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A200242 Decimal expansion of greatest x satisfying 3*x^2 - 3*cos(x) = 4*sin(x).

%I A200242 #19 Feb 12 2025 13:05:36
%S A200242 1,2,5,5,9,6,7,0,2,4,9,4,3,7,2,9,6,2,8,8,5,4,2,8,3,2,1,5,3,9,7,6,4,4,
%T A200242 4,0,2,9,8,0,6,0,3,7,6,1,1,7,9,2,9,5,7,7,3,0,3,4,6,6,1,3,9,2,6,3,8,4,
%U A200242 5,3,4,5,3,8,0,0,6,5,3,6,1,7,3,8,6,7,1,5,5,0,1,4,0,1,0,6,1,5,2
%N A200242 Decimal expansion of greatest x satisfying 3*x^2 - 3*cos(x) = 4*sin(x).
%C A200242 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200242 G. C. Greubel, <a href="/A200242/b200242.txt">Table of n, a(n) for n = 1..10000</a>
%H A200242 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200242 least x: -0.495594232798110803966694081360666...
%e A200242 greatest x: 1.2559670249437296288542832153976444...
%t A200242 a = 3; b = -3; c = 4;
%t A200242 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200242 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200242 r = x /. FindRoot[f[x] == g[x], {x, -.50, -.49}, WorkingPrecision -> 110]
%t A200242 RealDigits[r]   (* A200241 *)
%t A200242 r = x /. FindRoot[f[x] == g[x], {x, 1.25, 1.26}, WorkingPrecision -> 110]
%t A200242 RealDigits[r]   (* A200242 *)
%o A200242 (PARI) a=3; b=-3; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A200242 Cf. A199949.
%K A200242 nonn,cons
%O A200242 1,2
%A A200242 _Clark Kimberling_, Nov 15 2011