The most significant development of trigonometry in ancient times was in India. Influential works from the & the century AD, known as Siddhantas first defined the sine as the relationship between half an angle & half a chord, while also defining the cosine, versine ( cosine) & inverse sine.
Soon afterwards, another Indian mathematician & astronomer Aryabhata collected & expanded upon the developments of the Siddhantas in a path breaking work, the Aryabhatiya. The Siddhantas & the Aryabhatiya contain the earliest survivng tables of sine & versine values, in intervals from to , to an accuracy of decimal places. They used the words jya for sine, kojya for cosine, utkrama-jya for versine & otkram jya for inverse sine. The words jya & kojya eventually became sine & cosine after a mistranslation.
Aryabhata was the first one. Others after him expanded on these works of trigonometry. In the century AD, Varahamihira discovered the identity . He improved Aryabhata's sine table & discovered an early version of the Pascal's Triangle.
Such was the ingenuity of the ancient Indian mathematicians!
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Great Indians great mathematics