A 1D sinusoidal wave, time dependent, is described by the next formula:
y(t) = A\sin(2\pi f t + \phi)
The trick here is just the concept. When you use the formula $A\sin(\theta) $ you aren't specifying if $\theta$ is time-dependent and you are not thinking in the formula as a wave, but as a mere function. But when you use the argument $2\pi f t$ you are considering the angular frequency $2\pi f$ ($rad/s$), where $ f $ is the normal frequency, and the wave's phase $\phi$ (which represents a shift in the wave).
If you are working with a simple sine wave, you can assume a zero-shift, $\phi = 0$, and select a working frequency. Sample the wave and work normally with your DSP.
I hope it helps!
You can check sine wave description in WIKI