= Solution
For $r=0$, the <equilibrium points> satisfy $\sin x=0$, so $x_k=k\pi$ for every integer $k$. The derivative of the vector field is $f'(x_k)=-\cos(k\pi)=-(-1)^k$. Thus
$$
\boxed{x=2k\pi\text{ is attracting},\qquad x=(2k+1)\pi\text{ is repelling}.}
$$
Between an odd multiple and the next even multiple the sine is negative, so the flow points right; between that even multiple and the next odd multiple it points left. A compact phase-line sketch is
$$
(2k-1)\pi\quad\longrightarrow\quad 2k\pi\quad\longleftarrow\quad(2k+1)\pi.
$$
Every initial condition strictly between two adjacent repelling points approaches the even multiple between them. The repelling equilibria themselves remain fixed if initialized exactly there.
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