Do you teach trig? Do you wish your students had a solid understanding of how to relate trig ratios beyond 90 degrees to the unit circle? Are you tired of kids asking which button to press?

Well … I can’t say for sure if this solves your problem, because I haven’t used it in my class yet. But someone else has! And they said it works great!

The original I was shown is simply a full-circle protractor photocopied onto a co-ordinate grid. I decided to make a fancy-looking version in Illustrator. And since I’m all proud of it, I’m sharing it with all y’all.

unit circle protractor sheet

The idea is, if you want to look up sin or cos for a given angle, just find the angle and then read the y or x co-ord of the matching point on the unit circle. Kids should be able to visually estimate something close to two decimal values worth.

Enjoy!

Edit: You may also want to check out the matching 30-60-90 and 45-45-90 triangle cutouts that match.