8.36. а) tgα=0 б) tgα=1 в) tgα=-1 г) tgα=√3 д) tgα=-√3 е) tgα=√3/3 ж) tgα=-√3/3 з) tgα=2 и) tgα=-3 к) tgα=5 л) tgα=1/2 м) tgα=-1/3

Решим тригонометрические уравнения:

1. $$tg \alpha = 0$$ $$\alpha = \pi n, n \in Z$$
2. $$tg \alpha = 1$$ $$\alpha = \frac{\pi}{4} + \pi n, n \in Z$$
3. $$tg \alpha = -1$$ $$\alpha = -\frac{\pi}{4} + \pi n, n \in Z$$
4. $$tg \alpha = \sqrt{3}$$ $$\alpha = \frac{\pi}{3} + \pi n, n \in Z$$
5. $$tg \alpha = -\sqrt{3}$$ $$\alpha = -\frac{\pi}{3} + \pi n, n \in Z$$
6. $$tg \alpha = \frac{\sqrt{3}}{3}$$ $$\alpha = \frac{\pi}{6} + \pi n, n \in Z$$
7. $$tg \alpha = -\frac{\sqrt{3}}{3}$$ $$\alpha = -\frac{\pi}{6} + \pi n, n \in Z$$
8. $$tg \alpha = 2$$ $$\alpha = arctg 2 + \pi n, n \in Z$$
9. $$tg \alpha = -3$$ $$\alpha = arctg (-3) + \pi n, n \in Z$$ $$\alpha = - arctg (3) + \pi n, n \in Z$$
10. $$tg \alpha = 5$$ $$\alpha = arctg 5 + \pi n, n \in Z$$
11. $$tg \alpha = \frac{1}{2}$$ $$\alpha = arctg \frac{1}{2} + \pi n, n \in Z$$
12. $$tg \alpha = -\frac{1}{3}$$ $$\alpha = - arctg \frac{1}{3} + \pi n, n \in Z$$

Ответ: смотри выше.