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A200128 Decimal expansion of least x satisfying 2*x^2 - 4*cos(x) = sin(x), negated.

%I A200128 #12 Feb 12 2025 13:01:13
%S A200128 9,1,1,2,5,1,3,6,5,7,7,2,4,8,2,4,1,2,5,4,9,4,7,3,1,8,2,8,0,2,9,3,7,5,
%T A200128 4,5,8,5,3,9,1,6,1,5,9,8,2,1,2,5,4,4,8,1,0,6,1,2,1,6,3,7,4,6,8,9,5,1,
%U A200128 8,0,7,4,2,6,6,7,5,7,8,7,6,4,4,3,4,7,9,9,8,2,9,9,5,5,9,6,9,2,2
%N A200128 Decimal expansion of least x satisfying 2*x^2 - 4*cos(x) = sin(x), negated.
%C A200128 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200128 G. C. Greubel, <a href="/A200128/b200128.txt">Table of n, a(n) for n = 0..10000</a>
%H A200128 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200128 least x: -0.91125136577248241254947318280293...
%e A200128 greatest x: 1.13740119952686852650278803084...
%t A200128 a = 2; b = -4; c = 1;
%t A200128 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200128 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200128 r = x /. FindRoot[f[x] == g[x], {x, -.92, -.91}, WorkingPrecision -> 110]
%t A200128 RealDigits[r]  (* A200128 *)
%t A200128 r = x /. FindRoot[f[x] == g[x], {x, 1.13, 1.14}, WorkingPrecision -> 110]
%t A200128 RealDigits[r]  (* A200129 *)
%o A200128 (PARI) a=2; b=-4; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 01 2018
%Y A200128 Cf. A199949.
%K A200128 nonn,cons
%O A200128 0,1
%A A200128 _Clark Kimberling_, Nov 14 2011