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Math Help - Polar to cartesian

  1. #1
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    Polar to cartesian

    Find the cartesian equation of r^2 = 9\csc(20)?
    choices:
    A. xy = 9
    B. 3xy = 9
    C. 2xy = 9
    D. 4xy = 9

    This is what ive done

    (r^2= \frac{9}{\sin(20)}) \frac{1}{r}

    \sqrt{x^2 + y^2} = \frac{9}{y}

    x^2 + y^2 = \frac{81}{y^2}

    y^2(x^2 + y^2) = 81
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  2. #2
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    Re: Polar to cartesian

    Quote Originally Posted by TechnicianEngineer View Post
    Find the cartesian equation of r^2 = 9\csc(20)?
    choices:
    A. xy = 9
    B. 3xy = 9
    C. 2xy = 9
    D. 4xy = 9

    This is what ive done

    (r^2= \frac{9}{\sin(20)}) \frac{1}{r}

    \sqrt{x^2 + y^2} = \frac{9}{y}

    x^2 + y^2 = \frac{81}{y^2}

    y^2(x^2 + y^2) = 81
    Why has 1/r appeared - out of nowhere - in the first line?

    r^2 = \frac{9}{\sin \theta} \Rightarrow r = \frac{9}{r \sin \theta} \Rightarrow \sqrt{x^2 + y^2} = \frac{9}{y} \Rightarrow ....

    I don't agree with any of the given options.



    Edit: OK, this is what happens when someone uses poor notation to express an equation. No doubt the 20 is meant to be 2 \theta, in which case you have r^2 = \frac{9}{\sin (2 \theta)} \Rightarrow r^2 = \frac{9}{2 \sin (\theta) \cos (\theta)} \Rightarrow 1 = \frac{9}{2 r \sin (\theta) r \cos (\theta)} \Rightarrow ....

    Learn latex please!
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  3. #3
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    Re: Polar to cartesian

    Hello, TechnicianEngineer!

    \text{Find the cartesian equation of: }\:r^2 \:=\: 9\csc(2\theta)

    . . (A)\;xy \,=\, 9 \qquad (B)\; 3xy \,=\, 9 \qquad (C)\; 2xy \,=\, 9 \qquad (D)\; 4xy \,=\, 9

    This is the way I would do it . . .

    . . . . . . . . . . . . . r^2 \:=\:9\csc(2\theta)

    . . . . . . . . . . . . . r^2 \:=\:\frac{9}{\sin(2\theta)}

    m . . . . . . r^2\sin(2\theta) \:=\:9

    . . . . r^2(2\sin\theta\cos\theta) \:=\:9

    . . 2\overbrace{(r\cos\theta)}^{\text{This is }x}\underbrace{(r\sin\theta)}_{\text{This is }y} \;=\;9

    n . . . . . . . . . . 2xy \;=\;9 \quad\text{ answer (C)}

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  4. #4
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    Re: Polar to cartesian

    i apologize that the questionnaire was not well photocopied
    i myself thought it was csc(20)
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