Trigonometry – Natural sciences – Mathematic
We explain trigonometry, a little history about this branch of mathematics, and the most important concepts it uses.
What is Trigonometry?
According to the word’s etymological meaning, trigonometry is the measurement of triangles (from the Greektrigonalo and metron). Trigonometry is part of mathematical science and is responsible for studying the trigonometric ratios of sine, cosine, tangent, cotangent, secant, and cosecant.
Trigonometry is used where precision measurement is required and applied to geometry; it is unique to a unique study of spheres within spatial geometry; among the most common uses of trigonometryisisisisis measuring distances between stars or geographical points.
A bit of trigonometric history
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. Babylonian astronomers recorded the movements of the planets and eclipses. Two thousand years before Christ, the Egyptians already used trigonometry in a primitive way to build their pyramids.
The foundations of current trigonometry were developed in Ancient Greece, Indi, and at the hands of Muslim scholars. Scholars of ancient trigonometry were Hipparchus of NicaeaAryabhataa, Varahamihira, Brahmagupta, and Abu’l-Wafa, among others.
The first use of the sine function dates back to the 8th century BC. C. in India. Who introduced the analytical treatment of trigonometry in Europe was Leonhard Euler. They were then known as “Euler’s formula.”.
They started from the correspondence between the length of the sides of a triangle from the fact that they maintain the same proportion. If a triangle is similar,r, the relationship between the hypotenuse and a leg is constant. If we observe that hypotenusearesis twice the length, the legs will be.
Most essential concepts of trigonometric
Three units are used to measure angles:
The radian. Which is used more than anything in mathematics.
The sexagesimal degree. Most used in everyday life.
The decimal system. Used in surveying and construction.
Trigonometry is defined in certain functions 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: cotangent, secant,t, and cosecant.To carry out these operations,s it is necessary to consider certain concepts. The side opposite the right angle is the hypotenuse (h), the longest side of the triangle. The opposite leg is the one that is on the opposite side to the rise in question,n, while we call the one that is next to it adjacent.
To obtain the sine of a given angle, the length of the opposite leg and that of the hypotenuse must be divided (that is, the opposite leg over the hypotenuse: a/h).
The cosine is obtained from the ratio between the length of the adjacent leg and the hypotenuse (adjacent portion on hypotenuse: a/h).
To obtain the tangent, the length of both legs is divided (that is, the division is made: o/a).
For the cotangent function, the length of the adjacent leg is divided by the opposite leg (understood as a/o).
For the secant function, the length of the hypotenuse on the adjacent leg is related i.e.e: h/a).
Finally, to determine the cosecant function, the hypotenuse length is divided on the opposite leg (thus obtaining: h/o).
