11864 11 The graphs of the curves y = sin 2x and y = cos 2x are shown in Fig. 3 below. The curves intersect at the points A and B. 0 −1 B x y 1 R 3π 4 π 2 π 4 A Fig. 3 (i) Show that the x-coordinates of A and B are π 8 and 5π 8 [4] [Turn over 11864 The top section of a trophy is a flat metal sheet modelled in the shape of the shaded region R. (ii) Calculate the area of this region. [6] 11864 A circle has the equation x2 + y2 = 4 The base of the trophy can be modelled as the solid formed when the area bounded by this circle, the y-axis and the line x = 1 is rotated through 2π radians about the x-axis. (iii) Find the exact volume of the trophy base. [6] [Turn over 11864