Chapter 8 - Section 8.4 - Plane Curves and Parametric Equations - 8.4 Exercises - Page 617: 18

(a) See the graph (b) $x^2+y^2=1$

(a) $cos~0=1$ and $sin~0=0$ $cos~\frac{\pi}{2}=0$ and $sin~\frac{\pi}{2}=1$ $cos~\pi=-1$ and $sin~\pi=0$ $cos~\frac{3\pi}{2}=0$ and $sin~\frac{3\pi}{2}=-1$ $cos~2\pi=1$ and $sin~2\pi=0$ The curve moves counterclockwise. (b) $x=cos~2t~~$ ($-1\leq x\leq1$) $x^2=cos^22t$ $y=sin~2t$ $y^2=sin^22t$ $cos^22t+sin^22t=1$ $x^2+y^2=1$