27) tg 630° + sin 420°; 28) ctg 120° + cos(-600°)

Решение:

1. \( \operatorname{tg}(630^{\circ}) + \sin(420^{\circ}) = \operatorname{tg}(630^{\circ} - 360^{\circ}) + \sin(420^{\circ} - 360^{\circ}) = \operatorname{tg}(270^{\circ}) + \sin(60^{\circ}) \). \( \operatorname{tg}(270^{\circ}) \) не определён.
2. \( \operatorname{ctg}(120^{\circ}) + \cos(-600^{\circ}) = -\operatorname{ctg}(60^{\circ}) + \cos(600^{\circ}) = -\frac{\sqrt{3}}{3} + \cos(600^{\circ} - 360^{\circ}) = -\frac{\sqrt{3}}{3} + \cos(240^{\circ}) = -\frac{\sqrt{3}}{3} + \cos(180^{\circ} + 60^{\circ}) = -\frac{\sqrt{3}}{3} - \cos(60^{\circ}) = -\frac{\sqrt{3}}{3} - \frac{1}{2} \)

Ответ: 27) Не определено; 28) -√3/3 - 1/2.