给出下列各函数值:

(1) $\sin \left(-1000^{\circ}\right)$; (2) $\cos \left(-2200^{\circ}\right)$; (3) $\tan (-10)$; (4) $\frac{\sin \frac{7 \pi}{10} \cos \pi}{\tan \frac{17 \pi}{9}}$. 其中符号为负的是( )
解析: $\sin \left(-1000^{\circ}\right)=\sin 80^{\circ}>0$;

$\cos \left(-2200^{\circ}\right)=\cos \left(-40^{\circ}\right)=\cos 40^{\circ}>0 ;$

$\tan (-10)=\tan (3 \pi-10)<0$;

$\frac{\sin \frac{7 \pi}{10} \cos \pi}{\tan \frac{17 \pi}{9}}=\frac{-\sin \frac{7 \pi}{10}}{\tan \frac{17 \pi}{9}}$

$\because \sin \frac{7 \pi}{10}>0, \tan \frac{17 \pi}{9}<0, \therefore$ 原式>