Chapter 8 - Section 8.4 - Plane Curves and Parametric Equations - 8.4 Exercises - Page 617: 16

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

(a) $x=sin^2t$ and $y=cos~t$ are periodic functions. The maximum value of $cos~t$ is $1$ and the minimum is $-1$. In these points $y=cos~t$ change the directions. That is, $x$ and $y$ move back and forth from $(0,-1)$ to $(0,1)$. (b) $y=cos~t$ $y^2=cos^2t$ $x=sin^2t$ $sin^2t+cos^2t=1$ $x+y^2=1$