Sorry, this sketch requires a Java-compatible web browser to see.
To generate a sine wave, click the "spin x" and "increase time" buttons and the sketch will plot out a sine wave. Click the "X" to clear the graph. The circle is spinning at a constant speed and the time is moving forward at a constant speed. A sine wave is just the plot of the vertical position of a point moving on the edge of that circle as time goes by.
The red points can be moved by hand, so also experiment with only turning on spin and moving time by hand, or only turning on time and spinning the point X by hand.

This next sketch shows the same idea, only in a more complicated way. Sorry, this sketch requires a Java-compatible web browser to see.
Click "show" and then click "spin." As you can see, the sine wave is not actually moving. The points on it are just moving up and down. Each of those points is connected to a point on the circle, and as the circle turns, each point on the wave shows the vertical position of the point it's connected to on the circle. Same idea as the first sketch, just more interesting and complicated.