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Math Help - finding the value

  1. #1
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    finding the value

    How to find the value of this without using a calculator ?

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  2. #2
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    Re: finding the value

    Using the formulae in sections 16 and 17 of this page PlanetMath you can simplify \sin(10)\sin(30)\sin(50)\sin(70) to arrive at a value of 1/16.

    Similarly you can get \cos(10)\cos(30)\cos(50)\cos(70)=\frac{3}{16}.

    You also need to remember that \sin(x)=\sin(180-x).
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  3. #3
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    Re: finding the value

    Can you show me how did you apply these formulas to get these results ?
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  4. #4
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    Re: finding the value

    I'll get you started. I'll put in extra steps to try to be clear. I'll leave the denominator to you.

    \sin(10)\sin(30)\sin(50)\sin(70)

    =\frac{1}{2}\sin(10)\sin(50)\sin(70)

    =\frac{1}{2}\left(\frac{1}{2}(\cos(50-10)-cos(50+10))\right) \sin(70)

    =\frac{1}{2}\left(\frac{1}{2}(\cos(40)-cos(60))\right) \sin(70)

    =\frac{1}{2}\left(\frac{1}{2}(\cos(40)-\frac{1}{2}\right) \sin(70)

    =\frac{1}{4}\cos(40)\sin(70)-\frac{1}{8} \sin(70)

    =\frac{1}{8}(\sin(70+40)+\sin(70-40))-\frac{1}{8} \sin(70)

    =\frac{1}{8}\sin(110)+\frac{1}{16}-\frac{1}{8} \sin(70)

    =\frac{1}{16}

    The LaTeX is harder than the maths.
    Last edited by a tutor; April 19th 2012 at 12:38 PM.
    Thanks from Mhmh96
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  5. #5
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    Re: finding the value

    Thank you a tutor !,now i understand how to find it ,but which formula do i have to use for tan ?
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  6. #6
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    Re: finding the value

    \tan x =\frac{\sin x}{\cos x}
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  7. #7
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    Re: finding the value

    So the answer is 1/3 i think ,thank you for your time .
    Last edited by Mhmh96; April 19th 2012 at 02:09 PM.
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