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I have a question to convert $r^3 = − 7cos\theta$ into cartesian coordinates.

I'm having a hard time understanding what to do. I'm familiar with converting a polar coordinate to a Cartesian coordinate (say you're given $(\frac{\pi}{4}, 3)$ and asked to convert to Cartesian coordinates) but I'm not sure what to do with an actual equation.

Can anyone give me some hints?

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  • $\begingroup$ Do you know the general formula for converting cartesian coordinates $(x,y)$ to polar coordinates $(r, \theta)$? As a hint, you have $r = \sqrt{x^2 + y^2}$. Then plug this into your equation. $\endgroup$
    – PhoemueX
    Commented May 18, 2014 at 8:14

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Multiplying both sides by $r$, we obtain: \begin{align*} r^4 &= -7r\cos\theta \\ (r^2)^2 &= -7(r \cos\theta) \\ (x^2 + y^2)^2 &= -7x \end{align*}

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  • $\begingroup$ That makes sense, but how is that a "coordinate"? I was thinking they wanted something in the form of $(x, y)$. $\endgroup$
    – Sabien
    Commented May 18, 2014 at 8:32
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    $\begingroup$ I guess the question was a bit imprecise; they likely meant to say: "Convert the given polar equation into a Cartesian equation." $\endgroup$
    – Adriano
    Commented May 18, 2014 at 8:36
  • $\begingroup$ Ok cool, thanks. Just wanted to make sure I wasn't missing something. $\endgroup$
    – Sabien
    Commented May 18, 2014 at 8:56

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