In a nutshell, to differentiate itself from Karate. Introduced in a seminar in 1980.
Rayners Lane Taekwon-do Academy
This is of particular interest:
Sitting Stance Punch
Both subjectās punches with one hand were harder using the sine wave and their punches with the other were weaker using it. However the differences in power generated were small, as low as 0.25% in one case. On average, the difference in power generated using the sitting stance punch with and without sine wave was negligible.
Walking Stance Reverse Punch
One subject punched harder with one hand using sine wave and harder with the other without it. The other punched harder without sine wave with both hands. On average,
the force generated from a reserve punch in walking stance without using the sine wave was 4% higher than the same technique using sine wave.