Versine

Versed sine (also Versinus or Versus in formulas for short) and the cosine versus (also Koversinus, in formulas for short) are in trigonometry trigonometry functions rarely used today. Semi Versus (English Haversine, in formulas for short) is the half sine versus.

• 2.1 Definition

• 3.1 Definition
• 3.2 History and Use

Versed sine

Definition

The haversign is defined by means of the sine or cosine function as

The versed sine can be extended to the whole complex plane.

Properties

The derivative of the sine wave is the sine versus:

The antiderivative is given by

Cosine versus

Definition

The cosine versus the versed sine of the counter- argument:

Semi Versus

Definition

The Semi Versus is versus half of the sine:

History and Use

The page cosine law of spherical trigonometry played an important role for the nautical navigation by the stars in earlier times. To the multiplications required in this case to simplify the trigonometric functions of the lookup table values ​​, the semi- Versus was introduced.

It implies, among other things to the side cosine law: