Question

Find the values of the following trigonometric ratio:

\[\cos\frac{19\pi}{4}\]

Answer 1

We have: 

\[\cos\frac{19\pi}{4} = \cos 855^\circ\]

\[855^\circ = 90^\circ \times 9 + 45^\circ\]

\[855^\circ\text{ lies in the second quadrant in which the cosine function is negative . }\]

Also, 9 is an odd integer .

\[ \therefore \cos\left( 855^\circ \right) = \cos\left( 90^\circ \times 9 + 45^\circ \right) = - \sin\left( 45^\circ \right) = - \frac{1}{\sqrt{2}}\]