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Math Help - graphing transformations of trig functions

  1. #1
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    graphing transformations of trig functions

    could somebody please help me with my transformations.
    y = 0.5sin(x/4 - x/16) -5

    I might be dooing it wrong but i rearanged it to
    y = 0.5sin(x - x/4) -5

    is this correct?
    in any case, what would be the period and x translation?
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  2. #2
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    Quote Originally Posted by Plzhelp View Post
    could somebody please help me with my transformations.
    y = 0.5sin(x/4 - x/16) -5
    \frac{x}{4}- \frac{x}{16} = \frac{4x}{16}- \frac{x}{16} =  \frac{3x}{16}
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  3. #3
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    Quote Originally Posted by Plzhelp View Post
    could somebody please help me with my transformations.
    y = 0.5sin(x/4 - x/16) -5

    I might be dooing it wrong but i rearanged it to
    y = 0.5sin(x - x/4) -5

    is this correct?
    in any case, what would be the period and x translation?
    are you sure you didn't mean this equation ...

    \displaystyle y = 0.5\sin\left(\frac{x}{4} - \frac{\pi}{16}\right) - 5

    ???
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  4. #4
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    Quote Originally Posted by Plzhelp View Post
    could somebody please help me with my transformations.
    y = 0.5sin(x/4 - x/16) -5

    I might be dooing it wrong but i rearanged it to
    y = 0.5sin(x - x/4) -5

    is this correct?
    in any case, what would be the period and x translation?
    y = A\sin(Bx+C) + D

    A is the amplitude - this is how "high" the graph will go relative to \pm 1. For example if A = 2 the extrema will be \pm 2

    B affects the period of the graph. For B>1 the graph will have a shorter period and for B<1 a longer period. On a graph this means that the wave will be more or less "squashed" on the x axis respectively.

    C is the phase difference which determines the shift on the x axis of the graph. The shape doesn't change, just it's positions and intercepts. For C>0 the graph will move to the left and for C<0 to the right. C=0 is no change obviously enough

    D is the y-shift. In other words how much the whole graph is shifted either up or down the y axis.


    In your case you have

    • A = 0.5
    • B = 13/16
    • C = 0
    • D = -5

    I have plotted the graphs of y = 0.5\sin(13x/16) in orange, y = \sin(13x/16) in green and y = \sin(x) in blue for comparison purposes

    y = 0.5\sin(13x/16) - 5 is on a separate attachment
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  5. #5
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    @ skeeter, yes thats what i meant to write.

    ok thanks for the help e^, I get all of this I just don't know how to get the B from (x/4 - pi/16)



    nvm this is easy, thx for the fast response!
    Last edited by Plzhelp; November 28th 2010 at 01:29 PM.
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