Answer
Graph (III)
Work Step by Step
The parametric equations of a circle whose radius is $r$ are given as follows: $x=r \cos t ; y =r \sin t$
From the given problem, we have $x= \cos^2 t , y=\sin^2 t, z=t$
When the value of $t$ increases , then the value of $x$ goes from $1$ to $0$ but the value of $y$ goes from $0$ to $1$.
The value of the $x$ and $y$ are always positive an each vary from $0$ to $1$ .
Further, when $t$ changes its position then the value of $x$ goes from $0$ to $1$ but the value of $y$ is from $1$ to $0$.
This conclusion signifies the conditions indicated in the Graph (III).
