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Math Help - Rate of change of area of triangle.

  1. #1
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    Rate of change of area of triangle.

    the included angle of the two sides of constant equal lenght s of an isosceles triangle is theta. the area is given by A=(1/2)s^2sin(theta)
    if theta is increasing at the rate of (1/2) radian per minute, find the rates of change of the area when theta =pi/6 and theta=pi/3.


    Please dont tell do my homework this is emergency!! university depends on this question so please i plead you to help me out here
    Last edited by mr fantastic; October 23rd 2009 at 03:05 AM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by asadc12 View Post
    the included angle of the two sides of constant equal lenght s of an isosceles triangle is theta. the area is given by A=(1/2)s^2sin(theta)
    if theta is increasing at the rate of (1/2) radian per minute, find the rates of change of the area when theta =pi/6 and theta=pi/3.


    Please dont tell do my homework this is emergency!! university depends on this question so please i plead you to help me out here
    A' = (1/2)s^2*cos(theta)*theta' = s^2cos(theta)/4.
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  3. #3
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    differentiate 1/2 s^2

    f A=1/2 s^2 sin(theta)

    why are you only differentiating sin theta?
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  4. #4
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    Quote Originally Posted by asadc12 View Post
    differentiate 1/2 s^2

    f A=1/2 s^2 sin(theta)

    why are you only differentiating sin theta?
    The other factors are constants.
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  5. #5
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    doens't the derivative of a constant = 0?

    please help me out here
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  6. #6
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    know how to do this, except for one part:

    A=(1/2)s^2sin(theta)
    dA/dt=(1/2)s^2cos(theta)(d(theta)/dt)
    =(1/4)s^2cos(theta)

    When theta = pi/6, cos(theta)=sqrt(3)/2
    and dA/dt=(1/8)s^2sqrt(3)

    When theta = pi/3, cos(theta)=1/2
    and dA/dt=(1/8)s^2

    those are the correct answers, however i can't for the life of me figure out WHY 1s^2/2 was not differentiated
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  7. #7
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    Quote Originally Posted by asadc12 View Post
    doens't the derivative of a constant = 0?

    please help me out here
    The derivative of a constant times a function equals the constant times the derivative.
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