We explain what trigonometry is, a brief history of this branch of mathematics, and the most important concepts it uses. Please read other MTV articles for more information. If you share it, it will be of little help to us.
What is Trigonometry?
According to the etymological meaning of the word, trigonometry is the measurement of triangles (from the Greek trigono and metron). Trigonometry is part of the science of mathematics and studies the trigonometric ratios of sine, cosine, tangent, cotangent, secant, and cosecant.
Trigonometry is used wherever precise measurements are required and is applied to geometry, especially 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.
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A Brief History of TRIGONOMETRIC
Scholars in ancient Egypt and Babylon were already aware of the theorems regarding the measurement of similar triangles and the ratios of their sides. It is known that Babylonian astronomers recorded the motions of the planets and eclipses. The Egyptians, two thousand years before Christ, already used trigonometry in a primitive form to build their pyramids.
The foundations of modern trigonometry were developed in Ancient Greece, but also in India and at the hands of Muslim scholars. Scholars of ancient trigonometry included Hipparchus of Nicaea, Arybhata, Varahamihira, Brahmagupta, Abu’l-Wafa, among others.
The first use of the “sine” function dates back to the 8th century BC in India. The analytical treatment of trigonometry was introduced in Europe by Leonhard Euler. These formulas were then known as “Euler’s formulas.”
They were based on the correspondence between the lengths of the sides of a triangle, since 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 twice as long.
Most important trigonometric concepts
Three units are used to measure angles:
- The radian. Used primarily in mathematics.
- The sexagesimal degree. Most commonly used in everyday life.
- The decimal system. Used in surveying and construction.
Trigonometry is defined by certain functions that are applied in various fields to measure the relationship between the sides and angles of a right triangle or a circle. These functions are sine, cosine, and tangent. Inverse trigonometric ratios can also be performed, namely: cotangent, secant, and cosecant.
To perform these operations, it is necessary to keep certain concepts in mind. 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 opposite the angle in question, while the adjacent leg is the one adjacent to it.
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- To obtain the sine of a given angle, divide the length of the opposite leg by the hypotenuse (i.e., opposite leg by hypotenuse: a/h).
- The cosine is obtained from the ratio of the length of the adjacent leg to the hypotenuse (adjacent leg by hypotenuse: a/h).
- To obtain the tangent, divide the length of both legs (i.e., divide by: o/a).
- For the cotangent function, divide the length of the adjacent leg by the opposite leg (i.e., divide by: a/o).
- For the secant function, the length of the hypotenuse is related to the adjacent leg (i.e., h/a).
- Finally, to determine the cosecant function, the length of the hypotenuse is divided by the opposite leg (thus obtaining h/o).
