Chapter 11: Parametric Equations and Polar Coordinates - Section 11.1 - Parametrizations of Plane Curves - Exercises 11.1 - Page 647: 30

$x=a \cos \dfrac{l}{a}; y= a\sin \dfrac{l}{a}$; $0\leq l \leq 2a\pi$

The arc length of a circle is defined as: $l= a \theta$ $\implies \theta=\dfrac{l}{a}$ Now, the parametric $x=a \cos \theta; y= a\sin \theta$; $0\leq \theta \leq 2 \pi$ are: $x=a \cos \dfrac{l}{a}; y= a\sin \dfrac{l}{a}$; $0\leq l \leq 2a\pi$