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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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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