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#1 2012-10-26 20:54:41

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 2012-10-26 21:02:56

bobbym
Administrator

Online

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2012-10-26 21:55:21

Ronald
Guest

Re: Phi in trigonometry

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

#4 2012-10-26 21:56:47

Ronald
Guest

Re: Phi in trigonometry

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

#5 2012-10-26 22:05:51

bobbym
Administrator

Online

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#6 2012-10-26 23:12:28

Ronald
Guest

Re: Phi in trigonometry

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

#7 2012-10-27 00:26:51

bobbym
Administrator

Online

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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