Question

Find the value of the following trigonometric ratio :

\[ \cos\left(\frac{39\pi}{4}\right) \]

Solution

\[ \cos\left(\frac{39\pi}{4}\right) = \cos\left(\frac{39\pi}{4}-8\pi\right) \]

\[ = \cos\frac{7\pi}{4} \]

\[ = \cos\left(2\pi-\frac{\pi}{4}\right) \]

Using,

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

\[ = \cos\frac{\pi}{4} = \frac{1}{\sqrt2} = \frac{\sqrt2}{2} \]

Answer :

\[ \boxed{ \cos\left(\frac{39\pi}{4}\right) = \frac{\sqrt2}{2} } \]