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A200304 Decimal expansion of greatest x satisfying 4*x^2 - 3*cos(x) = 4*sin(x).

%I A200304 #12 Feb 12 2025 14:37:15
%S A200304 1,1,0,8,8,1,1,8,8,2,9,7,1,7,2,7,6,2,1,8,5,8,4,9,5,3,5,2,2,8,5,8,9,1,
%T A200304 7,2,5,5,4,0,0,8,9,9,4,0,1,9,4,8,5,0,6,8,1,9,7,6,4,9,9,3,1,5,7,1,7,8,
%U A200304 4,8,7,1,3,8,8,5,5,5,9,5,8,9,9,7,8,4,3,9,2,3,8,0,5,3,6,3,5,7,8
%N A200304 Decimal expansion of greatest x satisfying 4*x^2 - 3*cos(x) = 4*sin(x).
%C A200304 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200304 G. C. Greubel, <a href="/A200304/b200304.txt">Table of n, a(n) for n = 1..10000</a>
%H A200304 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200304 least x: -0.4676436322290565342035400494771...
%e A200304 greatest x: 1.10881188297172762185849535228...
%t A200304 a = 4; b = -3; c = 4;
%t A200304 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200304 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A200304 r = x /. FindRoot[f[x] == g[x], {x, -.47, -.46}, WorkingPrecision -> 110]
%t A200304 RealDigits[r]   (* A200303 *)
%t A200304 r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
%t A200304 RealDigits[r]   (* A200304 *)
%o A200304 (PARI) a=4; b=-3; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y A200304 Cf. A199949.
%K A200304 nonn,cons
%O A200304 1,4
%A A200304 _Clark Kimberling_, Nov 15 2011