A parameterization of the möbius-strip is given by :
$$\begin{align}M=\{ (x,y,z) \in \mathbb R^3: x &= \cos t(1+ s\cos(t/2)),\\ y &= \sin t(1+ s\cos(t/2)),\\ z &= s\sin(t/2), \\ t &\in[0,2π],s \in (−1/2,1/2) \}\end{align}$$
Given the parametrization of the möbius strip I need to find two charts that cover $M$. Can someone give me a hint on how to find those $2$ charts ? Is it possible to restric the parameters t and s so that two charts cover the manifold ? My problem is with the $t=0 , \pi\; $I could choose $(0,2\pi)\times(\frac{-1}{2};\frac{1}{2})\; $ for the first chart but how do I cover the edge at $t=0,\pi \;$ with the second chart.