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A199951 Decimal expansion of least x satisfying x^2 + cos(x) = 3*sin(x).

%I A199951 #17 Feb 08 2025 22:59:49
%S A199951 3,6,3,5,6,0,5,3,9,8,5,8,9,5,9,2,6,6,2,5,7,3,2,1,4,8,3,7,2,2,8,4,3,9,
%T A199951 8,5,6,6,8,9,5,7,9,0,7,4,2,5,0,8,4,0,8,0,7,4,4,2,0,4,5,7,1,8,4,0,3,1,
%U A199951 3,4,0,6,6,8,8,6,2,2,7,6,2,6,7,4,1,8,8,9,9,6,0,8,8,5,1,2,9,2,5
%N A199951 Decimal expansion of least x satisfying x^2 + cos(x) = 3*sin(x).
%C A199951 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A199951 G. C. Greubel, <a href="/A199951/b199951.txt">Table of n, a(n) for n = 0..10000</a>
%H A199951 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199951 least x:  0.36356053985895926625732148372284398566895...
%e A199951 greatest x: 1.771792952982026337265923586449094216220...
%t A199951 a = 1; b = 1; c = 3;
%t A199951 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A199951 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A199951 r = x /. FindRoot[f[x] == g[x], {x, .36, .37}, WorkingPrecision -> 110]
%t A199951 RealDigits[r]  (* A199951 *)
%t A199951 r = x /. FindRoot[f[x] == g[x], {x, 1.77, 1.78}, WorkingPrecision -> 110]
%t A199951 RealDigits[r]  (* A199952 *)
%o A199951 (PARI) a=1; b=1; c=3; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A199951 Cf. A199949.
%K A199951 nonn,cons
%O A199951 0,1
%A A199951 _Clark Kimberling_, Nov 12 2011