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A200026 Decimal expansion of least x satisfying x^2 - 3*cos(x) = sin(x) (negated).

%I A200026 #13 Feb 12 2025 04:59:00
%S A200026 9,5,5,9,0,8,7,9,8,4,8,1,6,1,3,4,1,3,5,3,7,3,0,1,4,3,9,5,8,4,4,0,6,1,
%T A200026 0,3,5,9,4,8,9,8,6,6,8,6,7,5,3,9,4,3,2,8,6,5,9,3,6,8,9,4,2,2,4,3,3,7,
%U A200026 9,9,4,8,6,9,8,5,4,7,3,9,0,1,1,1,9,1,2,8,8,5,8,4,3,9,8,0,0,6,3
%N A200026 Decimal expansion of least x satisfying x^2 - 3*cos(x) = sin(x) (negated).
%C A200026 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200026 G. C. Greubel, <a href="/A200026/b200026.txt">Table of n, a(n) for n = 0..10000</a>
%H A200026 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200026 least x:  -0.9559087984816134135373014395844...
%e A200026 greatest x: 1.31448560919776196551921986761091...
%t A200026 a = 1; b = -3; c = 1;
%t A200026 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200026 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200026 r = x /. FindRoot[f[x] == g[x], {x, -.96, -.95}, WorkingPrecision -> 110]
%t A200026 RealDigits[r]  (* A200026 *)
%t A200026 r = x /. FindRoot[f[x] == g[x], {x, 1.31, 1.34}, WorkingPrecision -> 110]
%t A200026 RealDigits[r]  (* A200027 *)
%o A200026 (PARI) a=1; b=-3; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y A200026 Cf. A199949.
%K A200026 nonn,cons
%O A200026 0,1
%A A200026 _Clark Kimberling_, Nov 13 2011