One weird trick! Click here!
Somewhere in my years of “tutoring calculus,” also sometimes referred to as “tutoring trigonometry,” I discovered a trick (here meaning a tool devoid of any conceptual knowledge of the topic at all) for evaluating the cosine (and therefore also sine) of the upper-right quadrant special angles . This can be extended to the rest of the unit circle in the usual way.
I rarely see this move discussed, and it is such an easy way to “memorize the unit circle” that I find this surprising. As with all academics, I should be writing, so here you go.