When you are at school learning the science of measuring triangles (trigonometry) you provably remember something about those three trigonometric functions that represents the relationship between an angle and two sides of the triangle: Sine, Cosine, and Tangent. They have inverse identities called Cosecant, Secant and Cotangent, respectively. Some students did understand it well and others do not, not everybody has the same aptitudes. If that was not enough, the functions arcsin, arcos and arctan were used to calculate an angle of the triangle with two of the sides.

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¿Too many mathematics? Well, still have to explain other ten identities.

In this post, I bring Steemit a look at these forgotten trigonometric identities. Historically other trigonometric functions had been important in their moment, but for different reasons (like the use of computers), they have no longer being used.

Versine and Coversine

Versine was one of the most important trigonometric functions but it has lost popularity because of the use of computers, why? For the simple reason that if calculators or computers does not exist you have to ask yourself how people did in ancient times to calculate for example Sin(43°) or Tan(77,9°)? The answer is Tables, yes, big tables with each angle and each value of every trigonometric function. It’s always a positive number, that was a historical advantage.

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Coversine and Covercosine

Guest this is totally new for you, and you are disappointed to know this is not taught in the current trigonometry classes.

Haversine, havercosine, havercoversine and havercovercosine

Interesting... Right?

The haversine was widely known in navigation for taking part in the haversine formula to calculate the distance between two points in a sphere given latitude and longitude.

In the time before digital calculations, navigators use nautical tables for the Haversine, inverse Haversine and its logarithms to help in the calculations on square roots, sines, etc. This reduces error in their calculations.

Exsecant and Excosecant

This identity was widely used in fields like surveying, astronomy, and spherical trigonometry. Currently, its use has been reduced by the same reasons that the other forgotten trigonometric identities.

Before the existence of computers, multiplications of trigonometric functions were a long process.

The next illustration expresses the geometrical meaning of these functions:

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In the end, whether if these functions are used or not, all trigonometric functions can be expressed in terms of one single identity: Sine. However, in many situations, it is necessary to define other identities to simplify the calculation process.

References:

• Matematicas10.net (2018). "Ejemplos de Exsecante". Recover from:
  https://www.matematicas10.net/2015/12/la-exsecante.html
• Gaussianos.com (2013). "¿Cuántas razones trigonométricas existen”. Recover from:
  https://www.gaussianos.com/cuantas-razones-trignonometricas-existen/
• https://en.wikipedia.org/wiki/Versine
• https://en.wikipedia.org/wiki/Haversine_formula
• https://en.wikipedia.org/wiki/Exsecant

Equations created by Microsoft World.