(solution) An object is moving around the unit circle with parametric

(solution) An object is moving around the unit circle with parametric

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 < ?/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