# When did the use of Sine and Cosine as functions become mainstream?

In the work of early physicists like Newton, everything is explained in terms of cumbersome (in today's standards) geometry. They don't talk about "cosines" of certain angle, but about proportions between the sides of triangles. But aren't sines and cosines known since antiquity? So why Newton, Copernicus, etc didn't make use of them.

When and how did trigonometric functions become mainstream?

Trigonometric functions became "mainstream" since the publication by Ptolemy (II AD) of trigonometric tables. To be sure he did not use our modern sine and cosine, but a single trigonometric function, the chord ($$=2\sin(t/2)$$). Modern definitions of sine and cosine were introduced by Indian mathematicians (Surya Siddhanta (V century AD), and reached Europe through Middle Eastern mathematicians. After the fall of Constantinople, this knowledge quickly spread in Europe. The first treatises on trigonometry in Europe were written by Peuerbach and Johann Muller (Regiomontanus) in 1464. Copernicus of course used trigonometry extensively, as well as Kepler.