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Math Help - Deriving an equation from a sin graph.

  1. #1
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    Deriving an equation from a sin graph.

    Here is the picture: 2011-11-15_11-07-53_425.jpg picture by Bashyboy - Photobucket

    The amplitude is easy enough to find--it is 3, and since it is a reflection, it is therefore -3--, but what I can't find is the coefficient for x, which is b. I understand the period to be 2pi/b, and in the answer key they are utilizing in this way: 2pi/b = pi. I don't understand, is pi the period? And if so, how am I able to deduce this from the graph?

    Thank you
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  2. #2
    Super Member Quacky's Avatar
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    Re: Deriving an equation from a sin graph.

    Not entirely sure what you are referring to, it is something like a general formula:

    y=asin(bx+c)?

    Here, we have:

    y=-3sin(bx+c)
    We deduce the value for b from the number of 'loops' of the graph - and as you say, this can be calculated through knowing the period. sin(x) is periodic in that it repeats itself every 2\pi radians. This means that:
    sin(x) has one full 'loop' between x=0 and x=2\pi Here, there are two full loops, so b=2

    The way your text describes it:

    \frac{2\pi}{b}=\pi

    b=\frac{2\pi}{\pi}=2
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  3. #3
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    Re: Deriving an equation from a sin graph.

    Yes, I am referring to that general formula. Now, how do I find the horizontal translation (denoted by c) mathematically?
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  4. #4
    Super Member Quacky's Avatar
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    Re: Deriving an equation from a sin graph.

    By looking at the x-intercepts, I would think. Compare where the graph cuts the x-axis of this graph with where it cuts the x axis of sin(x)
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  5. #5
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    Re: Deriving an equation from a sin graph.

    I am terribly sorry, I meant algebraically; but your method seems quite sensible. Thank you.
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