People have all sorts of odd mnemonics, and I’m an old grouch when it comes to most of them. There’s the SOHCAHTOA mnemonic (Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent) , which I think is potentially terrible since people sometimes can’t remember how to spell it, but I suppose people have to find their own way to memorize what sine and cosine is.
There’s also All Students Take Calculus which tells you that All (sin, cos and tan) are positive in Quadrant I; only Sine is positive in Quadrant II, only Tangent is positive in Quadrant III and Cosine is positive in Quadrant IV. I always particularly disliked that one, because if you look at the unit circle, all these things become obvious. I’ve talked to students who were amazed upon seeing the unit circle approach to that, as ASTC had led them to forget why things were true.
My favorite trig mnemonic was given to me by Mr. Hobson in 7th grade at Trinity School in New York (proper credit). He said, to remember the trig sum formulas, here’s a mnemonic so stupid that you’ll never forget it. Imagine Coco and friend are on a hill. The friend says, “See Coco See!” and Coco replied, “Coco see see!” I promise this works better out loud and if you make a big deal about it. The point is sin(x+y) = sin x cos y + cos x sin y (See Co Co See!) and cos(x+y) = cos x cos y - sin x sin y (Co Co See See!). You just have to remember that the x and y stay in place and the sign flips for the cosine (as it often does).
I told my students that I’d give them extra credit if they wrote “see coco see, coco see see” on their exams, and they usually would, along with voluntary illustrations.
And once you remember “see coco see…” you can immediately derive the double angle formulas by plugging in x+x, and by manipulating cos 2x, you can get the half angle formulas.
I don’t think it’s so important to remember these formulas, but the mnemonics have given my classes something to bond over and something amusing that sets them apart from other classes.
to discuss: hidilo, lodeehi.
– Eric Hsu 1998-08-09