Rectangular coordinates, also known as Cartesian coordinates, are a system for representing points in a two-dimensional space using two perpendicular axes, typically labeled x and y. The coordinates of a point are given by its distance from the origin along each axis.
Polar coordinates are an alternative system for representing points in a two-dimensional space. Instead of using perpendicular axes, polar coordinates use a point and a distance from that point, along with an angle from a reference axis, to specify the location of a point.
Rectangular and polar coordinates are two different ways to represent points in a two-dimensional space. They are related by a set of equations that allow you to convert between the two systems.
Polar coordinates are useful when working with circular or rotational systems, as the distance and angle from a reference point can more easily describe these types of movements. They can also simplify certain mathematical calculations, such as calculating complex numbers.
Rectangular coordinates are commonly used in map-making and navigation, as well as in computer graphics and engineering. Polar coordinates are used in physics and engineering to describe rotational and circular movements, and are also commonly used in polar plots and antenna design.