Answer
The sign in front of $\omega$ is negative.
Work Step by Step
$y(x, t) = (y_m) sin(kx \pm \omega t)$
$y(10~cm, t) = (5.0~cm) sin[1.0 - (4.0~s^{-1}) t]$
In the term $~~sin[1.0 - (4.0~s^{-1}) t]~~$ we can see that $\omega = (4.0~s^{-1})$ and the sign in front of $\omega$ is negative.
