Answer
$-1$
Work Step by Step
Since the trigonometric function $\sin$ is an odd function, we can write
$f(-\theta)=-f(\theta) \implies \sin ({-40^\circ})=-\sin (40^\circ)$.
Therefore, $\dfrac{\sin (-40^\circ)}{\sin (40^\circ) }=\dfrac{-\sin (40^\circ)}{\sin (40^\circ) } \\=-1$
