## Calculus: Early Transcendentals 8th Edition

$\bf{Graph{(III)}}$
The parametric equations of a circle having radius $r$ are; $x=r \cos t ; y =r \sin t$ Here, we have $x= \cos^2 t , y=\sin^2 t, z=t$ This shows that the $x$ and $y$ are always positive and each will vary from $0$ to $1$ and when $t$ increases the value of $x$ goes from $1$ to $0$ while $y$ goes from $0$ to $1$. When $t$ changes its position then the value of $x$ goes from $0$ to $1$ while $y$ goes from $1$ to $0$. This forms a sine wave and thus matches with $\bf{Graph{(III)}}$.