13.7. Вычислите: а) tg(5π/4); б) ctg(4π/3); в) tg(5π/6); г) ctg(7π/4).

1. а) \(\operatorname{tg}\frac{5\pi}{4}=\operatorname{tg}(\pi+\frac{\pi}{4})=1\).
2. б) \(\operatorname{ctg}\frac{4\pi}{3}=\frac{\cos(4\pi/3)}{\sin(4\pi/3)}=\frac{-1/2}{-\sqrt3/2}=\frac{\sqrt3}{3}\).
3. в) \(\operatorname{tg}\frac{5\pi}{6}=\operatorname{tg}(\pi-\frac{\pi}{6})=-\frac{\sqrt3}{3}\).
4. г) \(\operatorname{ctg}\frac{7\pi}{4}=\frac{\cos(7\pi/4)}{\sin(7\pi/4)}=\frac{\sqrt2/2}{-\sqrt2/2}=-1\).

Ответ: а) 1; б) \(\frac{\sqrt3}{3}\); в) \(-\frac{\sqrt3}{3}\); г) −1.