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Math Help - trig find value

  1. #1
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    trig find value

    Find the exact values for the following:


    cos(4*cos^-1(1/3))

    cosine of ( four times the inverse cosine of (1/3) )


    what I wrote above are the same, I just wanted to spell them out just in case.
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    Quote Originally Posted by Mr_Green View Post
    Find the exact values for the following:


    cos(4*cos^-1(1/3))

    cosine of ( four times the inverse cosine of (1/3) )


    what I wrote above are the same, I just wanted to spell them out just in case.
    cos(4t) = cos(2*(2t)) = 2*cos^2(2t) - 1 = 2*[2*cos^2(t) - 1]^2 - 1

    Let t = cos^{-1}(1/3).

    Then
    cos(4*cos^{-1}(1/3)) = 2*[2*cos^2(cos^{-1}(1/3)) - 1]^2 - 1

    = 2*[2*(1/3)^2 - 1]^2 - 1

    = 2*[2/9 - 1]^2 - 1

    = 2*[-7/9]^2 - 1

    = 2*49/81 - 1

    = 98/81 - 1

    = 17/81

    -Dan
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