What is trigonometry?

We explain what trigonometry is, a little history about this branch of mathematics and the most important concepts it uses.

1. What is trigonometry?

Trigonometry is, according to the etymological meaning of the word, the measurement of triangles (from the Greek trigon and metron ). Trigonometry is part of  mathematical science and is responsible for studying the trigonometric ratios of sine, cosine, tangent, cotangent, drying and harvesting.

Trigonometry is used where it is required to measure accurately and is applied to geometry , it is special to the study of spheres within spatial geometry. Among the most common uses of trigonometry are the measurement of distances between stars or between geographical points.

2. A little history about the trigonometric

Already the scholars of ancient Egypt and Babylon were aware of the theorems about the measurement of similar triangles and the proportions of their sides. It is known that Babylonian astronomers recorded the movements of planets and eclipses . The Egyptians, two thousand years before Christ, already used trigonometry in a primitive way to build their pyramids.

The foundations of the current trigonometry were developed in Ancient Greece, but also in India and in the hands of Muslim scholars. Scholars of ancient trigonometry were Hipparchus of Nicea, Arybhata, Varahamihira, Brahmagupta, Abu’l-Wafa, among others.

The first use of the “sine” function dates back to the eighth century BC. C. in India . Who introduced the analytical treatment of trigonometry in Europe was Leonhard Euler. They became known as the “Euler formulas”.

They started from the correspondence that exists between the length of the sides of a triangle from which they maintain the same proportion. If a triangle is similar then the relationship between the hypotenuse and a leg is constant. If we observe that a hypotenuse is twice as long, then the legs will be.

3. Most important trigonometric concepts

Three units are used to measure angles:

• the radian (which is used mostly in mathematics),
• the sexagesimal degree (most used in everyday life) and,
• the decimal system (used in topography and construction).

Trigonometry is defined in certain functions that are applied in various fields to measure the relationship between the sides and angles of a right triangle or a circumference. These functions are sine, cosine and tangent . Inverse trigonometric ratios can also be performed, namely: cotangent, drying and harvesting.

In order to perform these operations it is necessary to take into account certain concepts. The side opposite the right angle is called the hypotenuse ( h ) which is the longest side of the triangle. The opposite leg is the one that is on the opposite side to the angle in question while we call adjacent to the one on the side.

• To obtain the sine of a certain angle, the length of the opposite leg and that of the hypotenuse must be divided (ie opposite leg on the hypotenuse: a / h).
• The cosine is obtained from the relationship between the length of the adjacent leg and the hypotenuse (adjacent leg on the hypotenuse: a / h).
• To obtain the tangent , the length of both legs is divided (that is, the division is performed: o / a).
• For the cotangent function, the length of the adjacent leg is divided by the opposite (understood as: a / o).
• For the secant function , the length of the hypotenuse is related to the adjacent leg (ie: h / a).
• Finally, to determine the harvesting function , divide the length of the hypotenuse over the opposite leg (thus obtaining: h / o).