Cartesian coordinates refer to a system of coordinates in which a point is identified by its distance from two perpendicular lines, known as the x and y axes. On the other hand, polar coordinates use a distance from a fixed point and an angle to locate a point.
To convert from Cartesian to Polar coordinates, you can use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
Where r represents the distance from the origin and θ represents the angle in radians.
Polar coordinates are often used in situations where describing a point using Cartesian coordinates would be difficult or impractical. They are also useful in describing circular or symmetrical shapes in a more simple and efficient manner.
Yes, both the distance (r) and angle (θ) in Polar coordinates can be negative. A negative r value indicates that the point is located in the opposite direction of the positive r direction, and a negative θ value represents a point in the opposite direction of the positive θ direction.
Polar coordinates are commonly used in fields such as physics, engineering, and navigation. They are especially useful in situations involving circular motion, such as tracking the movement of planets or satellites. They are also used in radar and sonar systems to locate objects in two-dimensional space. Additionally, Polar coordinates are used in mapping and surveying, as well as in various computer graphics applications.