Today in Precalc we started graphing sine and cosine curves. I gave them these charts to fill out all of the sine, cosine, and tangent values of our favorite unit circle angles. Then I handed out
Then I asked...
It was fun to hear their observations. They started out a little slow (I don't think they're ever asked anything like this without there being a "right" answer) but after a few non-mathy things they jumped into odd/even, zeros, and maxima.
This was an easy segue into the "correct" terminology of amplitude and period, and the transformations followed from there.
Oh, and it was soooo nice to have the kids make a prediction on what a value would do to the graph (like a vertical translation) and then show it using the Desmos calculator. Love their sliders!