Using the identity cos 20 = 1-2 sin0, find [sined0. y 1 Figure 4 Figure 4...

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Using the identity cos 20 = 1-2 sin²0, find [sin²ed0. y 1 Figure 4 Figure 4 shows part of the curve C with parametric equations x = tan 0, y = 2 sin 20, 0 < 0 < 2 where k is a constant. 1 The finite shaded region S shown in Figure 4 is bounded by C, the line x = C and the x-axis. This shaded region is rotated through 27 radians about the x-axis to form a solid of revolution. (b) Show that the volume of the solid of revolution formed is given by the integral k sin ²0 de 0 (2) (5) (c) Hence find the exact value for this volume, giving your answer in the form pn²+ qn √3, where p and q are constants. (3) Using the identity cos 20 = 1-2 sin²0, find [sin²ed0. y 1 Figure 4 Figure 4 shows part of the curve C with parametric equations x = tan 0, y = 2 sin 20, 0 < 0 < 2 where k is a constant. 1 The finite shaded region S shown in Figure 4 is bounded by C, the line x = C and the x-axis. This shaded region is rotated through 27 radians about the x-axis to form a solid of revolution. (b) Show that the volume of the solid of revolution formed is given by the integral k sin ²0 de 0 (2) (5) (c) Hence find the exact value for this volume, giving your answer in the form pn²+ qn √3, where p and q are constants. (3)

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