Let p be a point at a distance d from the center of a circle of radius r. the curve traced out by p as the circle rolls along a straight line is called a trochoid. (think of the motion of a point on a spoke of a bicycle wheel.) the cycloid is the special case of a trochoid with d = r. using the same parameter θ as for the cycloid and, assuming the line is the x-axis and θ = 0 when p is at one of its lowest points, show that parametric equations of the trochoid are x=rθ-d sin θ , y = r - d cos θ. sketch the trochoid for the cases d < r and d > r.