History of Trigonometry

Semester Project Inductory Page Trigonometric Identity Proofs Unit Circle Relationship Application of Trigonometric Identities


1500BC

The development of trigonometry took place over several centuries and was contributed by several different mathematicians. The Egyptians and the Babylonians were the first to use ideas of trigonometric concepts at about 1500 BC ( (Massa, Romero, & Guevara, 2006). The Egyptians used ratios of similar triangles to construct their pyramids and the Babylonians used trigonometric functions to describe arc lengths and cords. The Egyptians and other civilization created shadow tables to track time by measuring the length of a sticks shadow. Trigonometric functions are used to describe this phenomenon. Even though these ideas were being utilized by societies; it wasn’t until the Ancient Greeks that trigonometry was formally defined as a branch of mathematics. They developed trigonometric theorems to explain their astronomy discoveries and their building constructions (Adamek, Penkalski, & Valentine, 2005).

300BC-30BC

Tara Adamek and colleagues said, “Hipparchus, a highly credited Greek astronomer who came to be known as the ‘father of trigonometry,’ had a great influence in the developments of trigonometry and is the first person whose use of trigonometry is documented.” He developed trigonometry in a geometrical perspective, also known as spherical trigonometry in the period of 300BC-30Bc. His work included looking at the relationship of chord lengths and angle measurements when triangles are inscribed in circles. From these observations of chords lengths and angle size he developed what is known as some of the first trigonometric ratio tables. His development of these tables led to the development of trigonometric functions and identities (Adamek, Penkalski, & Valentine, 2005).

127-141AD

Ptolemy, another Greek mathematician, came along shortly after the time of Hipparchus. He extended the ideas of spherical trigonometry by discovering the laws of sines and furthering the knowledge of spherical trigonometry. He also developed tables of sines based on half chords or half arcs which were more detailed than Hipparchus tables and included the idea of cosine, but in a geometric sense. His tables provided enough information that anybody can find all the lengths of a triangle if given one length and an angle. He laid the foundation for other trigonometric identities, for example the sum and difference identities, for other mathematicians to discover(Adamek, Penkalski, & Valentine, 2005). After the Greeks, trigonometry wasn’t explored or further developed by other civilization unit the Arabic civilization (Rogers, 2010).

940-998

They Arabic was the first civilization to represent trigonometry in algebraic and arithmetic terms. They used symbols to represent trigonometric functions instead of using geometric entities, for examples chords of a circle. Having trigonometry represented in a geometric and algebraic allowed mathematicians to discover new relationship in trigonometry, especially when moving between the two perspectives. Abu al-Wafa al-Buzjani was the first mathematician to start exploring relationships between the fundamental trigonometric functions. He established the relationship of all these functions with triangles inscribed in a circle. These relationships would inspire other mathematicians to develop other trigonometric identities (Rogers, 2010).

998-present day

His work inspired European mathematicians to develop the sum and difference formulas, as well as the double angle formulas by using the relationship of the unit circle (Rogers, 2010). These identities allowed mathematicians to analyze the functional relationship instead of finding computations of triangles. This is where the transition of spherical trigonometry to modern trigonometry began. Trigonometric identities are the foundation of modern trigonometry (Adamek, Penkalski, & Valentine, 2005).