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Math Help - General formula for Sine functions?

  1. #1
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    General formula for Sine functions?

    y = AsinB(x-C) +D.

    I know that A (amplitude) can be found by getting (max-min )/2, B = 2pi / current period, and D = average of max and min y.

    But how do you find C, once you've found those 3?
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  2. #2
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    I believe you solve these to get horizontal shift.

    bx-c=0

    bx-c=2\pi
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  3. #3
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    e^(i*pi)'s Avatar
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    C is the phase shift.

    Since \sin(x) passes through the origin, the value of C is the distance from the origin.


    When C = \frac{\pi}{2} you get cos(x)
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  4. #4
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    Quote Originally Posted by skoker View Post
    I believe you solve these to get horizontal shift.

    bx-c=0

    bx-c=2\pi
    Wait, huh? So if you have b...you just take a random x value to plug in? I don't think that's it....unless I am missing something?
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  5. #5
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    you solve for x. and find beginning and end point of period.
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  6. #6
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    ....huh? I thought we're finding c. o_o. So if my C is x now, what's the c in your formula then...?
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  7. #7
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    are you looking for the value of 0? or are you trying to find the critical points of a sine function with a phase/horizontal shift?
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  8. #8
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    I believe I'm looking for the horizontal shift of the graph, not a value of 0.
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  9. #9
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    e^(i*pi)'s Avatar
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    C is the horizontal shift of sin(B[x-c]) compared to sin(Bx)

    you can calculate it most easily at the origin because \sin(Bx) passes through (0,0) for all B. The value of \sin(B[x-c]) can be found by where it intersects the x axis (ie: y=0). For example if C=45 degrees then \sin(Bx-C) will be shifted to the right by 45 degrees compared to \sin(Bx)

    Post 2 shows the mathematical representation

    Edit: In case a picture helps:
    Attached Thumbnails Attached Thumbnails General formula for Sine functions?-snappy.png  
    Last edited by e^(i*pi); February 26th 2011 at 01:02 PM.
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  10. #10
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    Ah, I see. So the easiest way would be to find where the point that passed the origin is, and see how far has it gone from origin after all the shifts. Thank you.
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