Babylonian Trigonometry has been found to to pre-date Hipparchus' (Greek) trigonometry by 1,000 years, and to use a novel method of ratios instead of triangles and circles. The discovery has been made with the deciphering of the Plimpton 322 tablet by an Australian team of researchers at the University of New South Wales.

Sources:

New Atlas (popular article): http://newatlas.com/ancient-babylonian-tablet-trigonometry-table/51055/

Historia Mathematica (journal article): http://www.sciencedirect.com/science/article/pii/S0315086017300691