Q2. For the parametric curve given by x = t + sin 2t, y = cos 2t, (i) calculate the derivatives dy and dx da-2 ' (ii) find equations of all vertical and horizontal tangent lines to this curve in Cartesian coordinates, (iii) sketch the curve, vertical and horizontal tangent lines. Q3. The curve is given by r = 1 - 2 sind. (i) Sketch the curve. (ii) Describe how you trace this curve while e is changing from 0 to (enter here the smallest angle that allows to trace the whole curve only once). (iii) Find the area of the region bounded by the inner loop of the curve r = 1 - 2 sind. Q4. Calculate the exact length of the curve r = cost (9) . Hint: find first the interval for 0, for which the curve is traced exactly once