#### Answer

$x = cos~t$
$y = sin~t$
These parametric equations trace out the unit circle in the counterclockwise direction.
$x = cos~t$
$y = -sin~t$
These parametric equations trace out the unit circle in the clockwise direction.

#### Work Step by Step

$x = cos~t$
$y = sin~t$
When t = 0:
$x = cos~0 = 1$
$y = sin~0 = 0$
As t increases from $t = 0$ to $t = \frac{\pi}{2}$:
$x$ decreases from $x = 1$ to $x=0$
$y$ increases from $y = 0$ to $y=1$
Thus, starting from the point $(1,0)$, the points $(x,y)$ trace out the unit circle in the first quadrant as t increases from $t=0$ to $t = \frac{\pi}{2}$. This means that the unit circle is being traced in the counterclockwise direction.
$x = cos~t$
$y = -sin~t$
When t = 0:
$x = cos~0 = 1$
$y = -sin~0 = 0$
As t increases from $t = 0$ to $t = \frac{\pi}{2}$:
$x$ decreases from $x = 1$ to $x=0$
$y$ decreases from $y = 0$ to $y=-1$
Thus, starting from the point $(1,0)$, the points $(x,y)$ trace out the unit circle in the fourth quadrant as t increases from $t=0$ to $t = \frac{\pi}{2}$. This means that the unit circle is being traced in the clockwise direction.