If you’re reading this and you’re a mathematician you may not think this is very profound. This is just a little idea I had as I was thinking about the application of the unit circle before moving on with my students to graphing sine waves and other trig functions.
Say you’re on a Ferris Wheel at the county fair, and let’s superimpose the Ferris Wheel onto the unit circle. It’s easy to know when you’re all the way at the top of the Ferris Wheel () and when you’re all the way at the bottom (). Halfway is also pretty easy because it’s when you’re all the way to the sides( and ).