I meet a lot of people, at airports and music festivals. I’m a friendly, talkative kind of person (at least when I haven’t slept in a wet tent for two nights straight). When they ask me what I do for a living, I often say I’m a mathematician. Then they pretty much always tell me how much they hate math. When I ask why, they often suggest it was trigonometry that killed any interest they might have had for the subject.
I agree, trigonometry sucks. Fuck trigonometry. It’s a terribly unmotivated subject, and as a student you are expected to memorize double angle formulas with no proofs. It’s never clear why you’re learning it, except for the possibility of later memorizing the integrals and derivatives of said functions. It’s almost a case study in how to make someone feel like math is meant to be mysterious. A few comments before you decide I’m being unfair.
First, yes, trigonometric functions are needed in Fourier Analysis, which is hugely important nowadays for the sake of music files and information compression. But by the time you’re working with Fourier Analysis, you have more mathematical technology, and in particular you know the magic formula which makes all mysterious double and half angle formulas super easy, namely Euler’s Formula:
Understanding this formula, the Fourier Analyst is equipped to work with trig functions without all the mystery, and absolutely no memorization. In fact my mom did me the favor of explaining the above formula to me when I was in high school so I could avoid all the memorization. It helped, but even then I had memorized it, and it wasn’t until college that I understood it.
Next, this isn’t the first time I have pooped on trig. I wrote a post about statistics and algebra teaching in high schools a while ago, and in that post I suggested chucking trig from the curriculum. A few people stood up for trig in the comments. Here’s what they said.
- Someone mentioned it’s needed in “shop class.” But then they went on to explain the shop classes no longer exist.
- Someone mentioned that trig functions are great examples of periodic functions. While that’s true, we don’t need to go deeply into the subject – never mind double angle formulas – to explain that. Even just talking about an ant walking around the unit circle would be sufficient, especially if we asked for the x- and y- coordinates of the ant at a given time. Enough said. We could end the lesson with a historical remark along the lines of, by the way these functions have names, they’re called the sine and cosine functions, and you’ll learn more about them when you learn about the complex plane and Fourier Analysis.
- Someone mentioned that they use trig functions every day at work in the physical sciences. Again, I’m willing to bet they also know about the complex plane.
- Nobody mentioned that ship captains needed trig, but again we have GPS now.
When I mentioned my hatred of trigonometry to my husband, he countered with an argument that wasn’t mentioned so far. Namely, that we have really no reason to teach high school kids any given thing, so we just choose a bunch of things kind of at random. Moreover, he suggested, if we remove trig, then meeting people at an airport would just elicit some other reason for hating math. We’d be simply replacing trig with some other crappy topic choice.
I disagree. Although it’s not obvious that everyone needs higher level algebra in their daily lives (although they most definitely do need to solve systems of linear equations), it’s still more defensible to teach them to factor quadratic polynomials than it is to introduce arctan. And even though most people end up memorizing the quadratic formula, it is at least derivable using a simple completion of the square. In other words, it’s at least clear that there is an explanation, even if you don’t have it at your fingertips.