%I #14 Feb 07 2025 16:44:06
%S 6,8,4,8,5,3,0,7,8,6,2,3,2,0,1,1,5,9,5,6,3,6,9,4,4,6,8,6,4,9,5,4,2,8,
%T 8,8,4,5,1,8,4,2,6,1,0,3,1,8,2,0,2,6,7,1,9,2,8,2,6,1,9,9,7,6,4,6,0,2,
%U 2,5,8,4,0,3,1,2,9,4,4,3,2,7,9,2,2,5,9,2,5,2,4,0,4,6,8,1,0,2,3
%N Decimal expansion of greatest x satisfying 3*x^2 - cos(x) = sin(x).
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200133/b200133.txt">Table of n, a(n) for n = 0..10000</a>
%e least x: -0.4137517591447739376844002798989...
%e greatest x: 0.684853078623201159563694468649...
%t a = 3; b = -1; c = 1;
%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.42, -.41}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200132 *)
%t r = x /. FindRoot[f[x] == g[x], {x, .68, .69}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200133 *)
%o (PARI) a=3; b=-1; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018
%Y Cf. A199949.
%K nonn,cons,changed
%O 0,1
%A _Clark Kimberling_, Nov 14 2011