Understanding compund angle formulas

1. Nov 9, 2010

zeion

1. The problem statement, all variables and given/known data

I can make intuitive sense out of cofunction identities but the compound angle results completely blows my mind. Is there a way to make sense of them without having to think about the proof everytime? Or should I just memorize them

2. Relevant equations

3. The attempt at a solution

2. Nov 9, 2010

Mentallic

In the case of the formulae such as $$sin(A+B)=sinAcosB+cosAsinB$$ it is much easier and definitely quicker to memorize than to reproduce in an exam. But I prefer to reproduce the cofunction identities than to memorize them because they are easy to do so, which you might as well.

I think it's just best to memorize these formulae.

3. Nov 9, 2010

symbolipoint

I've been struggling with this on occasion too. Memorizing all of the identity formulas is too tough. There is a website, 'oakroadsystems' or something which gives advice on the Trigonometry identities. One idea that I had was to memorize (and also understand) a small number of very fundamental and easy ones, and learn to derive others from them. For the sum and difference of angles identities, just learn to derive a couple of them, and learn to derive many of the others using some algebraic steps. Use a graph picture to get started.

4. Nov 10, 2010

zeion

The proof for the addition/subtraction formula from my textbook seems completely arbitrary to me ~_~. I have found other proofs online that involve Euler's formula which I have not learned yet, as well as one that involves drawing two right angled triangles on top of each other. Which of the addition/subtraction formula proofs makes the most sense to you guys?

5. Nov 10, 2010

symbolipoint

At least you have access to a picture. Do you find a derivation of one of the angle addition or angle subtraction formulas which is based on a cartesian graph, and not just overlayed triangles? (I really should be looking for one such derivation in a textbook or online --- maybe later or someone else)