A259259 - OEIS

%I #10 Sep 24 2015 18:37:43

%S 4,4,3,1,4,3,6,4,5,7,8,0,4,6,9,7,4,3,1,0,5,8,1,5,1,9,3,8,5,2,4,1,8,8,

%T 1,5,7,2,4,3,3,1,3,9,2,0,8,7,7,3,7,8,7,8,7,6,1,0,3,3,3,8,9,9,9,0,7,4,

%U 5,8,3,7,0,6,5,1,8,2,6,8,4,6,2,3,9,3,6,0,9,3,5,4,8,9,7,6,2,6,7,2,3,9,8,6,8,4,2,6

%N Decimal expansion of the largest negative solution to sin(x) + cos(x) + tan(x) = 0 (negated).

%C There are two unique real solutions to this equation, up to a multiple of 2*Pi. One is x ~ 2*Pi*n - 2.18722 and the other is x ~ 2*Pi*n - 0.443144. This decimal expansion is for n = 0 in the second approximation. See A259258 for the other solution set.

%e -0.443143645780469743105815193852418815...

%t RealDigits[ArcCos[y/.Solve[y*(y^3+y^2-1)==1/2]][[4]],10,120][[1]] (* _Vaclav Kotesovec_, Jul 07 2015 *)

%o (PARI) default(realprecision,2000); s=abs(solve(x=-1,0,tan(x)+cos(x)+sin(x))); for(n=1,100, s*=10; print1(floor(s)%10,", "))

%Y Cf. A259258.

%K nonn,cons

%O 0,1

%A _Derek Orr_, Jun 22 2015