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:
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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).
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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.
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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.