$\"\"$

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

(a) Construct a table for $\"\"$ and $\"\"$ .

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$\"\"$

(b)

Graph:

(1) Draw the coordinate plane.

(2) Plot the $\"\"$ points obtained in the table.

(3) Connect the point using a smooth curve.

$\"\"$

(c)

Graph:

Graph the parametric equations $\"\"$ and $\"\"$ .

$\"\"$

(d)

Find the rectangular equation.

Consider $\"\"$ .

Squaring on both sides.

$\"\"$

$\"\"$ .

Consider $\"\"$ .

$\"\"$ .

Trigonometric property: $\"\"$ .

$\"\"$

The rectangular equation is $\"\"$ .

$\"\"$

Observe the graph:

Both the graphs seems to be similar on the interval $\"\"$ .

$\"\"$

(a)

Table:

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(b)

Graph of the parametric equations $\"\"$ and $\"\"$ connecting points $\"\"$ obtained in the table is

$\"\"$ .

(c)

Graph of the parametric equations $\"\"$ and $\"\"$ using graphing utility is

$\"\"$ .

(d) The rectangular equation is $\"\"$ .