12) cos(-510°); 13) ctg(7π/6); 14) ctg 270°; 15) ctg(7π/4); 16) tg 150°

Решение:

1. \( \cos(-510^{\circ}) = \cos(510^{\circ}) = \cos(510^{\circ} - 360^{\circ}) = \cos(150^{\circ}) = \cos(180^{\circ} - 30^{\circ}) = -\cos(30^{\circ}) = -\frac{\sqrt{3}}{2} \)
2. \( \ctg(\frac{7\pi}{6}) = \ctg(\pi + \frac{\pi}{6}) = \ctg(\frac{\pi}{6}) = \sqrt{3} \)
3. \( \ctg(270^{\circ}) = 0 \)
4. \( \ctg(\frac{7\pi}{4}) = \ctg(2\pi - \frac{\pi}{4}) = -\ctg(\frac{\pi}{4}) = -1 \)
5. \( \operatorname{tg}(150^{\circ}) = \operatorname{tg}(180^{\circ} - 30^{\circ}) = -\operatorname{tg}(30^{\circ}) = -\frac{\sqrt{3}}{3} \)

Ответ: 12) -√3/2; 13) √3; 14) 0; 15) -1; 16) -√3/3.