# How do you simplify the expression sin(arctan(x/5)) ?

Jun 20, 2016

$\pm \frac{x}{\sqrt{{x}^{2} + 25}}$.

#### Explanation:

Let $a = a r c \tan \left(\frac{x}{5}\right)$.

Then, $\tan a = \frac{x}{5} \ge < 0$ according as x>=<0#

Befittingly, the quadrant for a has to be chosen.

So, the given expression $= \sin a = \pm \frac{x}{\sqrt{{x}^{2} + 25}}$.