Вычислите: arcsin \frac{\sqrt{3}}{2} + arcsin (-\frac{1}{2}).

Решаем:

1. arcsin\[\frac{\sqrt{3}}{2}\] = \(\frac{\pi}{3}\) (или 60°)
2. arcsin\[(-\frac{1}{2})\] = \(-\frac{\pi}{6}\) (или -30°)
3. Суммируем: \(\frac{\pi}{3} + (-\frac{\pi}{6}) = \frac{\pi}{3} - \frac{\pi}{6} = \frac{2\pi - \pi}{6} = \frac{\pi}{6}\)

Ответ: \(\frac{\pi}{6}\)