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Math Help - Find the max value of a trigonometric function

  1. #1
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    Find the max value of a trigonometric function

    Find the maximum value of the function  f(x) =sin^3x-sin^2x+sinx-1
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  2. #2
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    Re: Find the max value of a trigonometric function

    Let z = \sin x where -1 \le z \le 1, so that we want to maximize

    z^3 - z^2 + z - 1

    Then \frac{d}{dz} = 3z^2 - 2z + 1

    The maximum value occurs either where d/dz = 0 or at z = \pm 1 Solving d/dz = 0 we have two non-real solutions, so the maximum occurs at either -1 or +1. Plugging in we see that z = sin x = 1 works, and the maximum value is 0.
    Thanks from shiny718
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