Coordinate System Summary

A coordinate system is a framework that allows you to locate points in space using numbers called coordinates. It defines a reference grid or plane and specifies how to assign values to points based on their position relative to a set of axes.

Main Types of Coordinate Systems:

1. Cartesian Coordinate System (Rectangular):

   • Uses two perpendicular axes (x and y) in 2D, and three (x, y, z) in 3D.
   • Points are defined by distances from these axes (e.g., (3, 4) in 2D).

2. Polar Coordinate System:

   • Used for 2D plane; defines points by a distance from the origin (radius, r) and an angle (θ) from the positive x-axis.
   • Useful for circular and rotational problems.

3. Spherical and Cylindrical Coordinate Systems:

   • Used for 3D space.
   • Spherical: Points are defined by radius, polar angle, and azimuthal angle.
   • Cylindrical: Points are defined by radius, angle, and height (r, θ, z).

Each system has its advantages and is chosen based on the geometry of the problem being solved.