The word, trigonometry" is derived from trigon = triangle + metry = measurement. It is based on the study of angles of a triangle and their properties. Although trigonometric ratios are often introduced to students in the context of triangles, their properties for all angles.
For example, trigonometric functions are well defined for angles with negative values as well as for more than 180 degrees even though no triangle can possibly have angles with such measures.
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Optics deals with light waves, and all waves relate in some way to trigonometry. Also, the reflection and refraction of light involves trigonometry.
plane trigonometry spherical trigonometry
The main kinds are plane trigonometry and solid trigonometry. The latter will include trigonometry in hyper-spaces.
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