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A200227 Decimal expansion of least x satisfying 3*x^2 - cos(x) = 4*sin(x), negated.

%I A200227 #11 Feb 12 2025 13:04:20
%S A200227 2,1,2,2,0,7,2,6,1,5,9,7,9,1,8,2,9,8,9,7,8,2,3,7,4,0,5,0,1,0,3,7,5,4,
%T A200227 0,3,7,3,2,0,7,9,1,5,7,5,0,6,1,9,7,1,1,7,0,2,4,0,1,5,1,2,3,5,4,5,2,5,
%U A200227 4,6,3,6,4,7,4,6,8,2,1,5,3,4,7,1,5,8,9,5,1,0,6,7,2,1,5,0,0,5,7
%N A200227 Decimal expansion of least x satisfying 3*x^2 - cos(x) = 4*sin(x), negated.
%C A200227 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200227 G. C. Greubel, <a href="/A200227/b200227.txt">Table of n, a(n) for n = 0..10000</a>
%H A200227 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200227 least x: -0.21220726159791829897823740501037540...
%e A200227 greatest x: 1.164720132600086548144173603917629...
%t A200227 a = 3; b = -1; c = 4;
%t A200227 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200227 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200227 r = x /.FindRoot[f[x] == g[x], {x, -.22, -.21}, WorkingPrecision -> 110]
%t A200227 RealDigits[r]   (* A200227 *)
%t A200227 r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
%t A200227 RealDigits[r]   (* A200228 *)
%o A200227 (PARI) a=3; b=-1; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 30 2018
%Y A200227 Cf. A199949.
%K A200227 nonn,cons
%O A200227 0,1
%A A200227 _Clark Kimberling_, Nov 14 2011