A carnival ride has a large rotating arm with diameter 44 feet centered 36 feet off the ground. At each end of the large arm are two smaller rotating arms with diameter 20 feet each. The larger arm rotates once every 8 seconds, while the smaller arms rotate once every 2 seconds. Suppose that you board the ride when the point $P$ is closest to the ground. Find parametric equations for your position over time (with the origin at ground level at the center of the ride).
$x(t) =$
$y(t) =$

Hint: