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Calculus - find average rate of change of the function over a given interval

  1. Oct 6, 2009 #1
    Calculus - plz help find average rate of change of the function over a given interval

    1. The problem statement, all variables and given/known data


    h(t) = sin t, [3pi/4,4pi/3]

    plz help me solve this, try to give me an explanation on every step plz. i checked but i can't find anything on this in the book. i am basically having problem with this because of the sin.



    13z31z.jpg

    2. Relevant equations



    3. The attempt at a solution
    25z5w9l.gif
    i got to there also but i dont know how to solve the sin part. how does the square root come in.
     
  2. jcsd
  3. Oct 6, 2009 #2

    Mark44

    Staff: Mentor

    Re: Calculus - plz help find average rate of change of the function over a given inte

    Do you know sin([itex]\pi/3[/itex]) = sin(60 deg.)?
    Do you know sin([itex]\pi/4[/itex]) = sin(45 deg.)?
    The sines of these angles are numerically equal to the sines, respectively, of the two angles you showed. There are a few angles whose sine, cosine, and tangent you should memorize.
     
    Last edited: Oct 6, 2009
  4. Oct 6, 2009 #3
    Re: Calculus - plz help find average rate of change of the function over a given inte

    [sin(4π/3) - sin(3π/4)] / (4π/3 - 3π/4)
    = (-√3/2 - √2/2) / (7π/12)
    = -6(√3 - √2) / (7π)

    this is what i got but its none of the 4 multiple choice answers. whats wrong in here?
     
  5. Oct 6, 2009 #4

    Office_Shredder

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    Staff Emeritus
    Science Advisor
    Gold Member

    Re: Calculus - plz help find average rate of change of the function over a given inte

    Your last line should be -6(√3+√2)/(7π)

    You didn't factor the - sign properly
     
  6. Oct 6, 2009 #5
    Re: Calculus - plz help find average rate of change of the function over a given inte

    Thank you very much. but if you guyz can plz explain a lil clearly to me how do u go from this step : (-√3/2 - √2/2) / (7π/12))
    to this:
    = -6(√3 - √2) / (7π)
     
  7. Oct 6, 2009 #6

    Mark44

    Staff: Mentor

    Re: Calculus - plz help find average rate of change of the function over a given inte

    (-√3/2 - √2/2) / (7π/12)) = -1/2(√3 + √2) * 12/(7π) = -6(√3 + √2)/(7π)

    BTW, my earlier post was slightly off: sin(π/3) = -sin(4π/3). Looks like you caught that.
     
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