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 .

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