Polar Curve Equation Confusion

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Homework Statement:

The graph of a polar equation is r=f(θ), or more generally F(r,θ) = 0, ...

Relevant Equations:

NONE.

What does "F(r,θ) = 0" mean here?

 

[SammyS]

Homework Statement:: The graph of a polar equation is r=f(θ), or more generally F(r,θ) = 0, ...
Relevant Equations:: NONE.

What does "F(r,θ) = 0" mean here?

The notation, F(r,θ) suggests that F is a function of two variables, or a function of an ordered pair. Likely it maps individual points in a plane each to a real number value. However in the case here, you are only interested in the zeros of F, i.e. you are only interested in those point which get mapped to zero.

A simple way to get a suitable function F, if you have the function f, is to define F as:

F(r,θ) = r − f(θ)