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Math Help - Range of Values Question

  1. #1
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    Range of Values Question

    Hi there,
    Can you help me with the following problem please?

    If f(x) = 2 sin(3x - pi/2) + 5, what is the range of the values of f(x)?

    I began by moving 5 over to the other side.

    2 sin(3x - pi/2) = - 5

    sin(3x - pi/2) = -5/2

    Am I going in the right direction?
    Thanks
    Cromlix
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  2. #2
    A Plied Mathematician
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    No, I wouldn't go in that direction. I would build up the function f(x) from the simpler components using inequalities, like this:

    -1\le\sin(3x-\pi/2)\le 1

    -2\le 2\sin(3x-\pi/2)\le 2.

    How could you finish?
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  3. #3
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    Hi Ackbeet,
    Thank you for replying: I would proceed:- -1=< sin(3x - pi/2) =< 1
    -2=< sin(3x - pi/2) =< 2

    Add +5 to each side.
    3=< sin(3x - pi/2) =< 7 Cheers, Cromlix
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  4. #4
    A Plied Mathematician
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    Right idea, but your notation is off on the last line. You want

    3\le\sin(3x - \pi/2)+5 \le 7.
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