Start by teaching the basic properties of different triangles because trigonometry is the science of triangles.
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Colleges offer multiple semester-long classes in trigonometry; it's not something we can teach you in a few paragraphs on a website. If you're really interested, I recommend you take a class at a community college.
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.