 With this in mind, the identity upon which trigonometry is based turns out to be the Pythagorean Theorem.Some of the early and very significant developments of trigonometry were in India.Influential works from the 4th–5th century, known as the Siddhantas (of which there were five, the most important of which is the Surya Siddhanta) first defined the sine as the modern relationship between half an angle and half a chord, while also defining the cosine, versine, and inverse sine.