Understanding compund angle formulas

[zeion]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[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.

 

[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.

 

[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?

 

[symbolipoint]

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?

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)