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Poweranimals
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What are the differences in the "uniqueness" of the representations in Cartesian coordinates and in polar coordinates?
Cartesian coordinates are based on a rectangular grid system, with two perpendicular axes (x and y) intersecting at the origin. Polar coordinates, on the other hand, are based on a circular grid system, with a central point (the origin) and a distance (r) from the origin, as well as an angle (θ) from a fixed reference line.
To convert from Cartesian to Polar Coordinates, you can use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
Keep in mind that the angle θ may need to be adjusted depending on which quadrant the point is in.
Cartesian coordinates are commonly used in graphing and mapping, as well as in computer graphics and engineering. Polar coordinates are often used in navigation and astronomy, as well as in describing circular or rotational motion.
The origin serves as the reference point for both Cartesian and Polar Coordinates. It is the point where the axes intersect and has a value of (0,0) in Cartesian coordinates and (0,0°) in Polar coordinates.
Yes, you can convert from Polar to Cartesian Coordinates using the following formulas:
x = r cos(θ)
y = r sin(θ)
Keep in mind that the angle θ may need to be adjusted depending on which quadrant the point is in.