So there I was, ready to brush up on my trigonometry, when I discovered to my amazement that the high school textbook I’d saved from my own early math years was next to useless. The explanations were awkward and convoluted, the examples didn’t seem to illustrate the accompanying instructions, and the diagrams barely supported the text. I spent a few minutes awash in astonishment that I’d learned anything at all in the company of the book before deciding that perhaps I’d prefer to do my brushing up with a more cooperative text. I was just about to call a friend who might have also saved a trig book when I remembered a little book my mom got me for my birthday one year. I think she bought it because she liked the looks of it and she still can’t believe she successfully raised a math-loving child. It’s a little tiny hardback called *Useful Mathematical & Physical Formulae*.

It features a little cartoon wizard who can be found throughout the book helping to demonstrate and illustrate various concepts. He makes the whole thing entertaining as well as useful. And it’s not just formulas – there are lots of helpful reminders about where the formulas came from as well as enough to explain many of them to beginners. It’s also artfully done – the kind of math book you might enjoy even if you definitely don’t enjoy math. It turned out that the section about trig was just exactly what I needed to remind myself how it all works, with the circles and the right triangles, etc. It’s a great gift for a math lover, and a great reference for anyone who uses the stuff. Thanks, Mom.

## My Favorite Math Reference

Posted on April 10, 2009 by Meredith

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Jonathan, on February 23, 2010 at 9:28 pm said:I’ll never understand why people have to make trig so hard. I think it’s part of technical people’s penchant for obfuscation designed to make themselves look smarter. We COULD call the function that takes an angle in a right triangle, and converts it into the ratio of the opposite side to its hypotenuse OppositeOverLong(Angle), and maybe when kids are used to it, we’ll let them abbreviate it as OppOLong or something. We could, but then you wouldn’t get the satisfaction of calling it something odd like sinusoid. We could call the angle the darn angle, but then you wouldn’t get to sound cool using greek letters like theta.

At the end of the day, trigonometry is actually pretty trivial. It’s just memorizing a taxonomy, except of an alien biology that is unfamiliar and therefore intimidates people. We have no problem memorizing species of fish, because we’ve seen a lot of fish and aren’t scared by new fish. But trigonometry is full of aliens, and so people are scared of it.

Some guy, probably a Greek, asked another guy “how the heck do I figure out the ratio of sides of a right triangle is if I only know some angles?” The other guy said “I don’t know, but let’s just imagine we know the answer and call it the tangent. Maybe someday people will invent techniques and machines to give the answers.” So, there’s nothing mysterious about the tangent function that somebody brilliant figured out it gives you this ratio. It’s a name for this thing people wanted to figure out. People hate not knowing stuff, so they at least gave the thing they couldn’t figure out a name. They hoped someday they’d find a way to compute it exactly, but we now know that you can only write programs to approximate the answer.

The bottom line is this: there are some buttons on your calculator that run programs inside the calculator designed to tell you various things about the sides of a triangle if you know an angle. The whole point of trig class–the WHOLE point–is to inform you of which button to push. That’s it.