The Unit Circle

So I totally stole this from another blogger who stole it from a student (how cool is that?!?).

I used different methods with each of my three classes and the best method I thought was to work with one triangle (I used the 45-45-90) all the way around the circle filling in the degrees and the coordinates.  Then I filled in the first quadrant with the other two triangles and let the students work their way around the circle based on what we had in the first quadrant (again just the degrees and ordered pairs).  We then came back and worked with converting the degrees to radians.

The templates can be found at this link (thanks to the original blogger - Math Teacher Mambo!)  

The coolest trig foldable!

I found this style of foldable browsing around one day and just KNEW it had to be a part of my class somehow!  It is the coolest thing since sliced bread when it comes to foldables.....and what's even better is that the students think so too!!!

This is my adaptation of the foldable for trig functions.  On the outside you can see the basic SohCahToa with triangles where you set up the ratios (including it related back to the unit circle in the coordinate plane).  Then there's a section where you solve for missing sides in triangles...both where the variable is up high (multiply) and down (divide).  The last section is where you would solve for angles.  In the secret section (cue the shocked faces of your students) is where they look at the graphs of sine and cosine (tangent wasn't in our AFM standards, but I'm sure you could find a way to fit in if needed).

This would also be a good spot to refer back to function transformations and discuss how it all relates.

Secret Door Trig foldable front view

Secret door trig foldable inside view

The magic

 

Building up to The Unit Circle

Trig has always been one of my favorite subjects.  We have reviewed right triangle trig and I'm trying to work towards graphing, but first we are going to have to make a stop at the Unit Circle.  

My plan is to develop the side measures of the special right triangles using Pythagorean theorem and right triangle trig before discussing converting degrees to radians.  Below is the very beginning of this lesson.  Stay tuned for the rest.

Btw...I have a super awesome secret door trig foldable for this unit.

Function Transformations Foldable

I have a confession.  I love foldables!  If information can be organized into a foldable you can bet I will be on that bandwagon with my foldable loving flag waving. 

For this post I'm going to highlight a foldable I used in my Advanced Functions and Modeling class for transformations of functions.  I didn't think of adding the mapping notation on the flaps until after they had already taken their tests, but hey...there's always room for improvement next year right?

I chose a set up similar to this.  

And without further ado....