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Math Help - Converting from a polar equation to a cartesian equation

  1. #1
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    Converting from a polar equation to a cartesian equation

    Hey guys here’s the equation that I had to convert from polar (r, theta) to Cartesian (x,y)…

    r = 4 sin (theta)


    and this is what I got…

    (x^2 +y^2) ^(5/2) = 4(x^4)(y) - 4(x)(y^3)

    Can someone check to see if I’m correct?
    Your time is GREATLY appreciated!
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  2. #2
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    Somewhat different answer

    Your equation
    <br />
r = 4 sin \theta<br />

    Multiply both sides by r
    <br />
r^2 = 4 r sin \theta<br />

    to get
    <br />
x^2 + y^2 = 4 y<br />
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  3. #3
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    whoops...

    im so sorry qmech... the actual question was

    r = sin 4(theta)

    sorry for the inconvenience
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  4. #4
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    <br />
r = sin ( 4 \theta )<br />

    <br />
r = 2 sin ( 2 \theta ) cos (2 \theta )<br />

    <br />
r = 2 (2 sin \theta  cos \theta  ) ( cos^2  \theta  - sin ^2 \theta )<br />

    <br />
r^5 = 2 (2 r sin \theta  r cos \theta  ) ( r^2 cos^2  \theta  - r^2 sin ^2 \theta )<br />

    <br />
(x^2 + y^2)^{5/2} = 4 x y ( x^2 - y^2 )<br />
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  5. #5
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    thanks alot mech.... you know your stuff
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