Monday, September 08, 2014

Unit Circle and Radians

Breaking News: Kids struggle with fractions!
Alert: Kids can't describe how 3π/4 relates to π.
News at 11: Radians? What new torture is THIS?!

I tried something new today in precalculus to help cement the "special angles" around the unit circle. Based on the spontaneous comment of one of my students ("this REALLY helped."), I am hoping for greater and sooner fraction success this year.

First I made templates and printed them on various colors of papers (one color for each special "radian"):

Each student trimmed the circles and pasted the yellow "unit circle" in their notebooks along with a blue slot to store wedges:

We then had a discussion about π/6 and I had them place various radians in standard position and we discussed reference triangles and values around the sides:

I made sure to do some negative angles:

We finally discussed the π/6 angles and worked through a problem:

 Now I sit back and wait to see if THIS year they are fraction geniuses!


  1. Could you please start doing awesome lessons two days before I teach the same topic instead if two days after??? :) but at least I can keep this in my back pocket for May in alg II! Thanks for sharing!

  2. Anonymous5:19 PM

    Hah! Meg, funny story: I was rushing rushing rushing through radians and special triangles and unit circle, and then I actually went back to look at our plan (after the fact) of what/how/when my buddy teacher and I would teach stuff, and Lo and Behold, I was supposed to slow down and do something like this a day or 2 ago. Oops. Better late than never, right? RIGHT?!?!?!? At least I'm telling myself that.

  3. Hi Shireen Dadmehr! I wish my Precalculus teacher in high school would have used this method of teaching. I probably would have stayed in the class instead of asking for a transfer. I loved the way you used the different colors for the radians and special reference angles and had the students place them on separate sheets in their notebook, making it easier to understand in their studies. I also I like how you use non-traditional ways to teach math. In the future, I tend to direct my students, that may be having problems in math, to your blog. I hope your blog will help them. Finally, I have included a link to my blog post for you to read. Have a great school year! Thanks for the advice!

  4. So I'm teaching trig for the first time this year and I understand nothing. Why IS that the reference triangle for 5pi/6? I have only done coterminal and reference angles in degrees so far. I was thinking I could use this to introduce radians and then have them practice coterminal and reference angles again in radians before reference trianlges. Does that even make sense? Please help :(

    1. cathy olshefski12:59 AM

      If you reflect the first orange triangle across the y axis you will see that the coordinates will be the same but x will have a different sign. So the values of sine and cosine are the same except for the sign of cosine so we call it the reference angle because if you know it in the first quadrant you can just reflect it for the other 3 quadrants (reflect twice to get to 3rd quad)

  5. I Love this. I already have the students do a unit circle project that I learned at NCTM. But, they still struggle with the fractions. I think this will be a wonderful addition to what I already do. Since we use a specific color for 30, 45, and 60, I plan to use the same color.

    Thank you!!!!!!