# How do you find the exact value of cos[ arctan (-4/3) - arcsin (3/5) ]?

May 24, 2016

Zero.

#### Explanation:

You may use calculator
$\tan x = - \frac{4}{3}$ --> $x = 126.86$ (or $- 53.14$)
$\sin y = \frac{3}{5}$ -->$y = {36}^{\circ} 86$
$x - y = {90}^{\circ}$

$\cos {90}^{\circ} = 0$