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#1 2008-05-14 06:16:31
- parseconds
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- Registered: 2008-05-13
- Posts: 3
Problem, please help?
It is always true that if
thenGive an example showing that
need not be true for all x.Offline
#2 2008-05-14 06:40:09
- mathsyperson
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- Registered: 2005-06-22
- Posts: 4,900
Re: Problem, please help?
x = 2π would be one example.
cos (2π) = 1
arccos (1) = 0 ≠ 2π.
Why did the vector cross the road?
It wanted to be normal.
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#3 2008-05-14 08:59:25
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: Problem, please help?
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#4 2008-05-14 11:25:29
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,713
Re: Problem, please help?
You could cut wood with it!
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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#5 2008-05-14 11:31:42
- Ricky
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- Registered: 2005-12-04
- Posts: 3,791
Re: Problem, please help?
So now the question becomes: why does it hold true that cos(acos(x)) = x for all x in the domain, but not acos(cos(x))?
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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