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Apophis
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What is the difference in the "uniqueness" of the representations of Cartesian coordinates and in polar coordinates? Also, what is the non-uniqueness?
Cartesian coordinates use a system of x and y coordinates to locate a point on a plane, while polar coordinates use a distance from the origin and an angle to locate a point on a plane.
Yes, a point can have different coordinates in Cartesian and Polar systems. For example, the point (3,4) in Cartesian coordinates would be equivalent to the point (5, 53.13°) in polar coordinates.
No, Cartesian and Polar coordinates are not unique. Multiple points can have the same coordinates in both systems. For example, the points (3,4) and (-3,-4) in Cartesian coordinates would both be equivalent to the point (5, 53.13°) in polar coordinates.
Neither system is inherently more accurate than the other. The accuracy of the coordinates depends on the precision of the measurements or calculations used to determine them.
To convert from Cartesian coordinates (x,y) to polar coordinates (r,θ), use the formulas r = √(x² + y²) and θ = arctan(y/x). To convert from polar coordinates (r,θ) to Cartesian coordinates (x,y), use the formulas x = rcosθ and y = rsinθ.