Results 1 to 4 of 4

Math Help - Converting a polar equation to a rectangular equation

  1. #1
    Newbie
    Joined
    Dec 2012
    From
    New Hampshire
    Posts
    8

    Converting a polar equation to a rectangular equation

    I was given the polar equation: r + 2cos(theta) = 3sin(theta)

    Which I converted (I believe correctly) to x^2+y^2=-2x+3y yet my professor circled my answer and circled the word "Equation" in the question. I feel like what I did was right but is there another form I am supposed to put this in? Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,964
    Thanks
    1008

    Re: Converting a polar equation to a rectangular equation

    Quote Originally Posted by beastcoast515 View Post
    I was given the polar equation: r + 2cos(theta) = 3sin(theta)

    Which I converted (I believe correctly) to x^2+y^2=-2x+3y yet my professor circled my answer and circled the word "Equation" in the question. I feel like what I did was right but is there another form I am supposed to put this in? Thank you.
    \displaystyle \begin{align*} r + 2\cos{(\theta)} &= 3\sin{(\theta)} \\ r + 2\left( \frac{x}{r} \right) &= 3\left( \frac{y}{r} \right) \\ r^2 + 2x &= 3y \\ x^2 + y^2 + 2x &= 3y \\ x^2 + 2x + y^2 - 3y &= 0 \\ x^2 + 2x + 1^2 + y^2 - 3y + \left( -\frac{3}{2} \right)^2 &= 1^2 + \left( -\frac{3}{2} \right)^2 \\ \left( x + 1 \right)^2 + \left( y - \frac{3}{2} \right)^2 &= \frac{13}{4} \\ \left(x + 1 \right)^2 + \left( y - \frac{3}{2} \right)^2 &= \left( \frac{\sqrt{13}}{2} \right)^2  \end{align*}

    So this is a circle of radius \displaystyle \begin{align*} \frac{\sqrt{13}}{2} \end{align*} units centred at \displaystyle \begin{align*} \left( -1, \frac{3}{2} \right) \end{align*}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121

    Re: Converting a polar equation to a rectangular equation

    Yes, that's obviously a circle but the question was, why did the professor circle it and write "equation"? beastcoast515, look closely at your paper again. Is it possible that you simply forgot to write "=" or that you wrote it quickly and it was not easily readable as an equality symbol?
    Other than that, if you actually wrote what you say here, I can think of no good reason.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,964
    Thanks
    1008

    Re: Converting a polar equation to a rectangular equation

    Quote Originally Posted by HallsofIvy View Post
    Yes, that's obviously a circle but the question was, why did the professor circle it and write "equation"? beastcoast515, look closely at your paper again. Is it possible that you simply forgot to write "=" or that you wrote it quickly and it was not easily readable as an equality symbol?
    Other than that, if you actually wrote what you say here, I can think of no good reason.
    Or if the question asked to DESCRIBE the curve given by the equation. There's nearly always an expectation of inference from doing a question...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Converting a Polar Equation to Rectangular
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: April 5th 2011, 09:36 AM
  2. Converting polar equation to rectangular
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 30th 2010, 10:25 AM
  3. Replies: 4
    Last Post: December 1st 2009, 03:45 PM
  4. Replies: 1
    Last Post: August 17th 2009, 10:43 PM
  5. Converting Polar Equation to Rectangluar Equation
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: September 14th 2008, 06:22 PM

Search Tags


/mathhelpforum @mathhelpforum