## Wednesday, October 2, 2013

### Derivatives of Trig Functions

One of the things I find challenging to balance is convincing kids of mathematical truths without overwhelming them.  Sometimes, I know, there is a time and a place for a bit of hand-waving.  And, sometimes, I know, there is a time and a place for formal proofs.[1]  But I think most of the time the sweet spot is somewhere in between a formal proof and "this is how it is--just memorize these rules."

In search of that happy medium, I created decks of 12 cards (6 with the graphs of the basic trig functions {orange} and 6 with the graphs of their derivatives {blue}).  I had students match them up with a partner.

Matching a function to its derivative using only graphs is new for my kids, so I knew this would be a challenge if I didn't lead them quite a bit.  However, gathering data from a graph is so heavily tested on the AP exam that I figured it wouldn't hurt to start making some connections.

After they matched them up, I followed up with these questions:

Here are the cards I made, if you're interested (thanks, Desmos!).

6 basic trig functions (enough for 16 decks):

6 derivatives (enough for 16 decks):

[1]  Although I'm beginning to think I show proofs more for myself than my kids.

1. My calculus course being at college, I suppose it makes sense I prove more with them. I made a 4-page handout proving that derivative of sine is cosine. They fought their way through that jungle admirably well.

I like these cards. I want to use them. Maybe on Thursday we can use this as a review activity for the upcoming test.

1. Definitely...when I taught calc at the community college I proved substantially more...but I'm still not certain how many of the students really followed. I remember reading your handout for the derivative of sine and thought it was awesome. I should use it as a follow up--especially for my more advanced kids.

Just as a warning--I included the the equations on the bottom of the cards, which would probably be a dead give away if your students already know their derivative formulas...so you may want to chop that part off the cards. :) Let me know how it goes!

2. Maybe I'll make my own - as a handout. It should take under an hour.

3. It took about an hour. I'm not happy with the quality yet, but I'm using it as-is for now. I used desmos to draw the graphs (struggled to get the right labels on the x-axis), and jing to save them. I can email you my handout if you want, but your stuff is nicer.

4. Please send it my way when you get a chance! My email is rebecka dot peterson at gmail

2. I have always sworn by flash cards for so many different subjects, but I have never tried them with something like a graph on them. It may take a bit of effort to prepare, but I can see how useful that would be, if for nothing else than purely quicker recognition. And that in itself is useful when it comes to testing!

Tell me what you think!