Consider the following first order autonomous nonlinear system

$$
\left\{
\begin{array}{c}
\cfrac{dx}{dt}=(1+y)\sin x,\\\
\cfrac{dy}{dt}=1-\cos x-y.
\end{array}\right.
$$

Consider two points $P_1(0,0)$ and $P_2(\frac{\pi}{2}, -1)$. Are they critical points of the system?