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A200027 Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = sin(x).

%I A200027 #11 Feb 12 2025 04:59:02
%S A200027 1,3,1,4,4,8,5,6,0,9,1,9,7,7,6,1,9,6,5,5,1,9,2,1,9,8,6,7,6,1,0,9,1,0,
%T A200027 6,0,0,1,2,8,8,8,9,4,4,1,4,1,6,8,4,7,5,3,8,0,0,2,1,2,0,7,0,0,4,7,7,1,
%U A200027 9,8,2,3,4,9,0,0,2,9,7,4,5,7,6,7,9,0,4,2,7,1,0,0,5,0,1,4,0,6,8
%N A200027 Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = sin(x).
%C A200027 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200027 G. C. Greubel, <a href="/A200027/b200027.txt">Table of n, a(n) for n = 1..10000</a>
%H A200027 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200027 least x:  -0.9559087984816134135373014395844...
%e A200027 greatest x: 1.31448560919776196551921986761091...
%t A200027 a = 1; b = -3; c = 1;
%t A200027 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200027 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200027 r = x /. FindRoot[f[x] == g[x], {x, -.96, -.95}, WorkingPrecision -> 110]
%t A200027 RealDigits[r]  (* A200026 *)
%t A200027 r = x /. FindRoot[f[x] == g[x], {x, 1.31, 1.34}, WorkingPrecision -> 110]
%t A200027 RealDigits[r]  (* A200027 *)
%o A200027 (PARI) a=1; b=-3; c=1; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y A200027 Cf. A199949.
%K A200027 nonn,cons
%O A200027 1,2
%A A200027 _Clark Kimberling_, Nov 13 2011