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Math Help - graph of equation over given interval

  1. #1
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    graph of equation over given interval

    Identify the graph of the equation over the given interval.

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

    x is greater than or equal to -pi/4 and x is less than or equal to 3pi/2.

    I think I found the period to be: pi
    the amplitude is 3.
    the phase shift is pi as well?

    I'm unsure as to what to do after this though.

    My choices are these, but I don't know how to determine which is correct. I'm not just looking for an easy answer, I really want to try to understand this. Thanks so much guys.








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  2. #2
    o_O
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    Actually, phase shift is \frac{\pi}{4} since: y = 3\sin \left(2x - \frac{\pi}{2}\right) = y = 3\sin \left[ 2\left(x - {\color{red}\frac{\pi}{4}}\right)\right]

    Now from your typical y = \sin x graph, make the changes accordingly. Change its amplitude to 3. Shift it to the right \frac{\pi}{4} units. Adjust the period.
    ____________________________

    Alternatively ...

    To make things easier, note that: \sin \left(\theta - \frac{\pi}{2}\right) = -\cos \theta

    So we have: y = 3\sin \left(2x - \frac{\pi}{2}\right) \ \Leftrightarrow \ y = 3 (-cos 2x) = -3 \cos (2x)

    Much easier to graph
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