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A199963 Decimal expansion of least x satisfying x^2 + 4*cos(x) = 3*sin(x).

%I A199963 #13 Feb 08 2025 23:06:16
%S A199963 1,2,3,9,7,5,1,1,5,4,8,3,0,7,0,3,3,2,2,6,6,3,0,9,4,2,9,8,7,0,9,1,8,2,
%T A199963 0,7,2,6,0,6,9,1,2,5,7,4,9,4,5,2,1,7,2,4,7,2,3,1,7,5,6,5,2,6,4,7,6,7,
%U A199963 4,5,9,6,3,6,0,1,8,5,6,2,6,2,6,5,9,7,5,8,2,5,7,9,2,3,1,8,7,4,8
%N A199963 Decimal expansion of least x satisfying x^2 + 4*cos(x) = 3*sin(x).
%C A199963 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A199963 G. C. Greubel, <a href="/A199963/b199963.txt">Table of n, a(n) for n = 1..10000</a>
%H A199963 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199963 least x:  1.2397511548307033226630942987091820...
%e A199963 greatest x: 2.178843303038438478747351546631120...
%t A199963 a = 1; b = 4; c = 3;
%t A199963 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A199963 Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
%t A199963 r = x /. FindRoot[f[x] == g[x], {x, 1.23, 1.24}, WorkingPrecision -> 110]
%t A199963 RealDigits[r]  (* A199963 *)
%t A199963 r = x /. FindRoot[f[x] == g[x], {x, 2.17, 2.18}, WorkingPrecision -> 110]
%t A199963 RealDigits[r]  (* A199964 *)
%o A199963 (PARI) a=1; b=4; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y A199963 Cf. A199949.
%K A199963 nonn,cons
%O A199963 1,2
%A A199963 _Clark Kimberling_, Nov 12 2011