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From: Ray Vickson on 7 Jul 2010 14:53
On Jul 7, 2:00 am, Fred Nurk <albert.xtheunkno...(a)gmail.com> wrote:
> Francois Grieu wrote:
> > <snip>
> > Hint: sin(1)^2 + cos(1)^2 = 1.
>
> Right. cos(1) = {1 - [sin(1)] ^ 2} ^ (1 / 2)
>               = (1 - a ^ 2) ^ (1 / 2)
>
> > Check the sign of cos(1).
>
> Why?

Well, either cos(1) = +sqrt(1 - a^2) or cos(1) = -sqrt(1 - a^2). Which
one should you choose?

R.G. Vickson


> It is now clear that the answer is C.
>
> > <snip>
>
> TIA,
> Fred

From: Fred Nurk on 10 Jul 2010 05:58
Francois Grieu wrote:
> Fred Nurk wrote:
>> <snip>
>>> Check the sign of cos(1).
>> Why? It is now clear that the answer is C.
>
> Because on the problem
>
> If z = sin(x) and sin(2) = a then, using the first order
> approximation, the value of sin(2.1) is equal to: A 0.1(1 - a ^ 2) ^ (1
> / 2)
> B 0.1cos(2)
> C 0.1(1 - a ^ 2) ^ (1 / 2) + a
> D a + 0.1
> E 0.1a
>
> the right answer would be: neither of the above, due to a sign issue.
> <snip>

I see now; thank you.

Fred
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