>The sine, cosine, and tangent functions are still just black boxes to me, I have no idea what they actually do They are functions which tell you how to relate

>The sine, cosine, and tangent functions are still just black boxes to me, I have no idea what they actually do They are functions which tell you how to relate different parameters of a triangle. Concepts in mathematics are often interconnected, and trig functions appear in a lot of other (interesting) contexts as well, but fundamentally I don't see them as anything "more" than the SOHCAHTOA you were taught at school. > or how I would calculate their values. Without a lookup table? You would need some kind of a way to express the functions in terms of other mathematical functions which you know how to do, like multiplications and additions. Sometimes you can do this with a series expansion. Computers sometimes use a variant of the CORDIC algorithm. Both of those things are clever ideas in their own right, but you don't need to understand them to know what trig functions do. > I often daydreamed about finding myself on a desert island, needing to make use of trigonometry to rebuild civilization, but not being able to find the angles that I needed. If you had a circle, a ruler, a pen and some paper then you'd get the idea to make yourself a lookup table pretty quickly! I think the point I'm making is that we get used to assuming that knowledge is so deep and complex a thing that we can never really know anything. But often, knowledge isn't as intricate as that. If everyone forgot about trig functions today, they'd be rediscovered tomorrow.