin is always a positive number, while the angle can be any number between 0 and 360 degrees.
- To plot a point in polar coordinate system, first find the distance from the origin and the angle. Then, use a compass to draw a circle with the given distance from the origin as the radius. Finally, draw an arrow from the origin to the point on the circle, and mark the angle.

## Converting Cartesian Coordinate System to Polar Coordinate System

- In a Cartesian coordinate system, points are located by their x- and y-coordinates. The x-coordinate is the point’s distance from the origin along the x-axis, and the y-coordinate is the point’s distance from the origin along the y-axis.
- In a polar coordinate system, points are located by their radius and angle. The radius is the point’s distance from the origin, and the angle is the point’s location around the origin.

## Converting Polar Coordinate System to Cartesian coordinate System

To convert a polar coordinate system to a Cartesian coordinate system, we use the following formula:

x = r cosθ

y = r sinθ

where r is the radius and θ is the angle.