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Prove if a function only have including the rational numbers and sin, cos, tan function and $r$, you always could write it in rectangular form. Ex. For $r=2/(2+2\cos\theta)$ it could be represent in rectangular form. Rectangular form is where the $r$ in the original function is $\sqrt{x^2+y^2}$ and you could create a function in terms of $x$ and $y$ that is $=0$ that is refer to the original function

Also, another question would be: What other trig function could involved in a function if it could be represent in rectangular form.

is there a complete answer for this question?

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    @deoxygerbe - yes, no composition2012-02-29

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Substitute $r = \sqrt{x^2+y^2}$, $\cos(\theta) = x/\sqrt{x^2+y^2}$, $\sin(\theta) = y/\sqrt{x^2+y^2}$, $\tan(\theta) = y/x$ in the polar equation. Is that what you mean?

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    yes, that is my meaning2012-02-29