There is no one or two or a few 'fathers of trigonometry.' Ancient Sumarians, Babalonians started using ratios of sides of triangles. The Greeks continued the study, but emphasized geometric methods instead of algebraic methods that used in trig. Egyptians, Persians, Arabic, and Indians all contributed to the development of trig. This whole process took about 2000 years, maybe more.
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based on my stock knowledge, i think hipparchus is the father of trigonometry.....
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.