Q1. For the following parametric equations, (a) x = cost, y = 1 - sint, 0

QI. Q2. Q4. For the following parametric equations, (b) = cos t, y 1 sin t, O < t < 2' ) a: t2+t,y t2 (i) sketch the curve, (ii) convert the parametric equations of a curve into the Cartesian (rectangular) form, (iii) indicate the orientation of the curve, that is, the direction that a point moves on the curve as t is increasing. For the parametric curve given by = t + sin 2t, y = cos 2t, dy 012 y (i) calculate the derivatives and d'X2 (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. The curve is given by r 1 2 sin 9. (i) Sketch the curve. (ii) Describe how you trace this curve while O is changing from O 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 sin O. ) Calculate the exact length of the curve r cos Hint: find first the interval for 9, for which the curve is traced exactly once.