Given the parametrized curve r(u) = a cos u(1 ? cos u)ˆi + a sinu(1 ? cos u)ˆj, u ? [0, 2? [ , (with a being a constant)
i) Sketch the curve (e.g. by constructing a table of values orsome other method)
ii) Find the tangent vector r 0 (u). What is the tangent vectorat u = 0? And at u = 2?? Explain your result.
iii) Is the curve regularly parametrized? Motivate your answerusing the definition.
iv) Compute the length of the arc corresponding to the interval[0, ?/2].
