8. Arc Length. When a wheel of radius b rolls around the outside of a circle of radius \( a \), a point on the wheel traces a curve called an epicycloid:
\[
\begin{array}{ll}
x=(a+b) \cos (t)-b \cos \left(\frac{a+b}{b} t\right) & \\
y=(a+b) \sin (t)-b \sin \left(\frac{a+b}{b} t\right) & 0 \leq t \leq 2 b \pi
\end{array}
\]
Desmos
Find the arc length of the epicycloid with \( a=5 \) and \( b=1 \). Show all your steps!
ARC LENGTH:
WORK: