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A200241 Decimal expansion of least x satisfying 3*x^2 - 3*cos(x) = 4*sin(x), negated.

%I A200241 #21 Feb 12 2025 13:05:41
%S A200241 4,9,5,5,9,4,2,3,2,7,9,8,1,1,0,8,0,3,9,6,6,6,9,4,0,8,1,3,6,0,6,6,6,2,
%T A200241 3,4,8,1,2,3,0,0,4,8,8,5,5,2,1,1,1,9,5,6,6,1,7,6,5,0,5,3,3,1,4,8,8,0,
%U A200241 6,1,9,9,6,4,2,7,5,6,6,0,3,9,4,8,5,9,8,0,7,7,1,0,7,1,4,6,6,2,3
%N A200241 Decimal expansion of least x satisfying 3*x^2 - 3*cos(x) = 4*sin(x), negated.
%C A200241 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200241 G. C. Greubel, <a href="/A200241/b200241.txt">Table of n, a(n) for n = 0..10000</a>
%H A200241 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200241 least x: -0.495594232798110803966694081360666...
%e A200241 greatest x: 1.2559670249437296288542832153976444...
%t A200241 a = 3; b = -3; c = 4;
%t A200241 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200241 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200241 r = x /. FindRoot[f[x] == g[x], {x, -.50, -.49}, WorkingPrecision -> 110]
%t A200241 RealDigits[r]   (* A200241 *)
%t A200241 r = x /. FindRoot[f[x] == g[x], {x, 1.25, 1.26}, WorkingPrecision -> 110]
%t A200241 RealDigits[r]   (* A200242 *)
%o A200241 (PARI) a=3; b=-3; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A200241 Cf. A199949.
%K A200241 nonn,cons
%O A200241 0,1
%A A200241 _Clark Kimberling_, Nov 15 2011