From: Deane Yang (deane_yang_at_[hidden])
Date: 2005-10-14 09:02:12
Matt Calabrese wrote:
> 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
Can you justify why the factors in the denominator should be in
"radians"? Can you do a similar analysis for me for the arcsin function?
If I understand your explanations, you would say that given an angle x
in radians, then both x and sin(x) are in radians. So this means you
would allow the expression "x + sin(x)" and "(sin(sin(x))". If you allow
all this, how is this better than just using pure floats or doubles as
Andy has suggested?