Matt Calabrese wrote:
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
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?