$\"\"$

The parametric equations are $\"\"$ and $\"\"$ and $\"\"$ .

Rewrite the equation.

$\"\"$

The sum of there squares are equal

$\"\"$

Trigonometric identity : $\"\"$ .

$\"\"$

The above equation is in form of general form of circle.

So the particle moves in circle path.

$\"\"$

Draw a table for different values of $\"\"$ ranging from $\"\"$ .

Determine the direction of the curve.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Graph:

The parametric equations are $\"\"$ and $\"\"$

$\"\"$

Observe the graph:

From $\"\"$ to $\"\"$ , thecircle completes it first revolution in clockwise.

Similarly the ellipse completes it second and third revolution at $\"\"$ and $\"\"$ .

The particle moves counter clockwise around the circle path.

$\"\"$

The particle moves counter clockwise around the circle path.

The equation is $\"\"$ .