Re: sin x / x tends to 1...

David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx> wrote:
> >Now, if I understood it correctly, you showed that sin x / x tended to
> >one when x was measured in "aradians".
>
> You might note that there was a factor of 1/2 missing in my
> definition of "aradian", which was cancelled by the missing
> 1/2 in the formula I was using for the area of a triangle.
> (Details... heh.)

Yes, of course - easily fixed.

> >Is there an easy way to show that
> >aradians and radians are the same?
>
> In the sense in which I would use the word "show",
> I doubt it - I don't think that we can even give an
> easy definition of area, much less arc length.

That's what I thought... As I said in my original post, I'm quite happy
using the area argument to establish the existance of a limit on [0,1],
but I'd like to know that it is 1... ;-)

OK, so I'm starting to give up on a neat proof for a bright 15 year old.
So, how about one for someone with a degree in mathematics and a PhD in
theoretical statistics... ;-) Assuming a power series definition of
sin x, that we can call psin x, the limit is (of course) obvious. Is
it very easy to show that psin x = sin x, where sin x is the usual
geometric definition (with regular radians)?

--
Dr Darren Wilkinson
mailto:d.j.wilkinson@xxxxxxxxxxxxxxx
http://www.staff.ncl.ac.uk/d.j.wilkinson/
.

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