Who invented sine and cosine

They were able to tabulate the values of these ratios. In particular, Bhaskara I used a formula equivalent to. In the 12th century, Bhaskara II discovered the sine and cosine expansions in roughly their modern form. Arabic mathematicians were also working in this area and, in the 9th century, Muhammad ibn Musa al-Khwarizmi produced sine and cosine tables. He also gave a table of tangents. The first mathematician in Europe to treat trigonometry as a distinct mathematical discipline was Regiomontanus.

The history of the trigonometric functions really begins after the development of calculus and was largely developed by Leonard Euler Courant and related material on web. To this particular question, haven't found an answer for long.

It is correct that Ptolemy operated not with sines, but with chords. Trigonometry was developed for the needs of astronomical computation. The whole idea was foreign to the classical Greek mathematics Euclides, Apollonius. They did not have even a fully developed number system, and did very little numerical computation, preferring pure geometric methods. Astronomical computations became possible after the adoption of the Babylonian sexagesimal notation for numbers.

Trigonometry is indispensable in most astronomical computations, the simplest one is passing from equatorial to ecliptic coordinates. This is needed for example when you compute such things as rising times, length of daylight, etc.

Spherical trigonometry was developed simultaneously with the plane trigonometry, and the main emphasis was on the spherical one. This happened in the the very end of the 1st century and is due to Menelaus. His book Spherics can be dated by an observation made in the year His trigonometric tables, if he made them, did not survive, and the earliest existing work where trigonometry is fully developed is Ptolemy's Almagest.

Almagest contains the first known trigonometric tables, and Neugebauer thinks that Ptolemy was the first to make them. At that time our usual trigonometric functions were not used. This function is tabulated in Almagest. Sine was introduced by Abu'l Wafa in 8th century, as a more convenient function, and gradually spread first in the Muslim world, and then to the West.

But apparently it was used in India centuries before him , as a more convenient function. However this new notation was adopted very slowly, it took centuries. Copernicus 16th century in fact used sine but calls it "half of the chord of double angle". But at the time before Copernicus there were already more advanced treatments of trigonometry, by J. Muller Regiomontanus. Sign up to join this community. The best answers are voted up and rise to the top.

Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Discovery of Sine and Cosine Ask Question. Asked 6 years, 7 months ago. Active 6 years, 7 months ago. Viewed 8k times. Improve this question.