In 2013, The Onion thrilled the nation’s math teachers by, at long last, mentioning them:
It’s a headline that bites right to the center of the Tootsie Pop that is our mathematical curriculum. If math is a deafening barrage of arbitrary things to memorize, then trig cranks the volume of gibberish up to 11. I mean, cot2(x) + 1 = csc2(x)? Why do I care again?
Of course, all of trig really just boils down to two functions:
This pair of functions has many offspring, several of which we ask students to learn. Evelyn Lamb lays out some more obscure cousins in a wonderful post:
As Lamb explains, every function in this motley crew once served a useful purpose, back in the days before automated computing. Now, they’re mostly obsolete. So that means we can narrow our attention to the essential few, like sine, cosine, and tangent, right?
Wrong, I say! In the spirit of life imitating The Onion, I propose that all humans memorize the following utterly essential trig functions:
An Open Letter to Students Wondering, “Why Do We Use Radians Instead of Degrees?”
Let me start with a question of my own. Did you know that you speak Babylonian?
You may not think that you do – you can’t ask for directions to a Babylonian bathroom, or order lunch off of a Babylonian menu, or ask a good-looking Babylonian out for coffee. But you’ve inherited Babylon’s legacy nevertheless.
You’ve probably noticed that our systems of counting and measuring are largely base 10. There are 10 years in a decade, 10 decades in a century, and 10 centuries in a millennium. But take a look at shorter time lengths: We don’t carve up the day into 10 hours, each 100 minutes long, even though this would make perfect sense. Instead, we divide our time up by multiples of 60 – 60 seconds in a minute, 60 minutes in an hour.
Why do we do this? Because our Babylonian uncles used a base 60 number system, and we’ve been following their example ever since.
Babylon left another relic in our system of measurements, one that requires a little deeper explanation, and which lies at the heart of your question (yes, I’m getting there): the degree. Continue reading