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Math Help - Calculate :sin,cos

  1. #1
    Super Member dhiab's Avatar
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    Calculate :sin,cos

    Calculate : \sin (6^\circ ),\cos (6^\circ )
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  2. #2
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  3. #3
    Senior Member pacman's Avatar
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    sin 6 degrees? hmnnnnn . . . . from this post http://www.mathhelpforum.com/math-he...tml#post350585

    cos 72 = sin 18 = (sqrt(5) -1)/4, also sin 3A = 3(sin A) - 4(sin^3 A); then


    sin 18 = 3(sin 6) - 4(sin^3 6); substituting

    (sqrt 5 - 1)/4 = 3(sin 6) - 4(sin^3 6); let x = sin 6.

    3x - 4x^3 = (sqrt 5 - 1)/4, rearranging

    4x^3 - 3x - (1 - sqrt 5)/4 = 0, graphing it we have 3 roots and only one is valid,

    that is . . . . x = sin 6 = (1/8)(-1 - sqrt 5 + sqrt(30 - 6 sqrt 5))

    to get cos 6 will have the same pattern
    Attached Thumbnails Attached Thumbnails Calculate :sin,cos-ok-ok.gif  
    Last edited by pacman; August 23rd 2009 at 06:48 AM.
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