Gen. Choi Hong Hi introduced in Taekwon-Do, a particular type of motion known as the “sine wave” motion.

In his book *Encyclopedia of Taekwon-Do, Volume 4, pages 203-204*, he mentions, *“In the course of stepping, the knee can create three different postures as follows:”*

Posture A creates a Sine Wave (Yulson), where the knee is slightly bent at about 30 degrees; Posture B creates a Horizontal Wave (Soopyongson), where the knee is extremely bent at about 90 degrees; and Posture C creates a Saw Tooth Wave (Topnal son), where the knee is straight at 180 degrees. In Posture B, the knee is sharply bent and so the mass remains the same, and the dynamic stability of the body is lost. In Posture C, the knee is straight, so the force of momentum is not continued, thus speed is reduced.

“*Among them, posture A is the only one used in Taekwon-Do. Posture A: Bending the knee slightly gives the leg greater flexibility, imparting more momentum and speed to the motion.” – Gen. Choi Hong Hi (Vol.4, pp.203-204)*

**Example of a Walking Stance, forward motion:**

The left leg pushes down on the ground, the left leg knee is raised as it comes forward, the left leg is planted forward on the ground. Pushing on the ground is the “low” movement, raising the knee about 30 degrees is the “high” movement, and planting the leg on the ground is the “low” movement, whereby mass is gained. Similar to a Walking Stance, the L-Stance and the Sitting Stance are also shown to exhibit the sine wave motion, where due to the spring action of the knee, mass is gained. So, the knee follows the “low-high-low” movement, which Gen. Choi labels it as a sine wave movement. Just like stepping forward, this same movement can be done for stepping backwards or stepping sideways also.

*Original Taekwon-Do / MMA & Fitness Center video “GENERAL CHOI HONG HI EXPLANATION OF SINE WAVE”:*

In the above video, Gen. Choi Hong Hi describes the sine-wave motion as “low-high-low”. Notice, that he refers the three parts, low-high-low, as two parts “1-2”. In one technique, the “low-high” can be taken as 1, and the “low” can be taken as 2. Similarly, in another technique, the “low” can be taken as 1, and the “high-low” can be taken as 2. Both 1 and 2 are executed with a sharp exhalation of breath. The 1 and 2 are continuous, there is no stopping in-between and they are executed as if they were a single motion, with speed.

## Why is a “low-high-low” motion called as a sine wave?

A sine wave is normally depicted as a “high-low-high” or a “up-down-up” graph. Then, why did Gen. Choi mention it as a “low-high-low” motion? To answer this question, let us examine the sine wave from a scientific perspective.

The following videos explain the sine wave and its complement the cosine wave. Notice that the sine goes high-low-high (or up-down-up), and the cosine wave goes low-high (or down-up).

*Learnability video “Sine Wave | Why didn’t my teacher explain it this way!? Simple explanation | Learnability”:*

*Learnability video “Cosine Wave | Simple Explanation on a Giant Wheel | Learnability”:*

### Two important sine waves

There are two important sine waves, where one has a phase of 0 and the other has a phase of π/2. Both are sine waves; hence, to distinguish them, one is named as a sine wave, while the other is named as a cosine wave. A sine wave with a phase θ = 0, is known as a sine wave; while a sine wave with a phase θ = π/2, is known as a cosine wave.

*Khan Academy video “Sine and cosine from rotating vector”:*

### Cosine leads the sine

*Flipping Physics video “Creating Circular Motion from Sine and Cosine Curves”:*

A sine wave is also known as a sinusoid or a sinusoidal wave. The term “sinusoid” is used to describe any wave that shows the characteristics of a sine wave. The complementary wave of a sine wave is known as a Complementary Sine wave, or in short a CoSine wave. The mathematical equation of a cosine is cos(x)= sin(x+ π/2), which is also a sine wave having a phase-shift of π/2 radians. Because of this phase shift, the cosine gets a head start and thus, is often known to lead the sine. Therefore, together the graph would be low-high-low-high-low … and so on.

**It seems Gen. Choi was aware that sine and cosine are actually both sine waves, and cosine leads the sine. Therefore, he may have decided to represent a sine wave movement as “low-high-low”.**

## The sine wave can be fast or slow

For slow movements, a sine wave is aesthetically pleasing to the eyes; however, in sparring or competitions, only fast sine wave movements are employed. To understand more, let us see the following video.

*Mike X Cohen video “Sine waves”:*

**Mathematical formula of a sine wave as a function (y) of time (t):**

*y(t) = Asin(2πft+θ)*where,

*A* = amplitude, the peak deviation of the function from zero.

*2πf* = angular frequency, the rate of change of the function argument in units of radians per second

*f* = ordinary frequency, the number of oscillations (cycles) that occur each second of time.

