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A199964 Decimal expansion of greatest x satisfying x^2 + 4*cos(x) = 3*sin(x).

%I A199964 #15 Feb 08 2025 23:06:23
%S A199964 2,1,7,8,8,4,3,3,0,3,0,3,8,4,3,8,4,7,8,7,4,7,3,5,1,5,4,6,6,3,1,1,2,0,
%T A199964 7,8,8,0,9,8,3,8,5,5,8,5,8,9,3,8,0,7,1,9,4,3,7,4,9,0,8,7,6,0,0,4,7,5,
%U A199964 6,4,2,6,7,4,4,8,5,4,0,4,7,5,3,2,0,2,9,5,4,4,4,8,4,5,2,5,9,8,6
%N A199964 Decimal expansion of greatest x satisfying x^2 + 4*cos(x) = 3*sin(x).
%C A199964 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A199964 G. C. Greubel, <a href="/A199964/b199964.txt">Table of n, a(n) for n = 1..10000</a>
%H A199964 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199964 least x:  1.2397511548307033226630942987091820...
%e A199964 greatest x: 2.17884330303843847874735154663112...
%t A199964 a = 1; b = 4; c = 3;
%t A199964 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A199964 Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
%t A199964 r = x /. FindRoot[f[x] == g[x], {x, 1.23, 1.24}, WorkingPrecision -> 110]
%t A199964 RealDigits[r]   (* A199963 *)
%t A199964 r = x /. FindRoot[f[x] == g[x], {x, 2.17, 2.18}, WorkingPrecision -> 110]
%t A199964 RealDigits[r]  (* A199964 *)
%o A199964 (PARI) a=1; b=4; c=3; solve(x=2, 3, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y A199964 Cf. A199949.
%K A199964 nonn,cons
%O A199964 1,1
%A A199964 _Clark Kimberling_, Nov 12 2011