# How do you evaluate cos ((11pi)/8) using the half angle formula?

Jul 29, 2016

First lets convert radian measure into degrees.
$\frac{11 \cdot \pi}{8} = 110$ degrees (its not mandatory ,but i feel comfortable in degrees than to solve in radians,so i converted.)

#### Explanation:

$\cos \left(110\right)$
$\implies \cos \left(90 + 30\right)$
$\implies \cos 90 \cos 30 - \sin 90 \sin 30$ (Applying the identity of cos(a+b))
$\implies \left(1 \cdot \frac{\sqrt{3}}{2}\right) - \left(0 \cdot \frac{1}{2}\right)$
$\implies \cos \left(110\right) = \frac{\sqrt{3}}{2}$
$\mathmr{and}$
$\implies \cos \left(\frac{11 \cdot \pi}{8}\right) = \frac{\sqrt{3}}{2}$