*t* = time

*θ* = phase, specifies (in radians) where in its cycle the oscillation is at t = 0.

**–If the amplitude (A) is less, then the sine waves are smaller. This means that the lesser the peak deviation of the function from zero, the smaller is the sine wave.**

In martial arts, this would mean that the lesser distance a martial artist covers from one point to another point, the smaller would be the sine wave. For example, if a shuffling of feet is done, then the low-high-low movement would not be perceptible at all.

**–If the frequency (f) is more, then the sine waves gets denser. This means the greater the number of cycles/sec, the greater is the number of sine waves.**

In martial arts, this would mean that the faster a martial artist executes a movement or movements, the faster would be the sine waves. For example, if a punch is executed speedily then the sine wave would also be executed speedily. If a combination is executed, like a punch and a kick, and both are executed rapidly one after the other, then the corresponding sine waves would also be executed rapidly. Thus, for an effective execution of a technique with sine wave, it should be executed with speed and the other components that contribute towards the power in Taekwon-Do.

The following video explains some sine wave movements.

*LDH TAEKWONDO video “Sine Wave_Taeryuk 45 Taekwondo Centralization”:*

## The sine wave is used to increase mass

As given in the Encyclopedia and as is evident from his video, Gen. Choi shows that the sine wave is used to increase mass (Zilyang). As a result of this increase in mass, more power is created. In his theory of power (Him Ui Wolli), Gen. Choi mentions:

Power in Taekwon-Do comes from a combination of the following:

**– Reaction force (Bandong Ryok)**

—— reaction force of your opponent

—— reaction force of your own

**– Concentration (Jip Joong)**

—— muscles concentrated towards the attacking or defending tool

—— muscles concentrated towards the opponent’s vital spot

**– Equilibrium (Kyun Hyung)**

—— dynamic stability (Dongtchuk Anjong)

—— static stability (Jungtchuk Anjong)

**– Breath control (Hohup Jojul)**

**– Mass (Zilyang)**

—— increase body weight by turning the hip

—— increase body weight by utilizing the knee in a spring action

**– Speed (Sokdo)**

—— speed and reflex (Sokdo wa Banung)

Thus, it is evident that mass can be increased by turning the hip, and/or utilising the knee in a spring action in a sine wave motion. For power generation, besides mass created by sine wave motion and/or hip turning, other factors like reaction force, concentration, equilibrium, breath control, and speed are also required.

## The sine wave is not bobbing up and down

Due to the bending and straightening of the knees, the height of the body fluctuates, which may seem as if the practitioner is “bobbing” up and down. However, this is only if the practitioner is executing the sine wave very slowly. The three parts of the sine wave “low-high-low” are executed in two parts either as “low” and “high-low”, or “low-high” and “low”, in a smooth continuous motion as if it were a single motion, without any gaps in-between and with speed, which does not make it apparent. Since it is not apparent, the bobbing is not visible. However, in some patterns, where slowness is required, the sine wave becomes apparent and in such instances, bobbing does occur; nonetheless, as it breaks the speed of execution, it provides an aesthetic beauty of its own and is pleasing to the eyes.

## The sine wave does not telegraph a move

For movements covering small distances, the sine wave is not perceptible at all. For example, bending the knee in a sine wave for a small shuffle of the feet can lead to a punch, a block, a kick, or to any other move. Then how can it telegraph any particular move?

For movements covering large distances, the sine wave is perceptible, yet it cannot telegraph a move. For example, in a walking stance executed with a sine wave, it is not necessary that a punch only would be executed. A block might be performed or the rear leg may be brought forward to throw a front kick, and in these instances, there is no telegraphing at all. A sine wave is evident in many fundamental movements of Taekwon-Do. For example, to execute a front kick, the front leg’s knee has to be bent about 30 degrees with the front leg pushing the ground (low); the rear leg is brought up with the knee bent forward and then snapped to the target with increased mass (high-low). This shows a sine wave low-high-low movement. This can be accomplished without any telegraphing at all and this one blow is enough for a knockout.

### Conclusion

A sine wave is applied in mathematics, physics, engineering, sports and in many other disciplines. However, it is easily associated with Korean culture and is thus appropriate to be included in Taekwon-Do, which is a Korean martial art. Korean traditional dance includes bending/straightening of knees, which is a sine wave motion. The application of the concept of sine wave in Taekwon-Do is an important contribution of Gen. Choi, and one that makes it a uniquely Korean martial art.

**References:**

1. Choi, H. H. (1985). *Encyclopedia of Taekwon-Do (Vols. 1–15)*. Vienna: International Taekwon-Do Federation.

2. Sine wave. webpage. Wikipedia. Available at: https://en.wikipedia.org/wiki/Sine_wave [Accessed on July 27, 2022].

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