Sine waves done visually

Sine waves underly all sorts of interesting mathematics, but they're actually very simple.
Imagine a spinning wheel with a dot of paint on it.
The dot's height goes up and down as it spins, in a repeating pattern.
So if you graph the height of that dot over time, you'll see something that also repeats: once per time the dot goes around the circle. And that's how you make a sine wave!
The exact graph might vary depending on your wheel, of course; if the wheel spins more quickly, the dot will move up and down at a higher frequency and make a wave that looks more squished. But that's all there is to it: looking at spinning things over time.