Question

Find the value of the following trigonometric ratio :

\[ \cos \frac{19\pi}{6} \]

Solution

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

Using,

\[ \cos(2\pi+\theta)=\cos\theta \]

\[ = \cos\frac{7\pi}{6} \]

\[ = \cos\left(\pi+\frac{\pi}{6}\right) \]

Using,

\[ \cos(\pi+\theta)=-\cos\theta \]

\[ = -\cos\frac{\pi}{6} = -\frac{\sqrt3}{2} \]

Answer :

\[ \boxed{ \cos\frac{19\pi}{6} = -\frac{\sqrt3}{2} } \]