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Change from polar to rectangular coordinates

  1. Dec 3, 2008 #1
    1. The problem statement, all variables and given/known data

    change from polar to rectangular coordinates

    2. Relevant equations

    [tex]\cos{theta}+r^2\sin{theta}=\tan{theta}[/tex]

    3. The attempt at a solution

    I got
    [tex]x^2 + y^2 + x + y = \frac{y}{x}\sqrt{x^2+y^2}[/tex]

    does that look right?
     
  2. jcsd
  3. Dec 3, 2008 #2
    Since [tex]r^2[/tex] is multiplied by [tex]\sin \theta[/tex] rather than added to it, shouldn't it be

    [tex]x + (x^2 + y^2)y = \frac{y}{x}\sqrt{x^2 + y^2}[/tex]?
     
  4. Dec 3, 2008 #3
    ooohh thanks
     
  5. Dec 4, 2008 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The simplest way to do this is to multiply the entire equation by r:
    [tex]r cos(\theta)+ r^2(r sin(\theta))= r tan(\theta)= r \frac{r sin(\theta)}{r cos(\theta)}[/tex]
    so
    [tex]x+ (x^2+ y^2)y= \sqrt{x^2+ y^2}\frac{y}{x}[/tex]
     
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