$\"\"$

(a).

The hypocycloid is a curve defined by the parametric equations.

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

Graph:

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

$\"\"$

(b)

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

$\"\"$ and $\"\"$ .

Trigonometric identity: $\"\"$ .

$\"\"$

The rectangular equation is $\"\"$ .

$\"\"$

(a)

Graph of the curve is

$\"\"$

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