An object is moving around the unit circle with parametric equationsx(t)=cos(t), y(t)=sin(t), so it's location at timetisP(t)=(cos(t),sin(t)). Assume0 < t < π/2. At a given timet, the tangent line to the unit circle at the positionP(t)will determine a right triangle in the first quadrant. (Connect the origin with they-intercept andx-intercept of the tangent line.)
The identitysin(2t)=2sin(t)cost(t)might be useful in some parts of this question.
With our restriction on t, the largest t so that a(t)=2 is