Chapter 14.1, Problem 56E

52–56. Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the surface.

$r(t)=\langle (3+\cos 15t)\cos t,(3+\cos 15t)\sin t,\sin 15t\rangle$; ${\left(3-\sqrt{x^2+y^2}\right)}^2+z^2=1$ (Hint: See Example 4.)