Mrs. Phyllis Sprinkle was one of my favorite teachers. One of the main reasons her pre-calculus class was fun was that she had fun teaching it! A highlight of each year was when she taught the identities which explained the sines and cosines of added angles (ex. sin(30°+45°). Once she teaches the equations, she does a little dance that helps the students remember them. Here are the words:
"Cosine, cosine, sine, sine! Cosine, cosine, sine, sine! Cosine, cosine, sine, sine! The sine has the same sign, but it's all mixed up!"
This is probably confusing to you even if you know those identities. I'll try to explain. the cosine identity, cos(A+B), is "cos(A)cos(B)-sin(A)sin(B)." (Cosine, cosine, sine, sine!) The sin(A+B), has the same sign (+ or -), but it's all mixed up --- cos(A)sin(B)+cos(B)sin(A). I hope that makes sense. If not, it's not the end of the world!