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Converting Polar To Cartesian

  1. Sep 11, 2010 #1
    I'm having issues getting converting Polar functions to Cartesian functions. Take for example:

    [tex]rcos(\theta)=1[/tex] I just figured that since it was going to always equal the same thing, and because [tex]x=rcos(\theta)[/tex] that the Cartesian equation was x=1, and I was right.

    However logic fails here:[tex]r=3sin(\theta)[/tex]

    Now I know I have the following tools to work with:
    [tex]x=rcos(\theta)[/tex]
    [tex]y=rsin(\theta)[/tex]
    [tex]r^{2}=x^{2}+y^{2}[/tex]
    [tex]tan(\theta)=\frac{y}{x}[/tex]


    I remember from an example in class that this form is a circle, but I want to be able to algebraically prove it. This looks simple compared to what's further down the page:
    [tex]r=tan(\theta)sec(\theta)[/tex]
    [tex]r=2sin(\theta)+2cos(\theta)[/tex]

    I'm completely at a loss as to where I should begin. Is there some usual procedure for solving these problems?
     
    Last edited: Sep 11, 2010
  2. jcsd
  3. Sep 11, 2010 #2

    cronxeh

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    Gold Member

    r=3sin(theta)

    r^2 = 3rsin(theta) = 3y

    x^2 + y^2 = 3y

    Circle centered at (0,1.5) with diameter of 3
     
  4. Sep 11, 2010 #3

    cronxeh

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    Gold Member

    Just keep chopping them down as you see them, find patterns, exploit them and convert them

    r=tan(theta)*sec(theta) is same as
    r=tan(theta)*1/(cos(theta))
    r*cos(theta) = tan(theta)
    x= tan(theta) = y/x

    x^2 = y A bloody parabola
     
  5. Sep 11, 2010 #4

    cronxeh

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    Gold Member

    I'll throw you one more freebie, by now you should've gotten the clue that these problems are not hard at all, all you need is those 4 tools and some basic trig identities

    r=2*sin(theta) + 2*cos(theta) multiply it out by r

    r^2 = 2*r*sin(theta) + 2*r*cos(theta)

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

    Its a circle centered at (1,1) with radius of sqrt(2)
     
  6. Sep 11, 2010 #5
    I just had to do one substitution to finish that...

    I see...
    It makes sense. I just needed to see the solutions to some, now I have a better idea of what to do. Thanks!
     
    Last edited: Sep 11, 2010
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