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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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