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Math Help - trigo

  1. #1
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    trigo

    By sketching the graph of y=3+ | sin x | for x is greater or equal to zero and smaller or equal to 2 pi , find the range of values of k such that the equation | sin x | = k-3 does not have any real root .
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  2. #2
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    Quote Originally Posted by mathaddict View Post
    By sketching the graph of y=3+ | sin x | for x is greater or equal to zero and smaller or equal to 2 pi , find the range of values of k such that the equation | sin x | = k-3 does not have any real root .
    In my sketch on paper of the graph of
    y = 3 +|sin x|,
    the range is 3 <= y <= 4. Or, y is between 3 and 4, inclusive.

    The
    |sin x| = k -3
    can be re-written as
    k = 3 +|sin x|

    For that to not have real roots, the curve must not touch the x-axis.
    So k must not be anywhere from y=3 to y=4, inclusive.

    Therefore, (k < 3) U (k > 4) ----------answer.
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