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Average rate of change of the area of the triangle?

  • Thread starter alaa amed
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Homework Statement


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


Homework Equations


a(t) = 1/sin2t

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! [/B]
 

Answers and Replies

  • #2
Ray Vickson
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Homework Statement


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


Homework Equations


a(t) = 1/sin2t

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! [/B]
Show your work.
 

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