Trigonometry was transformed into an ordered science by the ancient Greeks. The driving force behind the invention of trigonometry was Astronomy. The early development of trigonometry was in spherical trigonometry as its application was significant in it. The three important figures involved in devising Greek trigonometry are Hipparchus, Menelaus and Ptolemy.
Hipparchus needed the table of trigonometric ratios for his work in astronomy. He computed the first table of chords for this reason. According to him, every triangle is being inscribed in a circle such that each side becomes a chord. He generalized the idea of dividing the annual path of the sun into 360o and further dividing the diameter into 120 units by expressing them as the Babylonian style sexagesimal fractions.
Menelaus’s third book named Sphaerica from the three-book work is based on spherical trigonometry that consists of some important information which contributed to the development of trigonometry.
The greatest contributor to the Greek Trigonometry is Ptolemy. The table of chords that were equivalent and useful in the formulae of present-day trigonometric functions was given by him. Ptolemy devised the formula chord (p – q) = (1 / 2) (chord p chord (180 – q)) – (chord q chord (180 – p)) where p and q are angles.