# How do you simplify the expression sin(arctan(3/4))?

Jun 12, 2016

Using the formula $\sin \left(\arctan \left(x\right)\right) = \frac{x}{\sqrt{1 + {x}^{2}}}$.

#### Explanation:

We have the equation

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

$\sin \left(\arctan \left(\frac{3}{4}\right)\right) = \frac{\frac{3}{4}}{\sqrt{1 + \frac{3}{4}}}$
$= \frac{3}{4 \sqrt{\frac{7}{4}}}$
$= \frac{3}{2 \sqrt{7}}$.