# How do you simplify the expression sin(arctan(2))?

Nov 19, 2016

$\sin \left(\arctan \left(2\right)\right)$ does not exist.

#### Explanation:

$\sin \left(\arctan \left(2\right)\right) = \theta$,

then $\sin \theta = \tan 2$, where angle $2$ is in radians.

As $2$ is in radians and it is less than $\frac{3 \pi}{4} = 2.356$

Hence $\tan 2 < \tan \left(\frac{3 \pi}{4}\right)$ i.e. $\tan 2 < - 1$

Therefore $\sin \theta < - 1$,

but this is not possible.

Hence, $\sin \left(\arctan \left(2\right)\right)$ does not exist.