When the relationships between some physical quantities are expressed in equations, you see that some kind of geometry is involved. Some triangles, cubes, spheres, quadrilaterals, pyramids etc. are encountered in real life in physics and chemistry.
Also we model real life objects in to these shapes, as we can calculate quantities volume, mass, and other quantities related to these shapes.
These shapes are associated with ratios like Sine, Cosine, Tangent etc. Naturally the trigonometric ratios are used in all maths, physics, chemistry, civil engg, electrical engg, telecommunications engg, mechanical engg., space science etc.
Related to refractive index: μ_i Sine i = μ_r Sin r
In the above equation, Sine i and Sine r appear as they are related to speed of light in the medium and distance traveled by light. They are related to each other by these ratios of the angles.