Alternating series

$\begin{align} &S_1=\displaystyle\sum\limits_{n=1}^{\infty }{(-1)^n \sin(n+1)} \\\\ &S_2=\displaystyle\sum\limits_{n=1}^{\infty }{\sin(n+1)} \end{align}$ **Which series converges?** [[☃ radio 1]] **Based on your answer, what can we say about $S_1$?** [[☃ radio 2]]