求下列各三角函数值:

(1) $\sin \left(-\frac{8 \pi}{3}\right) ;(2) \cos \frac{19 \pi}{6} ;(3) \tan \left(-855^{\circ}\right)$.



10.若 $\cos \alpha=\frac{2}{3}, \alpha$ 是第四象限角, 求

$\frac{\sin (\alpha-2 \pi)+\sin (-\alpha-3 \pi) \cos (\alpha-3 \pi)}{\cos (\pi-\alpha)-\cos (-\pi-\alpha) \cos (\alpha-4 \pi)}$ 的值.
: (1) $\sin \left(-\frac{8 \pi}{3}\right)=\sin \left(-4 \pi+\frac{4}{3} \pi\right)=\sin \frac{4}{3} \pi$

$=\sin \left(\pi+\frac{\pi}{3}\right)=-\sin \frac{\pi}{3}=-\frac{\sqrt{3}}{2}$.

(2) $\cos \frac{19 \pi}{6}=\cos \left(2 \pi+\frac{7}{6} \pi\right)=\cos \frac{7}{6} \pi=\cos \left(\pi+\frac{\pi}{6}\right)$

$=-\cos \frac{\pi}{6}=-\frac{\sqrt{3}}{2}$.

(3) $\tan \left(-855^{\circ}\right)=\tan \left(-3 \times 360^{\circ}+225^{\circ}\right)=\tan 225^{\circ}=\tan \left(180^{\circ}+45^{\circ}\right)=\tan 45^{\circ}=1$.