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Math Help - show that this is an ellipse.

  1. #1
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    show that this is an ellipse.

    Given tha:

    x=4+4\cos \theta

    y+3=5\sin \theta

    Show that the above equations represents an ellipse.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by razemsoft21 View Post
    Given tha:

    x=4+4\cos \theta

    y+3=5\sin \theta

    Show that the above equations represents an ellipse.
    solving each equation for the trig functions gives.
    \frac{x-4}{4}=\cos(\theta) and
    \frac{y+3}{5}=\sin(\theta)
    And Remember that
    \sin^2(\theta)+\cos^2(\theta)=1
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    solving each equation for the trig functions gives.
    \frac{x-4}{4}=\cos(\theta) and
    \frac{y+3}{5}=\sin(\theta)
    And Remember that
    \sin^2(\theta)+\cos^2(\theta)=1
    \frac {(x-4)^2}{4^2}+\frac {(y+3)^2}{5^2}=1

    Thats clear, but why this method works
    all we do is finding \sin^2 \theta+\cos^2 \theta wich is always = 1

    and \sin^2 \theta+\cos^2 \theta =r^2 in polar coordinates
    I think we do not porve it this way !!
    what do you say ?
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  4. #4
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    Quote Originally Posted by razemsoft21 View Post
    \frac {(x-4)^2}{4^2}+\frac {(y+3)^2}{5^2}=1

    Thats clear, but why this method works
    all we do is finding \sin^2 \theta+\cos^2 \theta wich is always = 1

    and \sin^2 \theta+\cos^2 \theta =r^2 in polar coordinates
    I think we do not porve it this way !!
    what do you say ?
    I say you are mistaken.

    correction ...

    \sin^2 \theta+\cos^2 \theta \ne r^2

    \sin^2 \theta+\cos^2 \theta = 1 always. It's an identity.

    ... also x^2 + y^2 = r^2
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