I am not using a library, I am writing one. I have e.g. for x = 0.5, sinx = sin(x); cosx=cos(x); I want sinxx = sin(x + dx), cosxx = cos(x +dx) for dx << x. Is there some relationship that allows me to refine sinxx, cosxx simultaneously?
On Friday, October 16, 2015 at 10:23:05 PM UTC-4, Yichao Yu wrote: > > On Fri, Oct 16, 2015 at 10:14 PM, Jeffrey Sarnoff > <[email protected] <javascript:>> wrote: > > Is there a way to use sin(x)^2 + cos(x)^2 = 1 to refine very close > > approximations to sin(x), cos(x)? > > I am using an extended precision, so I have Float64 approximations for > > sin,cos for 'free'. > > > > I would guess any library you use to deal with those higher precision > numbers already handle this internally (e.g. `sin(::BigFloat)`) > > Also, I doubt sin^2 + cos^2 = 1 would help since it doesn't explicitly > include x. >
