Last week in Precalculus we finally started talking about radians. After doing the basics (what is a radian/complementary/supplementary/coterminal) and some not-so-fun angular and linear velocity problems, today we got to what will change my students' lives forever.
The Unit Circle.
Several years ago I started giving them an image like this one to fill out instead of the one above. It's so much more organized.
When we create the unit circle in class, I like for them to know where those darned ordered pairs come from. So in the past I would hand out a notecard for each kid and ask them to trace the 30 degree angle to create a 30-60-90 triangle. Once they realized that the hypotenuse of the triangle was the same as the radius of the circle (1), we could find the two legs of the triangle. The problem was that to trace the angle they had to be able to see through the notecard onto the unit circle below. I typically would have kids lined up along the back windows with their papers propped up so they could use the sunlight to help them see. Then we'd cut out the triangles and arrange them on the circle so the kids could see that the sides of the triangle were their paths to the ordered pairs. I thought it worked well (instead of just throwing the ordered pairs at them without any rhyme or reason) but the notecard density and having to cut them out slowed us down.
Then last year, two classes in to creating a unit circle, I thought about using patty paper instead of notecards.
And thus my life was changed forever.
(btw, here's the post where I wrote about it last year. Sorry for double posting on the same topic. It just makes me so happy!)
AND I just found a unit circle song that I'd embedded on my blog almost two years ago. THIS IS WHY YOU NEED TO BLOG, PEOPLE! (If your memory is as bad as mine is, anyway.)