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Thread: 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 $\displaystyle 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 $\displaystyle z = \sin x$ where $\displaystyle -1 \le z \le 1$, so that we want to maximize

    $\displaystyle z^3 - z^2 + z - 1$

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

    The maximum value occurs either where $\displaystyle d/dz = 0 $ or at $\displaystyle z = \pm 1$ Solving $\displaystyle d/dz = 0$ 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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