Unit Circle Trig

I have an odd love for the unit circle.  I bet most math teachers do.  I had a professor in graduate school who said, "There's nothing left to be discovered in the area of trigonometry.  Just draw the damn unit circle and you're done."  I think that's why I love it so much.  There's so much information you can gather from such a simple representation.

This year in PreCalc, my team and I actually started the year with trigonometry.  So, the kids were introduced to the unit circle on the second or third day of school, I believe (I know...this post is like five months late).  Since we use the unit circle so much, I really wanted to give the kids a visual understanding of where all the ordered pairs come from.  So, in addition to giving them blank unit circles to fill out, I also gave them three triangles that fit onto their circles:

This is, obviously, completely blank, but the kids' triangles' sides
were all labeled (both on the front and back).

Here are the unit circles (I stole this off the Internet sometime ago...let me know if they're yours!).

Blank Unit Circles 2014

And here are the three triangles that I created; each hypotenuse should be the same length as the radius of the circles in the previous document:

Special Right Triangles

Using what they remembered from geometry and given that each hypotenuse has a length of 1, the students labeled the remaining sides of the triangles (on both sides of the paper).  Then, they placed the triangle that fit on each coordinate and the x- and y- coordinates were (hopefully) clear to see.

I had the students tape both their completed circle and their three triangles to the very front of their composition notebooks.

*****

Another activity that we did, which I adapted from an article in Mathematics Teacher, was I created a huge "human unit circle."  I bought a cheap plastic tablecloth and drew a circle on it, but there are lots of ways to make one.  Then, I made cards for each coordinate on the circle.  I printed this twice on two separate colors: one for x-values and one for y-values:

Human Unit Circle

I had half the kids pick up a green card (x-value) and half the kids pick up a yellow card (y-value).  Then, I asked them to find a student who had the other part of their ordered pair (we discussed how for most of the cards there were two options).  Once they found their partner, I asked them to place their ordered pair on the correct location on the unit circle:

Once they finished placing their cards, I picked up random ordered pairs and had them give me the corresponding angle, in both degree and radian measure.  

I thought the kids did really well with the unit circle this year.  Now the trick is to keep practicing it with them even though we're done with our trig units... :)