# How do you simplify the expression Sin(Arctan (-4/3))?

$\sin \left(\arctan \left(- \frac{4}{3}\right)\right) = - \frac{4}{5}$
$\sin \left(\arctan \left(- \frac{4}{3}\right)\right)$
The restriction for the range of arctan x is $\left(- \frac{\pi}{2} , \frac{\pi}{2}\right)$. Since the argument is negative this means that our triangle is in quadrant IV with the opposite side -4 and adjacent 3 and therefore the hypotenuse is 5. Hence the ratio of sin x from our triangle is $- \frac{4}{5}$