On 10/13/05, Deane Yang <deane_yang@yahoo.com> 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