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3. (a) (10 points) Find the arclength of the curve 2 = 2 + sin(t), y = cos(t) for t from 0 to 27. (b) (10 points) Find the surface area of the surface of revolution generated by rotating this curve around the y axis. What shape in 3D is this? 9

2 sin(t) 5. Two loops of a helix of radius T = 2 can be parameterized by r(t) 2 cos(t) for 0 <t<41. t (a) (10 points) Determine the arc-length L of this curve. (b) (5 points) Show that the tangent vector to this curve is always at a constant angle with the z axis. (C) (5 points) Find the curvature of this curve. Use this to find the curvature of a circle.