TRIG IDENTITIES!!!

We started simplifying trig expressions this week in precalc. This is only my favorite stuff all year.  I know it starts out difficult for many of the kids (especially because they're just learning their identities) but after a couple of days in I've been really happy with the discussion I've heard.  They work SO WELL in their groups that I'm ticked I didn't do this last year.  And a few of the kids have even admitted to me that they kinda like these kinds of problems!

(When we went over the first assignment, I asked the class what we should do for a particular problem.  At the exact same time, two girls said, "Cry."  I had to admit it was pretty funny.)

I think some of the kids get frustrated with simplifying because they see that it's so easy for me, so the first day I tell them why. Aside from the fact that I think these types of problems are fun, I also have spent two weeks a year, three times a day, for the last 15 years working these problems. I would hope they'd be easy!

Today one of the kids decided I needed a challenge so he found a problem online to give me.  Here it is:

I admit to having no clue where to begin. I thought about power-reducing formulas and half-angle formulas and got nowhere. Then I tweeted the problem and got some help from a bunch of people who decided that it wasn't actually an identity. After tweeting at the student, he gave me the link to the problem where I discovered that you're given that a + b + c = 180.  So that changes things.  (I'll use that as my excuse tomorrow).  But many thanks to Steve, Glenn, Marshall, Nik, Matt, and David for trying to help a girl out!

It led me to an idea, though. I'm thinking maybe I'll have the precalc kids come up with what they think is a tough identity to simplify and see if they can stump me.  I tried something like it last year and got some good results, but I didn't incorporate the "Stump the Teacher" challenge.  We'll see.


The best moment of the day came in my general Algebra 1 course 7th period. There's a girl in there who is from Cambodia, and she's honestly amazing. She knew very very very little English when she started in August, but her math skills were (luckily) great and she did awesome. She's the perfect student: she does her homework every night (and usually does extra problems), she is always concerned about why she gets a problem wrong, and she is able to laugh at herself when she does something silly.  (Actually, it's usually an "Oh my goodness!" reaction.)  But today she walked into class as I was talking to the special ed teacher who's in here with me. The girl said something to me that I didn't catch, so I asked her to repeat it. Her comment?  "Mrs. Fouss, you look beautiful today!"  Oh my gosh, how sweet!

(This is what she did for our last homework problem today... think anyone else in this class would've had an inkling of what she was doing?! I felt bad because it was just  "read the graph" problem and she went way beyond. That would certainly be a language issue.)