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Deja Deleon
Mathematics
5 August, 11:05
How are polar and rectangular planes related?
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Kael Summers
5 August, 11:27
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Polar coordinates (r,ϑ) and Cartesian coordinates (x, y) are related as follows:
Cartesian - > Polar
x = r cos (ϑ)
y = r sin (ϑ)
Polar - > Cartesian
r^2 = x^2 + y^2
ϑ = arctan (y/x)
The polar coo's can be extended to cylindrical by introduction a dimension z - which is perpendicular to the polar plane, it follows that:
z = z
in between the systems (r,ϑ, z) and (x, y, z)
The polar coordinates are particularly useful when a problem has circular or cylindrical symmetry, i. e. it is usually "easier" to perform calculations on a circle (for example) using the polar coordinates.
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