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Math Help - Converting Polar equations into rectangular equations:

  1. #1
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    Converting Polar equations into rectangular equations:

    How do I convert r = 5sin(x) into an equivalent rectangular equation?
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by Neversh View Post
    How do I convert r = 5sin(x) into an equivalent rectangular equation?
    you mean

    r=5sin(\theta) to rectangular

    you should know that

    x=r cos(\theta)

    y=r sin(\theta)

    \sqrt{x^2+ y^2 } = r.....x^2+y^2=r^2

    use them to find the equation try
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  3. #3
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    Hello, Neversh!

    You know the conversion, right?

    . . \begin{array}{c}r\cos\theta  \:=\:x \\ r\sin\theta \:=\:y \\ r^2 \:=\:x^2+y^2 \end{array}


    How do I convert r = 5\sin\theta into an equivalent rectangular equation?

    We have: . r \:=\:5\sin\theta

    \text{Multiply by }r\!:\;\;\underbrace{r^2} \:=\:5\underbrace{r\sin\theta}
    . - . - . . . . . . . \uparrow\qquad\qquad\: \uparrow
    . . . . . . . . . . ^{x^2+y^2}\qquad\quad\;\; ^y

    And we have: . x^2+y^2 \:=\:5y

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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by Neversh View Post
    How do I convert r = 5sin(x) into an equivalent rectangular equation?
    First multiply both sides by r to get

    r^2=5r\sin(x)

    Now we know that r^2=x^2+y^2 and

    r\sin(x)=y

    Now we get

    x^2+y^2=5y \iff x^2+y^2-5y=0 \iff x^2+y^2-5y+\frac{25}{4}=\frac{25}{4}

    So finally we get

    x^2+\left(y-\frac{5}{2} \right)^2=\left( \frac{5}{2}\right)^2

    Edit too slow haha
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