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I'm currently learning about polar functions and their graphs in precalculus, and one of the questions on my homework is to identify the shape of the function $r=2\cos(\theta)$. We were taught that functions in the form $r=a\cos(n\theta)$ where $a>0$ are roses. So, were $a=2$ and $n=1$, wouldn't it form this function and be rose?

I ask because the graph is a perfect circle centered at polar coordinates (1,0).

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    Well, it's a flower with one perfectly circular petal. I hear that one-petal flowers can be found in nature, though I don't know how circular they get.2012-06-07

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I'd say that it's convenient to include it in the set of rose curves—it can be useful to think about $r=a\sin n\theta$ for noninteger values of $n$ (even starting at $0$), rather than just integers greater than $1$:

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Note that in polar coords

$x = r \cos \theta$

$y= r \sin \theta$

You have that $r = 2 \cos \theta$

That is

Then

$r^2 = 2r \cos \theta$

$x^2+y^2 = 2x$

$x^2-2x+1+y^2=1$

$(x-1)^2+y^2=1$

That is a circle centered at $(1,0)$ and radius $1$.

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    It is not the case here.2012-06-08