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A200237 Decimal expansion of least x satisfying 3*x^2 - 3*cos(x) = sin(x), negated.

%I A200237 #12 Feb 12 2025 13:08:50
%S A200237 7,2,5,7,7,3,9,3,1,3,7,5,0,9,8,1,4,8,9,5,1,8,1,3,2,6,4,6,5,2,3,1,3,6,
%T A200237 2,0,5,0,7,1,0,0,3,6,3,9,2,4,3,7,9,1,2,8,7,9,4,2,5,4,9,7,2,3,0,8,5,0,
%U A200237 1,2,8,3,0,9,4,0,3,4,8,6,7,3,5,7,4,1,1,8,6,2,0,6,8,6,3,3,7,9,2
%N A200237 Decimal expansion of least x satisfying 3*x^2 - 3*cos(x) = sin(x), negated.
%C A200237 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200237 G. C. Greubel, <a href="/A200237/b200237.txt">Table of n, a(n) for n = 0..10000</a>
%H A200237 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200237 least x: -0.725773931375098148951813264652313...
%e A200237 greatest x: 0.9300571100924892467882468144056...
%t A200237 a = 3; b = -3; c = 1;
%t A200237 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200237 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200237 r = x /. FindRoot[f[x] == g[x], {x, -.73, -.72}, WorkingPrecision -> 110]
%t A200237 RealDigits[r]   (* A200237 *)
%t A200237 r = x /. FindRoot[f[x] == g[x], {x, .93, .94}, WorkingPrecision -> 110]
%t A200237 RealDigits[r]   (* A200238 *)
%o A200237 (PARI) a=3; b=-3; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018
%Y A200237 Cf. A199949.
%K A200237 nonn,cons
%O A200237 0,1
%A A200237 _Clark Kimberling_, Nov 15 2011