Precalculus

Every point in the plane has exactly two polar coordinates.
A)The statement is true because every point in the plane has a unique polar representation.

B)The statement is false because left parenthesis r comma theta right parenthesis equals left parenthesis r comma theta plus 2 n pi right parenthesis(r,θ)=(r,θ+2nπ) for any integer n. These are all distinct polar coordinates.

C)The statement is false because left parenthesis r comma theta right parenthesis equals left parenthesis r comma theta plus n pi right parenthesis(r,θ)=(r,θ+nπ) for any integer n. These are all distinct polar coordinates.

D)The statement is false because left parenthesis r comma theta right parenthesis equals left parenthesis r comma 2 n pi theta right parenthesis(r,θ)=(r,2nπθ) for any integer n. These are all distinct polar coordinates.

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  1. well, every 2pi brings theta back to the same point, so ...

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