In geometry, I’m doing an introduction to trigonometry. We’ve been working without using SOH CAH TOA, and even without the ratios. Today we got to the point where at the end of class, we saw how having any two sides of a right triangle uniquely corresponds to a whole bunch of similar right triangles — and with that we can see how the angles come for free!
It’s a longer story than that, but the kids are using SOH CAH TOA in their physics classes, but clearly they’re not totally get what’s happening or why it’s working. And in our rushed end of the period, when we were summarizing some of these ideas, I saw some kids slowly start to see that there’s a connection between what’s been happening in their physics classes and what we’re doing here. They aren’t quite there yet, but they are about to be there.
I’m excited for that to happen.
A student last week emailed me a question about end behaviors as asymptotes. I left her with a challenge:
If you want a challenge, here’s an question I just thought of… Come up with a function whose end behavior looks like a sine function. So for large x-values, the function looks like a sine function!
This morning she responded with this graph:
Yup. She gets it! Huzzah!