Math Is Fun Forum

Anakin

Member

Registered: 2009-10-04

Posts: 145

Proving Trigonometric Identities: Strategies+Hints [Asking]

I was just wondering whether you guys had some specific advice, hints, or strategies involving proving trigonometric identities.

I can usually get them but it takes quite a long time for really complex ones, in which case I may not even end up proving it.

Most of them involve double angle formulas, half angle formulas, quotient identities, Pythagorean identities, and the reciprocal identities.

I know it's hard to get better at these without experience and seeing nearly all the sorts of examples but any advice would be appreciated.

Thanks!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Proving Trigonometric Identities: Strategies+Hints [Asking]

Hi Anakin;

That is a good question. I have seen books that recommend working with the side that is the most complicated and I have heard of working with the side of the identtity that is simplest. How do you determine which is more complex?

I can usually get them but it takes quite a long time for really complex ones, in which case I may not even end up proving it.

This is what I do:

1) Get good tables from the net of trig identities.
2) I work with the more complex side.
3) Make 1 and only one change (substitution, algebraic move, etc) per line.
4) Check the veracity of each line before going further.
5) Be neat!!!!
6) Expect that each identity will not be done quickly.
7) Hope for the best but expect the worst (you might not be able to do it).

And of course you must do lots of them.

I hope that other members will post their ideas.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Anakin

Member

Registered: 2009-10-04

Posts: 145

Re: Proving Trigonometric Identities: Strategies+Hints [Asking]

Thanks for the reply Bobbym.

Yeah sometimes I find a complex side easier, sometimes the simpler side's easier to prove. Usually I start with the complex as well.

1. http://www.sosmath.com/trig/Trig5/trig5/trig5.html Would that qualify as a good table?

As for everything else, I do try to do exactly what you mentioned. Especially checking the last step to verify if I made any mistakes, as that can be crucial.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Proving Trigonometric Identities: Strategies+Hints [Asking]

Hi Anakin;

That is a good table and I use it too. I also use this:

http://en.wikipedia.org/wiki/List_of_tr … identities

Google for trig identities and you will get some more. Point is, these are your weapons.

Couple of old books that I use:

A short table of integrals and of course the Abramowitz , Stegun book.

Those are relics, I am sure you can find more modern ones that will be just as good.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Anakin

Member

Registered: 2009-10-04

Posts: 145

Re: Proving Trigonometric Identities: Strategies+Hints [Asking]

Thanks for the link. I guess apart from knowing the different identities, it's experience that will allow one to decide while identity to use.

And if that doesn't work, I gotta go all the way back and try a new one.

I'll keep trying different examples, it'll help during exam time.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Proving Trigonometric Identities: Strategies+Hints [Asking]

Hi Anakin;

My answer only outlines my method of doing them. I can't say that it is optimal or even good. It is the result of a lot of trial and error. I am sorry that I couldn't provide you with a little more.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.