If I were to turn f(x) = 3 cos(2x) + 4 sin(2x) into a single function... Where would I want to start? Would I just use the double angle formulas and go from there?

Thanks,

-Tom

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- October 31st 2006, 04:49 PMTomCatSingle trigonometric functions...
If I were to turn f(x) = 3 cos(2x) + 4 sin(2x) into a single function... Where would I want to start? Would I just use the double angle formulas and go from there?

Thanks,

-Tom - October 31st 2006, 06:43 PMtopsquark
You mean a single trig function to represent that? I don't think it can be done. However, to answer your comment about the double angle formulas this is what you would get:

f(x) = 3cos(2x) + 4sin(2x) = 3(cos^2(x) - sin^2(x)) + 4*2sin(x)cos(x)

As it happens you can factor this:

f(x) = [3cos(x) - sin(x)][cos(x) - 3sin(x)]

But that doesn't give you the form you want.

If you mean can you get it just in terms of sine or cosine, THAT we can do:

-Dan - October 31st 2006, 07:01 PMThePerfectHacker
But,

Maybe in physics okay, but not heir. - October 31st 2006, 07:22 PMclassicstrings
I thought cos^2(x) + sin^2(x) = 1

Rearranging gives cos(x) = root(1 - sin^2(x))? - October 31st 2006, 07:22 PMtopsquark
- October 31st 2006, 07:33 PMThePerfectHacker
These are not equivalent statements.

---

Basically, look at the graphs show below.

~~~

Topsquark, you should define a function,

that is if otherwise

Then you can say,

I actually think my function can be useful. Look at the Heaviside function.

Can you express my function as a fourier series or will it lead to Gibbs phenomena? - October 31st 2006, 08:28 PMclassicstrings
How do I type sin^2 on my calculator? When I type sin it automatically gives me sin( .

- November 1st 2006, 12:47 AMearboth
- November 1st 2006, 04:00 AMTomCat
Okay... I need to get just one type (sin or cos).

- November 1st 2006, 05:30 AMCaptainBlack
- November 1st 2006, 01:47 PMTomCat
I think I get what you're saying. I was looking over this in class with a friend, and she was just confusing me more. I don't think she was doing it right either.

I would just do something similar for f(x)= Acos(bx) + Bsin(bx) correct?

Thank you!

-Tom - November 1st 2006, 02:48 PMCaptainBlack
- November 2nd 2006, 11:02 AMTomCat
Hmm... That was over the heads of everyone I showed that to. Are there any other ways to do it that are more Pre-Calcish?

- November 2nd 2006, 12:01 PMCaptainBlack
It was pure basic trigonometry, which should be pre-calculus (not that

I would know we don't have the stereotyped math sequence that you

seem to have in the US).

The only things you need to know to do it is the sin addition formula and

the trig form of Pythagoras's theorem, which are:

and:

and the rest is just basic algebra.

RonL - November 2nd 2006, 12:11 PMtopsquark