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Math Help - sinusoidal function

  1. #1
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    sinusoidal function

    the amplitude is (max -min)/2 = 13-1/2=6
    is b=2pi/period , the period seems to be about 6, so b=pi/3
    c = horizontal shift(I doesn't seem to be a horizontal shift). How do I calculate it?

    d= (max+min)/2 = 13 + 1/2=14/2=7
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  2. #2
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    Quote Originally Posted by terminator View Post
    the amplitude is (max -min)/2 = 13-1/2=6
    is b=2pi/period , the period seems to be about 6, so b=pi/3
    c = horizontal shift(I doesn't seem to be a horizontal shift). How do I calculate it?

    d= (max+min)/2 = 13 + 1/2=14/2=7
    Dear terminator,

    According to the details you have found,

    y=6\sin\{\frac{\pi}{3}\left(x+c\right)\}+7

    When x=0\Rightarrow y=7

    7=6\sin\{\frac{\pi}{3}\left(c\right)\}+7\Rightarro  w \dfrac{\pi c}{3}=n\pi~where~n\in Z

    c=3n~where~n\in Z

    Hope this will help you.
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  3. #3
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    Quote Originally Posted by Sudharaka View Post
    Dear terminator,

    According to the details you have found,

    y=6\sin\{\frac{\pi}{3}\left(x+c\right)\}+7

    When x=0\Rightarrow y=7

    7=6\sin\{\frac{\pi}{3}\left(c\right)\}+7\Rightarro  w \dfrac{\pi c}{3}=n\pi~where~n\in Z

    c=3n~where~n\in Z

    Hope this will help you.

    It's also true that \displaystyle y'>0 at \displaystyle x=0

    so, \displaystyle {{\pi c}\over{3}}\approx 2\pi n.

    Thus: \displaystyle c\approx 6 n.

    Since the simplest case of \displaystyle c\approx 6 n is when \displaystyle  n=0, I would choose \displaystyle c\approx 0\ .

    Also, it looks like the period is closer to 6.2 than it is to 6, (BTW: That's very close to \displaystyle 2\pi\ .) so I would say that \displaystyle b\approx {{\pi}\over{3.1}}\ , maybe even \displaystyle b\approx 1\ .

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