7) sin(-150°); 8) sin(-600°); 9) sin(5π/6); 10) sin(5π/3); 11) sin 225°

Решение:

1. \( \sin(-150^{\circ}) = -\sin(150^{\circ}) = -\sin(180^{\circ} - 30^{\circ}) = -\sin(30^{\circ}) = - \frac{1}{2} \)
2. \( \sin(-600^{\circ}) = -\sin(600^{\circ}) = -\sin(600^{\circ} - 2 \cdot 360^{\circ}) = -\sin(-120^{\circ}) = \sin(120^{\circ}) = \sin(180^{\circ} - 60^{\circ}) = \sin(60^{\circ}) = \frac{\sqrt{3}}{2} \)
3. \( \sin(\frac{5\pi}{6}) = \sin(\pi - \frac{\pi}{6}) = \sin(\frac{\pi}{6}) = \frac{1}{2} \)
4. \( \sin(\frac{5\pi}{3}) = \sin(2\pi - \frac{\pi}{3}) = -\sin(\frac{\pi}{3}) = -\frac{\sqrt{3}}{2} \)
5. \( \sin(225^{\circ}) = \sin(180^{\circ} + 45^{\circ}) = -\sin(45^{\circ}) = -\frac{\sqrt{2}}{2} \)

Ответ: 7) -1/2; 8) √3/2; 9) 1/2; 10) -√3/2; 11) -√2/2.