已知 $\alpha$ 是第二象限角, 且 $\cos \alpha=-\frac{12}{13}$, 则 $\tan \alpha$ 的值是 $(\quad)$
$\because \alpha$ 为第二象限角, $\therefore \sin \alpha=\sqrt{1-\cos ^{2} \alpha}=\sqrt{1-\left(-\frac{12}{13}\right)^{2}}=\frac{5}{13}, \therefore \tan \alpha=\frac{\sin \alpha}{\cos \alpha}=\frac{\frac{5}{13}}{-\frac{12}{13}}=-\frac{5}{12}$.

答案: D