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Math Help - Axis rotation with fractional angles

  1. #1
    Junior Member Greymalkin's Avatar
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    Axis rotation with fractional angles

    Part of the algebra I'm doing with this is producing bad results, please tell me why.

    Graph: 11x^2+7xy-13y^2=621
    arccos 24/7 is a fraction so:
    sin\theta=\sqrt{\frac{1-\frac{24}{7}}{2} x=x'\frac{31}{14}-y'\frac{-17}{14}
    cos\theta=\sqrt{\frac{1+\frac{24}{7}}{2} y=x'\frac{-17}{14}+y;\frac{31}{14}

    I try to solve and eliminate x'y' but end up with odd fractions:

    11[x'\frac{31}{14}+y'\frac{17}{14}]^2+7[x'\frac{31}{14}+y'\frac{17}{14}][x'\frac{-17}{14}+y'\frac{31}{14}]-13[x'\frac{-17}{14}+y\frac{31}{14}]^2=621

    ~~~~~~~~~~~~~~~~~~~~~

    Which when I calculate gives me:

    11[x'^2\frac{961}{196}+2x'y'\frac{527}{196}+y'^2\frac  {289}{196}]+7[x'^2\frac{527}{196}+x'y'\frac{961}{196}-x'y'\frac{289}{196}+y'^2\frac{527}{196}]-13[x'^2\frac{289}{196}-2x'y'\frac{527}{196}+y'^2\frac{961}{196}]=621

    Which can't be right because the x'y' will not equal 0.
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    Re: Axis rotation with fractional angles

    Quote Originally Posted by Greymalkin View Post
    Part of the algebra I'm doing with this is producing bad results, please tell me why.
    Graph: 11x^2+7xy-13y^2=621
    arccos 24/7 is a fraction so:
    sin\theta=\sqrt{\frac{1-\frac{24}{7}}{2} x=x'\frac{31}{14}-y'\frac{-17}{14}
    cos\theta=\sqrt{\frac{1+\frac{24}{7}}{2} y=x'\frac{-17}{14}+y;\frac{31}{14}
    What is the question? There does't not appear to be any question there.
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  3. #3
    Junior Member Greymalkin's Avatar
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    Re: Axis rotation with fractional angles

    Quote Originally Posted by Plato View Post
    What is the question? There does't not appear to be any question there.
    Graph 11x^2+7xy-13y^2=621

    "Part of my algebra is producing bad results, please tell me where/why my calculations are producing x'y' terms that are irreducible.", with algebra below.
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  4. #4
    Junior Member Greymalkin's Avatar
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    Re: Axis rotation with fractional angles

    Seems that I found "an" error in cos2\theta yet am still getting bad results with the algebra, am I doing anything illegal above??

    Edit: Here is my new work with the above error taken into account,

    sin\theta=\sqrt{\frac{1-\frac{24}{25}}{2} =\frac{1}{50} --- x=x'\frac{49}{50}-y'\frac{1}{50}
    cos\theta=\sqrt{\frac{1+\frac{24}{25}}{2} =\frac{49}{50} --- y=x'\frac{1}{50}+y'\frac{49}{50}

    Continuing on>>>

    11x^2+7xy-13y^2=621

    11[x'\frac{49}{50}-y'\frac{1}{50}]^2+7[(x'\frac{49}{50}-y'\frac{1}{50})(x'\frac{1}{50}+y'\frac{49}{50}]-13[x'\frac{1}{50}+y'\frac{49}{50}]^2=621

    ~~~~~~~~~~~~~~~~~~~~~~~~~

    11[x'^2\frac{2401}{2500}-2x'y'\frac{49}{2500}+y'^2\frac{1}{2500}]+7[x'^2\frac{49}{2500}+x'y'\frac{2401}{2500}-x'y'\frac{1}{2500}-y'^2\frac{49}{2500}]-13[x'^2\frac{1}{2500}+2x'y'\frac{49}{2500}+y'^2\frac{  2401}{2500}]=621

    After simplifying, something is wrong because the x'y' terms, yet again, will not dissapear for me.
    Last edited by Greymalkin; September 5th 2012 at 04:40 AM.
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  5. #5
    Junior Member Greymalkin's Avatar
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    Re: Axis rotation with fractional angles

    Bump- Still haven't solved this yet, please help!
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