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Math Help - quick polar coordinates question

  1. #1
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    quick polar coordinates question

    In 3r = sin A, r and A represent polar coordinates, write each polar equation as an equation in rectangular coordinates (x,y).

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  2. #2
    MHF Contributor red_dog's Avatar
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    r=\sqrt{x^2+y^2} and \displaystyle \tan A=\frac{y}{x}.
    We have \displaystyle \sin A=\frac{\tan A}{\sqrt{1+\tan ^2A}}=\frac{y}{\sqrt{x^2+y^2}}.
    Replacing r and \sin A in the given relation, we have
    \displaystyle 3\sqrt{x^2+y^2}=\frac{y}{\sqrt{x^2+y^2}}\Leftright  arrow 3(x^2+y^2)=y
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  3. #3
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    Hello, Andy!

    I assume you know the conversion formulas:
    . . x \,= \,r\cos\theta,\;\;y \,= \,r\sin\theta,\;\;x^2 + y^2 \:=\:r^2


    In 3r \:= \:\sin\theta,\;\theta and r represent polar coordinates.
    Write the equation in rectangular coordinates (x,y)
    \text{We have: }3r \;=\;\sin\theta

    \text{Multiply both sides by }r\!:\;\;3r^2 \;=\;\underbrace{r\sin\theta}
    . . . . . . . . . . . . . . 3\overbrace{(x^2+y^2)} \:=\:y

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