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From: Matt Calabrese (rivorus_at_[hidden])
Date: 20051013 21:55:47
On 10/13/05, Deane Yang <deane_yang_at_[hidden]> wrote:
> Given an angle x in radians,
>
> sin(x) = x  x^3/3! + .....
>
> Does your approach to radians work coherently with this formula? In
> other words, does it assign the right "units" to each term and to the
> "sin(x)"? I don't see how this can be done, because x^3/3! has to have
> the same units as x in order to allow the addition.
I would say yes. I describe radians as being untransformed ratios of two
quantities of the same dimension, much like wikipedia. The value where
factorial is being applied is an untranformed ratio (hense, as I believe,
radians).
An analysis being:
"x in radians"  ( x^3 in radians^3 ) / ( 3 radians * 2 radians * 1 radian )
... etc
Note that the second term is radians^3 / radians^3. This pattern repeats
always having radians^n / radians^n for terms. As I described radians as
untransformed ratios of units of the same dimension, the overall result
would also be in radians, which would be convertible to a raw value. The
function would work perfectly and the terms would be able to be combined
fine.
 Matt Calabrese
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