Wednesday, May 1, 2013

when working with polar coordinates, remember that there are several ways to represent the same point.  For example, the point (2, Pi) is the same as the point (-2, 0), (-2, -Pi), (2, 0).

You can check this by converting the polar coordinates to rectangular coordinates.
If the polar coordinate is represented as (r, A) where r is the radius and A is the angle, then
x = rcos(A),   y = rsin(A)

Using the above example,

x= 2cos(Pi)
y= 2sin(Pi)  converts to (-2,0) in rectangular coordinates

Likewise using the same formula for the polar coordinates (-2, 0), (-2, -Pi), (2, 0) also convert to (-2, 0) in rectangular coordinates.

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