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A200132 Decimal expansion of least x satisfying 3*x^2 - cos(x) = sin(x), negated.

%I A200132 #14 Feb 12 2025 13:03:00
%S A200132 4,1,3,7,5,1,7,5,9,1,4,4,7,7,3,9,3,7,6,8,4,4,0,0,2,7,9,8,9,8,9,2,7,5,
%T A200132 6,4,5,9,9,2,2,5,1,3,8,5,5,5,7,8,6,6,1,8,6,3,7,5,1,5,2,8,7,7,7,8,7,6,
%U A200132 3,1,5,3,2,0,3,3,8,4,9,9,6,1,7,4,1,5,9,0,0,6,9,1,1,8,7,6,2,3,7
%N A200132 Decimal expansion of least x satisfying 3*x^2 - cos(x) = sin(x), negated.
%C A200132 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200132 G. C. Greubel, <a href="/A200132/b200132.txt">Table of n, a(n) for n = 0..10000</a>
%H A200132 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200132 least x: -0.4137517591447739376844002798989...
%e A200132 greatest x: 0.68485307862320115956369446864...
%t A200132 a = 3; b = -1; c = 1;
%t A200132 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200132 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200132 r = x /. FindRoot[f[x] == g[x], {x, -.42, -.41}, WorkingPrecision -> 110]
%t A200132 RealDigits[r]   (* A200132 *)
%t A200132 r = x /. FindRoot[f[x] == g[x], {x, .68, .69}, WorkingPrecision -> 110]
%t A200132 RealDigits[r]   (* A200133 *)
%o A200132 (PARI) a=3; b=-1; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018
%Y A200132 Cf. A199949.
%K A200132 nonn,cons
%O A200132 0,1
%A A200132 _Clark Kimberling_, Nov 14 2011