Chapter 11.5, Problem 72E

Closed plane curves Consider the curve r(t) = (a cos t + b sin t)i + (c cos t + d sin t)j + (e cos t + f sin t)k, where a, b, c, d, e, and f are real numbers. It can be shown that this curve lies in a plane.

72. Graph the following curve and describe it.

$\begin{array}{c}r(t)=(2\cos t+2\sin t)i+(-\cos t+2\sin t)j\\ +\text{ (}\cos t-2\sin t)k\end{array}$