Derivatives of Trigonometric Functions

I. Stink. At. Blogging.

I have been working hard to get to know my new kiddos, my new colleagues, my new town, and still walk my dog and talk to my husband occasionally. Oh, and I've slept in my own bed exactly 0 of the last 5 weekends (#weddingseason). Unfortunately, that meant blogging was the first thing to go. 

This post is NOT groundbreaking, nor is it going to be long, but you have to start somewhere. This is me at least showing up at the gym and walking on the treadmill. It's no spin class, but it's a start back to getting in shape! So here goes.....

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I have always believed in allowing kids to discovery something whenever it's developmentally appropriate for them to do so; it's a pillar of my educational philosophy. My very first year of teaching high school, I had a student who would stay after school with me to derive formulas that I'd deemed not worth deriving with the class as a whole because it would bother her to not know "why." She understood that these formulas weren't "magic" and that math should make sense and I still think of her often when I am working to discover something with my kiddos.  

One of the issues I had my first time as a Calculus teacher was students who had been good at the "skills" of math, but hadn't always been great at the conceptual part. They really say math as a list of things to memorize and as long as they could do that, they would do well. So much is lost when we approach Calculus this way, so I've worked to build more conceptual understanding into a curriculum that an all to often be skills-based. 

In the past, I've built up my arsenal of awesome Desmos and GeoGebra activities since I was working in a one to one environment with technology. And while I am loving my new district, it was a jolt back into the real world of having to share computer carts and wait 5-7 minutes for PC's to boot up before an activity could start (I know....I sound spoiled. I am aware I lived in a technological fantasy land for the past 3 years of my teaching career).  Sometime, it's just not worth the 7 minute boot up time for a 5 minute activity. So instead of breaking out some Desmos wizardry, I wrote a good old exploration for the graphing calculator to derive the derivatives of trig functions. What I wound up loving about this was the ability to introduce some new functions of the calculator, since that will be their trusty friend during the AP exam anyway. 

First I had the students use the calculator to graph the derivatives of y=sinx and y=cosx.

Then, I had them use the quotient rule and trigonometric identities to derive the other 4 trig derivatives.  

Like I said, not groundbreaking, but it got them talking and thinking about the magical fact that Calculus is, in fact, not just magic. It should all make sense! 

Derivatives of Trigonometric Functions Discovery