Difference between Polar and Cartesian Coordinates
Polar and Cartesian Coordinates are two different coordinate system to represent various different point in 2D space. Key differences between these coordinates are:
Polar vs Cartesian Coordinates | ||
|---|---|---|
| Aspect | Cartesian Coordinates | Polar Coordinates |
| Dimension | Can be used in 2D and 3D (x, y, z) | Primarily used in 2D (r, θ) |
| Representation | Points are located by their distance from two perpendicular axes (x and y) | Points are located by their distance from a fixed origin (r) and angle from a fixed reference direction (θ) |
| Visualization | Grid of horizontal and vertical lines | Origin with concentric circles radiating outward and lines at regular angular intervals |
| Strengths | Simple and intuitive for rectangular shapes and straight lines | Efficient for representing circular and radial relationships |
| Weaknesses | Can be cumbersome for circular shapes and angles | Can have ambiguity for certain points (e.g., negative radii) |
| Applications | Plotting points, calculating distances and areas, linear equations, motion in straight lines | Describing circular motion, planetary orbits, wave patterns, polar plots |
| Example | Plotting the location of a house on a map (x, y) | Describing the position of a planet around the sun (r, θ) |
Polar Coordinates System
The polar coordinate system is a two-dimensional coordinate system that employs distance and angle to represent points on a plane. It’s similar to a regular coordinate system, but instead of using x and y coordinates, it uses:
- Radius (r): The distance from a fixed reference point, known as the origin or pole.
- Angular coordinate (θ): The angle measured counterclockwise from a fixed direction, referred to as the polar axis.
Key features of the polar coordinate system:
- Points are identified with an ordered pair (r, θ). An example would be the point (2, π/3), meaning it lies 2 units away from the origin while maintaining an angle of π/3 (or approximately 60 degrees) from the polar axis.
- The angle θ ranges between 0 and 2π (360 degrees). However, negative angles are valid too; these simply imply moving counterclockwise past the polar axis.
- Variable ‘r’, representing the radius, accepts non-negative values only. When r equals 0, it indicates that the point sits right on top of the origin.
In this article, we will discuss the Polar Coordinate System in detail, including its Properties, Graph, Formula, and Examples.
Table of Content
- What is Polar Coordinate System?
- What are Polar Coordinates?
- Graph of Polar Coordinates
- Polar Coordinates Formula
- Cartesian to Polar Coordinates Conversion
- Polar to Cartesian Coordinates Conversion
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