1. Вычислите: а) \(\sin\frac{9\pi}{4}\); б) \(\cos\left(-\frac{4\pi}{3}\right)\); в) \(\operatorname{tg}\left(-\frac{7\pi}{6}\right)\); г) \(\operatorname{ctg}\frac{5\pi}{4}\).

1. \(\sin\frac{9\pi}{4}=\sin\left(2\pi+\frac{\pi}{4}\right)=\frac{\sqrt2}{2}\).
2. \(\cos\left(-\frac{4\pi}{3}\right)=\cos\frac{4\pi}{3}=-\frac12\).
3. \(\operatorname{tg}\left(-\frac{7\pi}{6}\right)=\operatorname{tg}\left(-\frac{\pi}{6}\right)=-\frac{\sqrt3}{3}\).
4. \(\operatorname{ctg}\frac{5\pi}{4}=1\).

Ответ: а) \(\frac{\sqrt2}{2}\); б) \(-\frac12\); в) \(-\frac{\sqrt3}{3}\); г) \(1\).