What are some examples of sets of data which can be modelled by a sinusoidal function?
Would tidal waves be a good example? What else can be modelled by it?
Tidal waves are solitary waves and not pure sinusoids. However they can be modelled as a superposition of sinusoids (as can any well behaved waveform - this is harmonic analysis).
You might consider the level of the tide or daily temprature.
That are are periodic can be modeled by sines and cosines. But the more you use the better. In fact anything (in real life math) can be expressed just in terms of sines and cosines (possibly infinitely many times).