While shopping the other day, I saw some of those decorative garden windmill things for sale at 50 cents each. Normally they would be the type of thing I would just walk past and ignore (not really one for gardening), but this time I had an light-bulb moment. So I bought a handful and came up with this creation:
Before and after: the original “Windmill” and my Unit Circle Spinner.
Close up view.
If you look at it from side on it gives a visual demonstration of sin (or cos from above), represented by the amount of yellow paper you can see and the direction it’s pointing in. For example, this is roughly showing that sin(π/6)=0.5:
(Trying to balance the spinner in the right place while simultaneously taking a photo was easier said than done.)
I’m not completely sure destroying a garden decoration was necessary to make this, but sometimes it’s good to take inspiration from wherever you find it.
I hope this will help my students understand the definitions of sin and cos (and tan) better than they have in the past. A lot of my previous students have seemed pretty happy to rely on mnemonics like “CAST” to remember where the different functions are positive or negative. Sometimes I wish I could tear that page out of their textbooks.