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Math Help - sin graph troubles

  1. #1
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    Exclamation sin graph troubles

    a minimum value of a sinusoidal function is at (pi/4,3). The nearest maximum value to the right of this point is at (7pi/12,7). Determine an equation of this function
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  2. #2
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    Quote Originally Posted by nightrider456 View Post
    a minimum value of a sinusoidal function is at (pi/4,3). The nearest maximum value to the right of this point is at (7pi/12,7). Determine an equation of this function
    So 7pi/12 - pi/4 gives half the period.

    And 7-3 gives twice the amplitude, where amplitude is distance from center position to either maximum or minimum.

    So you'll want to transform \sin x as a\sin(bx)+c to fit those requirements (or you could use cosine).
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  3. #3
    Senior Member nikhil's Avatar
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    let
    f(x)=Asin(ax+b)+c
    at (pi/4,3) we have minimum value for this sin(ax+b) should be minimum that is equal to -1
    3=-A+c............................................... .....1
    at (7pi/12,7) we have maximum value for that sin(ax+b) must be maximum that is equal to 1 therfor
    7=A+c............................................. ........2
    solving equation 1 and 2 we get
    A=2
    c=5
    now
    f(x)=2sin(ax+b)+5
    we know two points that are (pi/4,3) and (7pi/12,5) using them we get
    1) 3=2sin(api/4+b)+5 or
    sin(api/4+b)=-1
    api/4+b=-pi/2.......................................3
    2) similarly for (7pi/12,7) we get
    7api/12+b=pi/2......................................4
    solving equation 3 and 4 we get
    a=3 and b=-5pi/4
    therfor
    f(x)=2sin(3x-5pi/4)+5
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