Question

Find the values of the following trigonometric ratio:

\[\cos\frac{39\pi}{4}\]

Answer 1

We have: 

\[\cos\frac{39\pi}{4} = \cos 1755^\circ\]

\[1755^\circ = 90^\circ \times 19 + 45^\circ\]

\[1755^\circ\text{ lies in the fourth quadrant in which the cosine function is positive . }\]

Also, 19 is an odd integer .

\[ \therefore \cos\left( 1755^\circ \right) = \cos\left( 90^\circ \times 19 + 45^\circ \right) = \sin \left( 45^\circ \right) = \frac{1}{\sqrt{2}}\]