(a) Find the points, in rectangular coordinates, where the curve z(t) = t + v/2 cost, y(t) = 1 + sint, t [0, 2] has vertical tangents and has horizontal tangents. (b) Consider the circle 7 = a, where a > 0 is arbitrary. Find the tangent line to the circle at = /4. (c) The graph 7 = sin(48) is an 8-petalled rose. Give an interval of 8 which traces one petal of the rose. No justification is required