0
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ 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 May 18 '14 at 8:14
1
$\begingroup$

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*}

$\endgroup$
  • $\begingroup$ That makes sense, but how is that a "coordinate"? I was thinking they wanted something in the form of $(x, y)$. $\endgroup$ – Sabien May 18 '14 at 8:32
  • 1
    $\begingroup$ I guess the question was a bit imprecise; they likely meant to say: "Convert the given polar equation into a Cartesian equation." $\endgroup$ – Adriano May 18 '14 at 8:36
  • $\begingroup$ Ok cool, thanks. Just wanted to make sure I wasn't missing something. $\endgroup$ – Sabien May 18 '14 at 8:56

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.