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#1 2012-10-25 21:54:41

Ronald
Guest

Phi in trigonometry

During class I faced a problem- cos^4(x)+cos^2(x)=1,my friend told me that x=acos(sqrt(phi-1)).when I checked it using calculator,it was correct.how is phi involved in this,please explain.

#2 2012-10-25 22:02:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Phi in trigonometry

Hi Ronald;

You make the substitution y = cos(x) and then solve.

Another substitution, u=y^2.

Now it is easy.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2012-10-25 22:55:21

Ronald
Guest

Re: Phi in trigonometry

I get acos(sqrt(sqrt(1.25)-1)),so?

#4 2012-10-25 22:56:47

Ronald
Guest

Re: Phi in trigonometry

Sorry it is (sqrt(sqrt(1.25)-.5))

#5 2012-10-25 23:05:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Phi in trigonometry

Please check your work I am not getting that. For one root I am getting.

That is what you wanted to show.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#6 2012-10-26 00:12:28

Ronald
Guest

Re: Phi in trigonometry

Wait a minute,1/2(sqrt(5)-1) and sqrt(1.25)-.5 is same!

#7 2012-10-26 01:26:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Phi in trigonometry

Yes, it is the same but there is no reason to convert to decimal. You should avoid unnecessary simplifications. The way it is done in post #5 is fine.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

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