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A199952 Decimal expansion of greatest x satisfying x^2 + cos(x) = 3*sin(x).

%I A199952 #15 Feb 08 2025 22:59:46
%S A199952 1,7,7,1,7,9,2,9,5,2,9,8,2,0,2,6,3,3,7,2,6,5,9,2,3,5,8,6,4,4,9,0,9,4,
%T A199952 2,1,6,2,2,0,1,5,8,2,4,5,5,1,8,6,3,0,8,9,1,8,9,2,1,1,4,7,0,0,9,3,4,5,
%U A199952 2,5,6,5,1,6,7,0,3,5,0,8,1,3,9,7,8,1,6,1,4,4,3,8,7,0,4,5,5,8,7
%N A199952 Decimal expansion of greatest x satisfying x^2 + cos(x) = 3*sin(x).
%C A199952 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A199952 G. C. Greubel, <a href="/A199952/b199952.txt">Table of n, a(n) for n = 1..10000</a>
%H A199952 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199952 least x:  0.36356053985895926625732148372284398566895...
%e A199952 greatest x: 1.771792952982026337265923586449094216220...
%t A199952 a = 1; b = 1; c = 3;
%t A199952 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A199952 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A199952 r = x /. FindRoot[f[x] == g[x], {x, .36, .37}, WorkingPrecision -> 110]
%t A199952 RealDigits[r]  (* A199951 *)
%t A199952 r = x /. FindRoot[f[x] == g[x], {x, 1.77, 1.78}, WorkingPrecision -> 110]
%t A199952 RealDigits[r]  (* A199952 *)
%o A199952 (PARI) a=1; b=1; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A199952 Cf. A199949.
%K A199952 nonn,cons
%O A199952 1,2
%A A199952 _Clark Kimberling_, Nov 12 2011