A1.5 The curve x = at - a sint and y = a - a cost where t 2 0 is a cycloid; this represents the motion of a point on the rim of a rotating wheel. (i) Show that dy sin t = cot dx 1 - cost [3] (ii) Show that the length along the curve from the point (x(0), y(0)) = (0, 0) to the point (a (7), y( TT)) = (an, 2a) is 4a. [2]