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

I'm having a bit of a formula overflow at the moment...

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...

## Discussions

Most of them can be grouped together and derived from one. For example if you can remember:

sin^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

Yes, when I was in high school (25-30 years ago), we still had to memorize trig identities and definitions. If you are interested in any kind of career in science or engineering, you will use these frequently. That will help you to remember them without as much explicit effort. Also, most good enginneering handbooks have them printed, often inside the back cover or something.

How frequently do you use the fact that 3

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.

I've used it in three phase electric machine design.

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

Steve

Most of those derivations you're dealing with in class are specifically intended to get you used to manipulating the different trig relationships in order to change bases as needed for a problem.

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.

The 3 in the upper line was intended to be cube, and was in the right place when I've written the comment :(

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.

My memory is not THAT bad;) I mean 2 sin a cos b = sin (a-b) + cos(a+b) and that sort of thing.

I still remember it as an acronym or word. SOHCAHTOA.

Thought I posted an answer, but I'm not seeing it now...

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.

Totally unpleasant and ultimately unproductive for me the first time around. I'm having to relearn some of them 20 years later for another math class (that I wouldn't be in if I'd done better in it the first time I took it around 15 years ago). One difference this time is the professor is relating all the useful identities back to either the sine and cosine rules:

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.

Yes, anyone of my generation had to learn their identities for our 18 year old exams "A" levels.

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