sine and cosine are really vector components

You can make totally sweet graphs with sine and cosine. Im in calculus, and for one of my portfolio questions (we come up with them to demonstrate concepts) I invented a related rates problem which used sine and cosine a ton. One of them was a hyper rectangle(4D rectangle), and each dimension was going in varying sine and cosine curves with respect to time, and I calculated the instantaneous rate of change of the diagonal of the hyper rectangle, and the content (4D volume) of the rectangle at several instances.

I also had one that was a sine wave that was bounded by a circle (so it looked like a normal sin(x) graph, except that it looped back onto itself in parametric mode), and I calculated where a particle landed, and I found the instantaneous force of gravity down at the point it landed by calculating the angle of the incline at the instant the particle landed, and because slope is y/x I just used inverse tangent of the slope at the instant the particle landed to get the angle of incline. oh yeah i also gave the particle a certain mass.

so yeah all of the trig functions have a ton of totally sweet uses and im a nerd and i don't get laid very often