An object is moving around the unit circle so its x and y coordinates change with time as x=cos(t) and y=sin(t). Assume 0 /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 as shown where two corners are at the x and y intercepts and the third one is at the origin. (Note that both the point and the slope of the tangent line you need for the line equation will depend on t.) The identity sin(2t)=2sin(t)cost(t) might be useful in some parts of this question. (a) The area of the right triangle is a(t)= (b) lim a(t)= t - pi/2 (c) lim a(t)= t - 0* (d) lim t - pil a(t) =(e) With our restriction on t, the smallest t so that a(t)=2 is (f) With our restriction on t, the largest t so that a(t)=2 is (g) The average rate of change of the area of the triangle on the time interval [7/6,7/4] is (g) The average rate of change of the area of the triangle on the time interval [7/4,7/3] is