Teaching an Old Dog New Tricks

Today, during our chapter review for tomorrow's trig test, a few students came up to ask me how to do a certain problem. That let me know that I hadn't covered that topic well, and I hit upon an idea of how to make it clear to them. An example of the problem would be:

The point (-3,5) is on the terminal side of an angle. What is the sine of that angle?

The formulaic approach is to say that sine (A) = y/r, where r is the radial distance from the point to the origin. But that formula is just for memorizing, so I came up with an alternate explanation about "shrinking" the entire triangle down until it would fit into the unit circle. To do so you'd have to divide all 3 sides by r (in this case, root 34), and the new y-value would be the sine: 5/(root 34), or (5 root 34)/34.

Just seeing the diagram made it very clear to them. And it's the first time I've ever thought to teach it that way, even though I've taught the course, sometimes more than once a year, for 8 different years.