Chapter 6, Problem 15PS

(a)

To determine

To graph: The hypocycloid with parametric equations $x=\left(a-b\right)\cos t+b\cos \left(\frac{a-b}{b}t\right)$ and $y=\left(a-b\right)\sin t-b\sin \left(\frac{a-b}{b}t\right)$ with graphing utility for the pair of values $a=2,b=1$.

(b)

To determine

To graph: The hypocycloid with parametric equations $x=\left(a-b\right)\cos t+b\cos \left(\frac{a-b}{b}t\right)$ and $y=\left(a-b\right)\sin t-b\sin \left(\frac{a-b}{b}t\right)$ with graphing utility for the pair of values $a=3,b=1$.

(c)

To determine

To graph: The hypocycloid with parametric equations $x=\left(a-b\right)\cos t+b\cos \left(\frac{a-b}{b}t\right)$ and $y=\left(a-b\right)\sin t-b\sin \left(\frac{a-b}{b}t\right)$ with graphing utility for the pair of values $a=4,b=1$.

(d)

To determine

To graph: The hypocycloid with parametric equations $x=\left(a-b\right)\cos t+b\cos \left(\frac{a-b}{b}t\right)$ and $y=\left(a-b\right)\sin t-b\sin \left(\frac{a-b}{b}t\right)$ with graphing utility for the pair of values $a=10,b=1$.

(e)

To determine

To graph: The hypocycloid with parametric equations $x=\left(a-b\right)\cos t+b\cos \left(\frac{a-b}{b}t\right)$ and $y=\left(a-b\right)\sin t-b\sin \left(\frac{a-b}{b}t\right)$ with graphing utility for the pair of values $a=3,b=2$.

(f)

To determine

To graph: The hypocycloid with parametric equations $x=\left(a-b\right)\cos t+b\cos \left(\frac{a-b}{b}t\right)$ and $y=\left(a-b\right)\sin t-b\sin \left(\frac{a-b}{b}t\right)$ with graphing utility for the pair of values $a=4,b=3$.