What makes them sine?

Ans) Fourier tells that only a sine wave has no harmonic content. The math works out that if you have any wave shape other than a sign wave, you can break it down into a parts of sine waves of dissimilar harmonic frequency, phase, and amplitude. All those harmonics go to zero when the wave shape is a pure sine. We can tell that radio waves behave like a sine, you can run them by a narrowband filter, and no energy is lost. Maxwell's equations predict propagation and fields based on a sine wave, and anything other than that propagates as if it is multiple frequencies, which do not propagate energy as well.