Question

Find the values of the following trigonometric ratios :

\[ \tan \frac{11\pi}{6} \]

Solution

\[ \tan \frac{11\pi}{6} = \tan \left(2\pi-\frac{\pi}{6}\right) \]

Using,

\[ \tan(2\pi-\theta)=-\tan\theta \]

\[ = -\tan\frac{\pi}{6} \]

\[ = -\frac{1}{\sqrt3} = -\frac{\sqrt3}{3} \]

Answer :

\[ \boxed{ \tan\frac{11\pi}{6} = -\frac{\sqrt3}{3} } \]