According to recent (August 2017) research by the University of New South Wales, it was an unknown mathematician (or mathematicians) in Babylon. They produced a tablet, known as Plimpton 322, which contains tables of trig ration. This was some 1500 years before the Greek astronomer Hipparchus who, until now, was regarded the father of trigonometry.
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Ancient Indian mathmatician aryabhatta is credited as inventor of trignometry.
plane trigonometry spherical trigonometry
The main kinds are plane trigonometry and solid trigonometry. The latter will include trigonometry in hyper-spaces.
Hipparchus is the father of trigonometry.
Trigonometry based on a unit circle and radians and trigonometry based on a right triangle.