# Did you learn trigonometry rules off by heart at school and how did you manage to survive it?

Actually, the idea of learning 32 of them and reciting in class sounds a bit 19-century to me.

I was even more disappointed when I opened an English Maths textbook and didn't see any signs of such terrifying practice.

Did anyone here learn it, and how did you manage to survive???

PS The worst part is that we have to be able to recognise them pronounced and pronounce them, and not only be able to write them...

active| newest | oldestsin^2 + cos^2 = 1

Divide the entire equation by sin^2 and cos^2 to get the other two identities.

sin^2/sin^2 + cos^2/sin^2 = 1/sin^2

= 1 + cot^2 = csc^2

sin^2/cos^2 + cos^2/cos^2 = 1/cos^

= tan^2 + 1 = sec^2

sin(3a)=sin a sin(a+pi/3) sin (pi/3-a)=3sina - 4sin a?

I've only come across it used once, in a large scary limit-calculating problem, which was obviously made up by someone who thought it was nice to teach the kiddies to use that very fact.

Give it 30 years, and then come back and say you don't know what it was for.....

Steve

I have frequently used the double angle and half angle formulas (because they show up in computing amplitudes and transistion matrices for weak decays). For example, the CP-violating term in B meson decays works out very naturally in the form cos(2b).

The sin(3a) and higher relationships are most likely to come into play if you are picking off harmonics from a Fourier transform. I'm not 100% sure you've written down the relationship correctly -- the last expression "3 sin a - 4 sin a" is nothing but -(sin a), which can't be correct.

Actually, first formulas I've learned was tangent of sum, which I remembered written on the blackboard as Lorenz formulas for the previous generation of the Wheeler and Teylor book readers. I was twelve or thirteen then...

Sine=Opp/Hyp

Cosine=Adj/Hyp

Tan=Opp/Adj

I remembered it all these years so it must have worked.

Think of these as like your times-tables. You want to get to the point where you can apply them without needing to stop and think, because when you need them later on you may not have the time to look them up or re-derive them.

You may never need them. Or you may need them in a hurry. Learning them well now will make using them later easier.

One of the things you are learning, at your age, is HOW TO LEARN EFFECTIVELY. In a very real sense, that's a more important lesson than exactly what subjects you're studying. Yes, it's a bit painful... but, again, what you're doing is building up a library/toolkit of problem-solving techniques that will be helpful later on.

cos(A+/-B) = cos(A)cos(B) -/+ sin(A)sin(B)

sin(A+/-B) = sin(A)cos(B) +/- sin(B)cos(A)

or Euler's identity:

e^(ix) = cos(x)+i sin(x)

and also back to coordinates along the perimeter of a unit circle.

Not that those will help much with the memorization, and less with recitation, but they may help with understanding. This page isn't too far off from what I'm seeing this time around.

I always looked at them as part of my toolkit - I STILL carry them around and use them occasionally, and because I learned them by rote, they float in front of my eyes when I look at problems that might need them.

Steve

Rules are things you have to learn.

But, if you know the subject well you'll know the rules better.

L