Question

Find the values of the following trigonometric ratio:

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

 

Answer 1

 We have: 

\[\cos\frac{19\pi}{6} = \cos 570^\circ\]

\[570^\circ = \left( 90^\circ \times 6 + 30^\circ \right)\]

\[ 570^\circ\text{ lies in the third quadrant in which the cosine function is negative .} \]

Also, 6 is an odd integer.

\[ \therefore \cos\left( 570^\circ \right) = \cos \left( 90^\circ \times 6 + 30^\circ \right) = - \cos \left( 30^\circ \right) = - \frac{\sqrt{3}}{2}\]