The sine ratio plays an important part in the refraction of light at the interface of two media through which the light travels - such as the interface between air and the glass of a lens.
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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.
I personally study trigonometry because it is absolutely exhilarating for me.
geometry
algebra
Trigonometry is specificly the study of a right triangle. For example, what is the cosine? Geometry is the study on shapes.