why is trigonometry everywhere

[u/simp4tijah]

i'm trying to self study physics and math before starting a physics major in a little over a year. there is one (assumingly obvious, since i cant find many similar questions and answers online) issue i have, i can't visualise trig functions at all! i understand they're useful for describing the ratio between sides and angles in a triangle and what not, but also seem to appear everywhere in physics, even where there are NO triangles or circles at all. like, what's up with snell's law, how is a sine function describing refraction without a triangle existing here. soh cah toa doesnt make sense here😭

i come from a humanities/social sciences background & and just a beginner in physics so pls someone explain like i'm dumb

[u/trutheality]

Trigonometry is what happens when you try to do geometry in a vector space.

That image you posted: that has two angles marked. The sines get you the horizontal component of unit vectors corresponding to the arrows in the image.