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

$\sin \left(\arctan x\right) = \frac{x}{\pm \sqrt{{x}^{2} + 1}}$

#### Explanation:

The solution:

$\arctan x$ is an angle whose tangent function $= \frac{x}{1}$

Considering the sides of the right triangle. We have opposite side $= x$, adjacent side $= 1$ and hypotenuse $= \sqrt{{x}^{2} + 1}$

Therefore the sine of this angle $= \left(\text{opposite side")/("hypotenuse}\right) = \frac{x}{\sqrt{{x}^{2} + 1}}$

God bless....I hope the explanation is useful.