Sine, Cosine, Cosine, Sine. Cosine, Cosine, Sign, Sine, Sine

I overheard Paul VanWieren in the hallway asking about sin(x + y). This reminded me of something I learned from my Math 226 (Calculus III) TA:

"sine, cosine, cosine, sine."
"cosine, cosine, sign, sine, sine."

Say it out loud and you'll never forget it. Here's how it works:

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

Notice that "sign" means to change the sign-- to a minus sign (-). Clever, huh?

Very useful tip, especially for someone with poor memory like myself.