We just wrapped up our intro to radian measure in Trig, which includes the unit circle. My personal philosophy is that students don’t really need to memorize the unit circle, because if you understand where it comes from, you can always derive it. I’ve done a “build the unit circle” activity for a few years, but I’ve never blogged about it, so here it it is.
Basically students get a blank unit circle and bunch of 30-60-90º and 45-45-90º triangles with the hypotenuse labeled as one unit and then they have to find the rest of the side lengths and use them as measuring tools to figure out the coordinates of the points on the unit circle.
At this point my students do have the two special triangles memorized, have thought about 60º = π/3 because it’s 1/3 of the way to 180º, and know that sin(ø) = y/r, etc. I don’t allow them to use calculators or really give them any help during this activity. They struggle a little bit a first, but they get there.
I like this activity because I think it helps students see the connection between the unit circle, coordinate definitions of the trig functions, and right triangle definitions of the trig functions. It’s also a nice hands on day to mix it up. I remember that making the handout so that the angles and triangles actually work in the circle was a pain, so I thought I’d share!
1ntegration by Parts 