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Thread: 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
    $\displaystyle \frac{x}{4}- \frac{x}{16} = \frac{4x}{16}- \frac{x}{16} = \frac{3x}{16}$
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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 ...

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

    ???
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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?
    $\displaystyle y = A\sin(Bx+C) + D$

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

    B affects the period of the graph. For $\displaystyle B>1$ the graph will have a shorter period and for $\displaystyle B<1$ 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 $\displaystyle C>0$ the graph will move to the left and for $\displaystyle C<0$ to the right. $\displaystyle C=0$ 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

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

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

    $\displaystyle y = 0.5\sin(13x/16) - 5$ 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; Nov 28th 2010 at 01:29 PM.
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