Because those sinusoidal waves are merely projections (in the real and complex plane) of the true elemental component of the FT, the complex exponential, which is really a helix: http://m.eet.com/media/1068017/lyons_pt2_3.gif

A while ago I made some drafts for a series of diagrams to help visualize this (http://imgur.com/vEcnVdn) but unfortunately never got around to finish it (https://en.wikipedia.org/wiki/Wikipedia:Graphics_Lab/Illustr...).

Anyway, for those who find it easier to think of sinusoidal curves, the animation in the Wikipedia article (https://commons.wikimedia.org/wiki/File:Fourier_transform_ti...) is a very good visualization (also, BetterExplained's rant on sines being explained as circles may resonate: http://betterexplained.com/articles/intuitive-understanding-...)