A discrete-time sinusoidal signal can be represented by the following function:
$\forall n \in \mathbb{Z}, x(n) = \sin(\omega n)$
$x: \mathbb{Z} \rightarrow [-1,1] $
Where $\omega$ is the angular frequency (in rad/s) that is related to the frequency $f$ (in Hz or samples per second) by:
$ \omega = 2 \pi f$
and with the [[fundamental period]]:
$ \omega = \frac{2 \pi}{N_0} $