Answer Happy

1.1. The formulas x = t - sint, y = 1 – cost (t € R) parametrize a plane curve. Graph this curve. You may use software and turn in computer output. Also include a few tangent lines at judiciously chosen points. (E.g. find all tangent lines with slope 0, +1, and ...) To compute tangent lines, recall that the tangent vector at a point (x, y) of the curve has components dx/dt and dy/dt. In your plot, identify all points where the curve is not a manifold. 1.2. Same questions as in Exercise 1.1 for the parametrized curve x = 3t/(1 + 13), y = 3t2/(1+13), where 0 < t < 00. 1.3. Parametrize in Cartesian coordinates the space curve wrapped around the cone shown in Section 1.1.