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A200120 Decimal expansion of least x satisfying 2*x^2 - 3*cos(x) = sin(x), negated.

%I A200120 #11 Feb 12 2025 12:59:42
%S A200120 8,1,5,2,3,3,2,2,3,4,1,0,5,1,4,1,3,1,2,0,5,9,2,1,2,0,0,0,2,2,2,2,0,9,
%T A200120 7,0,3,0,0,7,3,1,1,5,4,3,9,1,2,1,5,4,0,2,0,2,5,7,2,7,1,6,8,7,7,0,1,3,
%U A200120 5,7,9,2,2,8,9,8,8,1,8,1,7,6,1,0,0,3,9,4,0,2,9,3,5,5,6,3,0,9,3
%N A200120 Decimal expansion of least x satisfying 2*x^2 - 3*cos(x) = sin(x), negated.
%C A200120 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200120 G. C. Greubel, <a href="/A200120/b200120.txt">Table of n, a(n) for n = 0..10000</a>
%H A200120 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200120 least x: -0.815233223410514131205921200022220970300...
%e A200120 greatest x: 1.0743092065060468901083577789286306342...
%t A200120 a = 2; b = -3; c = 1;
%t A200120 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200120 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200120 r = x /. FindRoot[f[x] == g[x], {x, -.82, -.81}, WorkingPrecision -> 110]
%t A200120 RealDigits[r]  (* A200120 *)
%t A200120 r = x /. FindRoot[f[x] == g[x], {x, 1.07, 1.08}, WorkingPrecision -> 110]
%t A200120 RealDigits[r]  (* A200121 *)
%o A200120 (PARI) a=2; b=-3; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 29 2018
%Y A200120 Cf. A199949.
%K A200120 nonn,cons
%O A200120 0,1
%A A200120 _Clark Kimberling_, Nov 14 2011