angle can be defined as sin-1=O/H, cos-1=/H, or Tan-1=O/A
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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.
Hipparchus of Nicaea