Let be $$ γ(t) = (a(t−sin t), a(1−cost)). $$ Consider $γ : [0, 4π] → \mathbb R^2$. I want to show that $γ(t)$ is piecewise smooth.
I know that $γ'(t)= (a(1-cos(t)), asen(t))$, and $γ'(t)$ is continous for all $t$
I know that $γ(t)$ is not smooth, because $γ'(t)$ is $0$ for $t=2\pi,0,4\pi$
But how do I find a partition P that $γ(t): [t_{i-1},t_i]$ be smooth.