## Wednesday, 1 November 2017

### Cofunction Angle Identities

Every year many of my grade 12 Advanced Functions students struggle with cofunction angle identities. Let me back up. They actually struggle with the entire second unit of trig. This includes proving identities and solving equations, but begins with cofunction angle identities. This is often where the confusion begins and it snowballs through the unit. I asked myself what I could do better, or differently, this time around so here is my attempt to help my students better understand the difference between related acute angles and cofunction angles.

I started by creating this investigation.

They worked in random groups on large whiteboards and definitely needed some coaching from me along the way. I feel that they finished the class with a strong understanding of the relationship between sine and cosine of complimentary angles.

We consolidated together and then recapped the following day with this:

I think that changing the acute angle to the vertical to α (not q) helped some see the difference between related acute angles and cofunction angles. It also helped me refer to what they had seen in the investigation - "Remember how alpha was the angle between the terminal arm and ...".

I wanted to build on what they had learned as we continued to move forward with compound angle identities so I decided to make a warm-up. I created a "game" that we have played for the last two days and we will play round 3 tomorrow. Each student got a small whiteboard and marker. On day 1, they had to write T for transformation, R for related acute angle or C for cofunction on their whiteboard. Each expression was on its own slide and students put up their whiteboards with each answer, which we discussed briefly. Here is the "game" for day 1:

They did well for the most part. Well enough that both they and I wanted to do another game the following day, so on to part 2. This time I asked for three things: T/R/C (same as day 1), quadrant and equivalent expression. Once again they each wrote their answers on a small whiteboard and held it up when they were ready. Here is the set of questions - students did not get to see the answers which are shown below:

Again, it went well.

This morning I shared the first two "games" with a colleague and she suggested making another one. We settled on giving an expression and a choice of potentially equivalent expressions, of which more than one could be correct. We made three of them and my colleague did them with one of her classes today and her feedback was that they really made the students think. She also pointed out how perfect these were as we head into proving identities.

My hope is that this daily practice will solidify their originally tenuous understanding of new concepts which will in turn give them more opportunities for success when they are working with identities and equations.

If anyone would like any of the files, please let me know.