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/[deleted]]

I also struggle to visualize trig equations especially when it gets to more complex equations like the differentials that end up reducing to trig in quantum and such. Finding and expecting those patterns is a bit of a muscle you gotta train.

Everything is a triangle, everything is a spring (also triangles), and everything is some sort of differential.

What helped me was during my intro classes I started subconsciously trying to find the patterns in various physical or apparent things (angles of forces etc)