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Math Help - period and amplitude

  1. #1
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    period and amplitude

    Find the amplitude and period of:

    y=5sin(2x) + 4sin(7x)



    i got 8.886 for the amplitude

    how do i get the period?

    thanks
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  2. #2
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    Quote Originally Posted by Mr_Green View Post
    Find the amplitude and period of:

    y=5sin(2x) + 4sin(7x)

    i got 8.886 for the amplitude

    how do i get the period?

    thanks
    Hello,

    you have to consider 2 different periods:
    p_1 = \frac{2\pi}2=\pi and
    p_2 =\frac{2\pi}7=\frac27 \cdot \pi

    You get the period of the combined function if the equation
    n \cdot p_1 = k \cdot p_2~, n,k~\in~\mathbb{Z} is true. Therefore:

    n \cdot \pi= k \cdot \frac27 \cdot \pi
    \frac nk = \frac27. The first possible values for n and k are:

    \frac nk ~\frac{\rightarrow}{\rightarrow}~ \frac27. If n = 2 then p_1 = 2\pi and if k = 7 then p_2 = 2\pi, thus the period of your function is 2\pi
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