your point about sin^2 + cos^2 is well taken --
On Friday, October 16, 2015 at 10:35:39 PM UTC-4, Jeffrey Sarnoff wrote: > > 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]> 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. >> >
