نکته: $\tan (2\pi +\alpha )=\tan \alpha ,\tan (-\alpha )=-\tan \alpha $ نکته: $\operatorname{Sin}(\pi +\alpha )=-\operatorname{Sin}\alpha ,\operatorname{Sin}(-\alpha )=-\operatorname{Sin}\alpha $ مقدار خواسته شده برابر است با: $\frac{\tan \frac{5\pi }{3}}{\operatorname{Sin}(\frac{-7\pi }{6})}=\frac{\tan (2\pi -\frac{\pi }{3})}{-\operatorname{Sin}\frac{7\pi }{6}}=\frac{-\tan \frac{\pi }{3}}{-\operatorname{Sin}(\pi +\frac{\pi }{6})}=\frac{-\tan \frac{\pi }{3}}{-(-\operatorname{Sin}\frac{\pi }{6})}=\frac{-\sqrt{3}}{\frac{1}{2}}=-2\sqrt{3}$