415. Calculate $\sin 210^{\circ}$.
Solution. Represent $210^{\circ}$ as $180^{\circ}+30^{\circ}$. Applying the $1^{\circ}$ and $2^{\circ}$ rules and considering that the angle $210^{\circ}$ ends in the III quadrant, we find

$$
\sin 210^{\circ}=\sin \left(180^{\circ}+30^{\circ}\right)=-\sin 30^{\circ}=-1 / 2
$$