MATH 09C – HW 10 - PARAMETRIC EQUATIONS –PAOLO MANTERODue to Friday 03/14/2014This is the last hw assignment for Math 09C. Since the material of the last sec-tion is covered only on Wednesday 03/12, all the problems of that section are bonusproblems.Thanks for a nice quarter together, and good luck with your finals!Exercise 1.Sketch and identify the curves defined by the parametric equations.Also, iftis interpreted as time and starts fromt= 0, describe how the objectmoves on each curve:(1)x=t+ 2,y=t2.(2)x= 2 cos(t),y= 5 sin(t).(3)x= cos(t),y= cos3(t).(4)x=-cos(t),y=-sin(t), where0t⇡.(5)x=-cos(t),y= sin(t), where0t⇡.(6)x= sin(t),y= cos(t), where0t⇡.(7)x= sin(t),y=-cos(t), where0t⇡.Exercise 2(Similar to Sample Exam 3, Problem 9).A wheel of radius4rollsalong a straight line, say thex-axis. A point on the rim of the wheel will trace outa curve, called acycloid. Assume the point starts at the origin; find parametricequations for the curve (provide work).What is the equation of the tangent line att=⇡/6?Exercise 3.