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Math Help - [SOLVED] Trigonometric equation?

  1. #1
    Super Member fardeen_gen's Avatar
    Joined
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    [SOLVED] Trigonometric equation?

    Find the values of x which satisfy the equation 8^(1+│cos x│+ cos^2 x +cos^3 x│+.........infinite terms) = 4^3

    ^ - raised to
    │- Absolute value

    Answer: {x│x = 2nπ π/3} U {x│x = 2nπ 2π/3}

    How do we solve this problem?


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  2. #2
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
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    Quote Originally Posted by fardeen_gen View Post
    Find the values of x which satisfy the equation 8^(1+│cos x│+ cos^2 x +cos^3 x│+.........infinite terms) = 4^3

    ^ - raised to
    │- Absolute value

    Answer: {x│x = 2nπ π/3} U {x│x = 2nπ 2π/3}

    How do we solve this problem?


    8^{1+|\cos x| + |\cos^2 x| + |\cos^3 x| + ...}

    1+|\cos x| + |\cos^2 x| + |\cos^3 x| + ... is a geometric series with r=|\cos x|

    so we have the sum as \frac{1}{1- |\cos x|}

    and so we have 8^{\frac{1}{1- |\cos x|}} = 4^3

    \frac{1}{1- |\cos x|} \ln 2^3 = \ln 4^3 = \ln 2^6

    3\frac{1}{1- |\cos x|} \ln 2 = 6\ln 2

    simplifies to \frac{1}{1- |\cos x|} = 2

    i hope you can finish this already..
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