In order to understand the sine-wave motion in ITF Taekwon-Do you need to be familiar with two things -- (1) the Taekkyeon (aka Taekkyun) connection and (2) the Wave / Circle Principle.
1. Taekkyeon
ITF Taekwon-Do grew out of a number of martial arts; the most influential of these were Shotokan Karate and Taekkyeon. When people complain about the "bobbing" in ITF Taekwon-Do it is because they expect Taekwon-Do to look and work more like Karate. The thing is, however, that Taekkyeon also influenced Taekwon-Do greatly and it seems that General Choi (who trained in Taekkyeon as a teenager) in his later years steered ITF Taekwon-Do in a direction that applied more Taekkyeon principles. Now if you are familiar with Taekkyeon, the "bobbing" movements in ITF Taekwon-Do does not look that strange at all.
I discuss the influences of Shotokan Karate and Taekkyeon here:
http://sooshimkwan.blogspot.com/2010/09/sine-wave-motion-linear-karate-movement.html
2. Wave / Circle Principle
The sine wave motion (or as someone said, cosine wave) is actually just an icon for some greater principle --someone on this thread used the word "metaphor," to which I would agree.
"The
sine wave motion is an icon, i.e. a simplification, of the
wave principle. The
sine wave motion is almost always seen in its basic relax-up-down form; however, the
wave principle transcends this rigid confinement of three phases. The
wave principle could sometimes be seen as a reversal, for instance up-down-up; or it could be expressed horizontally, for example as left-right-left; or even cyclically. It need not have three parts, but could only involve up-down, or may oscillate numerous times. It is recognizable when boxers bob and weave, or when you naturally extend or retract a limb to maintain balance. If you understand the
wave principle you will notice it in throws and joint locks."
You can read more about the differentiation of the sine wave motion versus the wave principle
here.
I also discussed the
wave principle here. The wave principle on which the sine wave motion is build is used in many martial arts, particularly the soft styles, such as Aikido,
Tai Chi Chuan, Systema, and others.
I hope I have added something to the discussion.