This is for my homies in maths class. I know many of you fear the sin & cos.
They’re just a way to convert from circular coordinates to square coordinates.
You want to get to the red dot. If you’re at sea you set your bearing θ and sail straight there. If you’re in the city you walk north and then east.
Cosine tells you how far you have to walk crosstown; sine is how far uptown.
That’s basically it. If you think uptown and crosstown look like legs of a right triangle, you’re thinking along the right track to understand where the many sin & cos formulæ come from.
Here’s a GPL’ed picture of why we think of cosine as a wave: