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@zor
Zor Shekhtman
commented
Yes, unfortunately, non-negativity of the #r# is not shared by many authors. In defense of this requirement I'd say that if negative #r# is allowed, any point on a plane, except the origin, would have two different pairs of polar coordinates: #(r, theta)# and #(-r, theta+pi)#. This is not a good property of any coordinate system to have two different numeric representation of the same point.
on
How do you graph #r=-1#?
@zor
Zor Shekhtman
commented
Traditionally, only non-negative radius is accepted in Polar coordinates with an angle being in the range from 0 to 360 degrees. However, in some cases it was decided that, say, #r=1, theta=200^o# is equivalent to #r=-1, theta=20^o# So, in this case we have to be careful, the answer might be an empty set if we accept the traditional definition.
on
How do you graph #r=-1#?