Average rate of change of the area of the triangle?

[alaa amed]

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]

 

[Ray Vickson]

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.