Mathematically, a sine represents the circular angle of a unit circle in a Cartesian coordinate system. The circle angle has the length "x" in such a coordinate system, it starts at 0, becomes positive up to its maximum "1", falls again to "0" and then goes into the negative maximum and ends at "0".
As a sine signal, it is a harmonic-free oscillation that moves uniformly around zero. The time function of the sine signal results from the sine function of the ratio of the relative time (t) to the period (T) multiplied by 2Pi: sin(2Pi x t/T). The spectral representation of a sine signal corresponds to a single spectral line at the sine frequency.
Sine signals are generated by oscillators and function generators.