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Math Help - trigonometry equation

  1. #1
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    trigonometry equation

    Hello,

    I am a tad stuck on this question, so any help would be welcome.



    y = (2x 1)Tan 2x

    Has a minimum Turing point at P, the x co-ordinate of P is K

    Show that K satisfies the following



    4K + sin 4K -2 = 0

    thank you for the help

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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by sillyhacker View Post
    Hello,

    I am a tad stuck on this question, so any help would be welcome.



    y = (2x 1)Tan 2x

    Has a minimum Turing point at P, the x co-ordinate of P is K

    Show that K satisfies the following



    4K + sin 4K -2 = 0

    thank you for the help

    Take the first derivative:
    y = (2x - 1)*tan(2x)

    y' = 2*tan(2x) + (2x - 1)* sec^2(2x)*2

    At the minimum point y' = 0, so given the x = K:
    2*tan(2K) + (2K - 1)* sec^2(2K)*2 = 0

    Now, tan(2k) = sin(2K)/cos(2K) and sec(K) = 1/cos(K), so:
    2*sin(2K)/cos(2K) + 2*(2K - 1)/cos^2(2K) = 0

    Now multiply both sides by cos^2(2K):
    2*sin(2K)*cos(2K) + 2*(2K - 1) = 0

    But 2*sin(2K)*cos(2K) = sin(4K), so
    sin(4K) + 4K - 2 = 0
    which is your relationship.

    -Dan
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