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Math Help - Amplitude, Period, and Displacement?

  1. #1
    Newbie Smokinoakum's Avatar
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    Amplitude, Period, and Displacement?

    Hi all...after finishing my homework tonight I decided to keep going in the chapter to get ahead. Yeah, I was also enjoying myself too!

    The next part of the chapter deals with Amplitude, Period, and Displacement.

    Here is a sample question from the book.

    Determine the amplitude, period, and displacement of the given function. Then sketch the graph of the function.

    \displaystyle y = 2\ cos \displaystyle \left(x\, + \frac{\pi}{12}\right)

    Could someone break this type of problem down to it's parts so I can work my way through this section of the chapter?

    Once again, I'm taking my math online which means I've basicly become my own teacher.
    Last edited by Smokinoakum; March 19th 2011 at 08:53 PM.
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  2. #2
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    Hey,
    you could plot the function against the graph of y = cosx, Translate the graph in stages, i.e change the amplitute y = 2cosx and observe the result. Then you can look at the graph of y = cos(x+\frac{\pi}{12}) (Phase shift of \frac{\pi}{12}.), how to draw y = 2cos(x+\frac{\pi}{12}) should become obvious.
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  3. #3
    Newbie Smokinoakum's Avatar
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    Quote Originally Posted by Oiler View Post
    Hey,
    you could plot the function against the graph of y = cosx, Translate the graph in stages, i.e change the amplitute y = 2cosx and observe the result. Then you can look at the graph of y = cos(x+\frac{\pi}{12}), how to draw y = 2cos(x+\frac{\pi}{12}) should become obvious.
    Thanks for responding Oiler. I think first I need to understand the proper way to find the amplitude, period, and displacement of the given function. After that I know I could use the calculator to see the graph.

    Does that make sense?
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  4. #4
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    Given, f(x) = A sin(Bx-C) + D
    The Amplitude is A
    The vertical shift is D
    The period will be given by \frac{2\pi}{B}
    And you can work out the frequency by f = \frac{1}{period} = \frac{1}{\frac{2\pi}{B}}=\frac{B}{2\pi}
    The phase shift is \frac{C}{B}
    Hopefully that helps..
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  5. #5
    Newbie Smokinoakum's Avatar
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    Quote Originally Posted by Oiler View Post
    Given, f(x) = A sin(Bx-C) + D
    The Amplitude is A
    The vertical shift is D
    The period will be given by \frac{2\pi}{B}
    And you can work out the frequency by f = \frac{1}{period} = \frac{1}{\frac{2\pi}{B}}=\frac{B}{2\pi}
    The phase shift is \frac{C}{B}
    Hopefully that helps..
    Yes that helps a lot. I have added that to my notes.

    So after looking this over this is what I came up with.

    Determine the amplitude, period, and displacement of the given function. Then sketch the graph of the function.

    \displaystyle y = 2\ cos \displaystyle \left(x\, + \frac{\pi}{12}\right)

    The Amplitude is = 2

    The period =  \frac{2\pi}{1} = 2\pi

    The displacement = -\frac{\pi}{\frac{12}{1}} = -\frac{\pi}{12}
    Last edited by Smokinoakum; March 19th 2011 at 11:18 PM.
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  6. #6
    Newbie Smokinoakum's Avatar
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    I've worked through about ten like the previous post and they were progressively getting harder and then a came upon this one...

    Find the function and graph it for a function of the form \displaystyle y = 7\ sin \displaystyle \left(7x\ + c)\right that passes through \left(-\frac{\pi}{5}, 0)\right and for which c has the smallest possible positive value.

    This one has me a bit intimidated.

    How do I go about this one?
    Last edited by Smokinoakum; March 20th 2011 at 08:13 AM.
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