1. A cycloid arch is described by the parametric equations x = a(t − sint) and y =
a(1 − cost), where 0 ≤ t ≤ 2π.
(1) Find the area A enclosed by one arch of the cycloid and the x-axis.
(2) Find the surface area Ax formed when one arch of the cycloid is rotated about
the x-axis.
(1)
(2)
2
2
2
2. Find the arc length of the astroid curve 𝑥 3 + 𝑦 3 = 𝑎3 .
3. Convert the equation r = 3sinθ into Cartesian coordinates, and then plot the
graph of this equation.
4. Find the area inside cardioid r = 1 + cosθ and outside the circle r = 1.