Question

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

Answer 1

`sin(arctan(-4/3))=-4/5`

Explanation:

`sin(arctan(-4/3))`

The restriction for the range of arctan x is `(-pi/2,pi/2)`. 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 `-4/5`