A rectangular equation that is not a function may be a function in the polar coordinate system. true or false? And please explain why.

Question

anonymous · Answer

whats ur definition to a function :O
and yes its true

anonymous · Answer

Consider the polar function $r=1$, the unit circle centered at the origin. In Cartesian (rectangular) coordinates, the equation becomes $x^2+y^2=1$, which is not a function because the equation is true for $(x,y)=\left(\dfrac{1}{\sqrt2},-\dfrac{1}{\sqrt2}\right)$ and $(x,y)=\left(\dfrac{1}{\sqrt2},\dfrac{1}{\sqrt2}\right)$.

Graphically, you can think of this in terms of the vertical line test:
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