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A199953 Decimal expansion of least x satisfying x^2 + cos(x) = 4*sin(x).

%I A199953 #14 Feb 08 2025 23:03:52
%S A199953 2,6,1,5,7,3,9,3,6,4,7,4,8,1,1,3,0,2,1,2,2,9,6,4,2,0,1,7,8,3,1,2,1,1,
%T A199953 6,0,3,9,7,8,2,8,5,9,1,3,8,4,8,6,7,6,7,1,5,3,4,2,1,3,6,8,5,6,7,6,5,2,
%U A199953 1,0,9,0,9,6,7,0,9,2,1,2,9,5,8,5,1,2,1,9,9,4,6,8,6,6,9,1,3,7,3
%N A199953 Decimal expansion of least x satisfying x^2 + cos(x) = 4*sin(x).
%C A199953 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A199953 G. C. Greubel, <a href="/A199953/b199953.txt">Table of n, a(n) for n = 0..10000</a>
%H A199953 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199953 least x:  0.26157393647481130212296420178312116039782...
%e A199953 greatest x: 2.011137342229330846002506540879639388630...
%t A199953 a = 1; b = 1; c = 4;
%t A199953 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A199953 Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
%t A199953 r = x /. FindRoot[f[x] == g[x], {x, .26, .27}, WorkingPrecision -> 110]
%t A199953 RealDigits[r]  (* A199953 *)
%t A199953 r = x /. FindRoot[f[x] == g[x], {x, 2.0, 2.1}, WorkingPrecision -> 110]
%t A199953 RealDigits[r]  (* A199954 *)
%o A199953 (PARI) a=1; b=1; c=4; solve(x=0, .5, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A199953 Cf. A199949.
%K A199953 nonn,cons
%O A199953 0,1
%A A199953 _Clark Kimberling_, Nov 12 2011