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Average rate of change of the area of the triangle?

  1. Jul 1, 2016 #1
    1. The problem statement, all variables and given/known data
    An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location at time t is P(t)=(cos(t),sin(t)) . Assume 0 < t < π/2. At a given time t, the tangent line to the unit circle at the position P(t) will determine a right triangle in the first quadrant. (Connect the origin with the y-intercept and x-intercept of the tangent line.)

    The average rate of change of the area of the triangle on the time interval [π/6,π/4] is


    2. Relevant equations
    a(t) = 1/sin2t

    3. The attempt at a solution
    I tried plugging in the π/6 once and π/4, added them together and divided by 2, but I got the wrong answer!
     
  2. jcsd
  3. Jul 1, 2016 #2

    Ray Vickson

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    Show your work.
     
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