What is trigonometry: Definition & History

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (CSC). The figure shows these six trigonometric functions concerning a right triangle. The ratio between the side opposed to an angle and the side opposite to the right angle (the hypotenuse), for instance, is known as the sine of the angle, or sin A; additional trigonometric functions are defined in a manner akin to this.

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Before computers rendered trigonometry tables obsolete, these functions—characteristics of angle A regardless of the triangle size—were listed for numerous angles. In geometric figures, unknown angles and distances are derived from known or measured angles using trigonometric functions.

Trigonometric history

The Greek words trigonal ("triangle") and metron ("to measure") are the origins of the word trigonometry. Trigonometry was primarily concerned, up until the early 16th century, with estimating the numerical values of the missing parts of triangles (or other shapes that could be divided into triangles), given the values of the remaining parts. For instance, the third side and the other two angles of a triangle can be determined if the lengths of the first two sides and the enclosed angle are known. These computations set trigonometry apart from geometry, which most studies qualitative relationships.

Egyptian antiquity and the Mediterranean region

Several prehistoric civilizations, including the Egyptian, Babylonian, Hindu, and Chinese, had a significant understanding of practical geometry, including certain ideas that served as a foundation for trigonometry. Five of the 84 math, algebra, and geometry questions in the Rhind papyrus, an ancient Egyptian work from around 1800 BCE, deal with the seed.

A detailed examination of the text and the supporting images indicates that this phrase refers to the incline's slope, information that is crucial for massive construction projects like the pyramids.

For instance, issue 56 asks: "What is a pyramid's asked if its side is 360 cubits long and 250 cubits high?" Given 51/25 palms per cubit, the answer is comparable to the pure ratio of 18/25 because one cubit equals 7 palms. This is the pyramid in question's "run-to-rise" ratio, which is essentially the cotangent of the angle between the base and face. It demonstrates that the Egyptians at least had a basic understanding of the mathematical relationships in triangles, or "proto-trigonometry."

The Greeks invented trigonometry in its contemporary form. The first person to create a table of values for a trigonometric function was Hipparchus (c. 190–120 BCE). Every triangle, whether spherical or planar, was seen by him as having its sides inscribed in a circle, creating chords (that is, a straight line that connects two points on a curve or surface, as shown by the inscribed triangle ABC in the figure).

One must determine the length of each chord as a function of the central angle that subtends it—or, alternatively, the length of a chord as a function of the corresponding arc width—to calculate the various triangle components.

Modern trigonometry

Trigonometry started transitioning from a purely geometric science to an algebraic-analytical study in the 16th century. The creation of symbolic algebra, which was led by the French mathematician François Viète (1540–1603), and the development of analytic geometry by two other Frenchmen, Pierre de Fermat and René Descartes, were the two events that sparked this shift. Viète demonstrated how trigonometric expressions might be used to express the solution to various algebraic equations.