Derived from the Greek words trigonon (“triangle”) and metron (“to measure”) trigonometry was chiefly concerned with the computation of numerical values from the absent numerical value of a portion of the triangle (or shapes that could be dismembered into triangles) when the values of other parts were given until the 16th Century. Pythagoras, Aristotle, or the ancient civilization of the Greeks, Egyptians, and Babylonians may come to mind while looking at the dawn of trigonometry.
Pythagoras, the author of the Pythagorean Theorem, was afraid of beans and had a cult to worship triangles, his followers were not only vegan but also didn’t eat beans because they believed that a part of their soul escaped every time they passed gas. What we traditionally know as the Pythagorean Theorem is that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of the other two sides of the right-angled triangle which is simply formulated as a2 + b2= c2 (for e.g. (3)2+(4)2=(5)2).
The Rhind papyrus (1800 BCE) was an Ancient Egyptian Collection of 84 mathematical problems to the likes as Arithmetic, Algebra, and Geometry. The Geometry portion also consisted of five issues dealing with the seked or what we now refer to as the hypotenuse.
The 56th problem of the Rhind papyrus was a problem pertaining to a pyramid that was 250 cubits high and 360 cubits long, and the solution of the problem was given as 51/25 palms per cubit, and, since one cubit equals 7 palms, this fraction is equivalent to the pure ratio 18/25. This referred to the “run-to-rise” ratio of the pyramid in question—in effect, the cotangent of the angle between the base and face, from this we can examine the Egyptians’ extent of knowledge of the numerical relations in a triangle along with trigonometry.
Trigonometry in its modern sense began with the Greeks and the construct of the table of values for trigonometric functions was formulated by Hipparchus (120 BCE). He was mainly interested in spherical triangles being an astronomer himself would find fictional triangles shaped by three stars on the celestial sphere. Still, he was also familiar with the basic formulas of plane trigonometry.
The symbols for trigonometry were formulated only in the 17th Century. Ptolemy’s Almagest was the first major ancient work on trigonometry to reach Europe that uses some elementary trigonometry that lead to Ptolemy’s geocentric system being a succession of the heliocentric system of Nicolaus Copernicus.
The Babylonians used the Pythagorean Theorem some 1,000 years before Pythagoras was born. They wrote it down on a tablet now known as Plimpton 322. The ancient Egyptians, Chinese, and Indians all used versions of it centuries before Pythagoras. An ancient Babylonian tablet used the Pythagorean Theorem 1200 years before Pythagoras was born.
India and the Islamic world were also great contributors to trigonometry which makes you wonder about the true importance and value of Mathematics as recent research shows us that 4000 years ago Neanderthals also had a basic sense of Mathematics.