# How do you simplify  arctan(sin((7pi)/2))?

May 2, 2016

$\arctan \left(\sin \left(7 \frac{\pi}{2}\right)\right) = - \frac{\pi}{4}$

#### Explanation:

As $\sin \left(\frac{7 \pi}{2}\right) = \sin \left(4 \pi - \frac{\pi}{2}\right) = - \sin \left(\frac{\pi}{2}\right) = - 1$

$\arctan \left(\sin \left(7 \frac{\pi}{2}\right)\right) = \arctan \left(- 1\right)$

As $\tan \left(- \frac{\pi}{4}\right) = - 1$

$\arctan \left(- 1\right) = - \frac{\pi}{4}$

Hence $\arctan \left(\sin \left(7 \frac{\pi}{2}\right)\right) = - \frac{\pi}{4}$