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A199606 Decimal expansion of greatest x satisfying x^2+3*x*cos(x)=sin(x).

%I A199606 #8 Feb 08 2025 10:08:49
%S A199606 3,0,1,7,9,6,3,0,8,1,0,6,8,6,2,8,8,7,2,6,6,7,8,1,4,4,3,3,8,8,5,7,6,8,
%T A199606 9,7,0,3,7,8,3,2,7,2,9,4,7,3,8,3,3,3,0,9,4,0,6,2,7,6,8,4,4,5,7,5,7,0,
%U A199606 0,2,3,7,8,0,9,9,2,1,2,9,5,1,4,6,0,3,3,7,8,7,6,8,4,3,4,7,5,0,7
%N A199606 Decimal expansion of greatest x satisfying x^2+3*x*cos(x)=sin(x).
%C A199606 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199606 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199606 least: -0.93049500263597010976334102402547851258644...
%e A199606 greatest:  3.01796308106862887266781443388576897037832...
%t A199606 a = 1; b = 3; c = 1;
%t A199606 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199606 Plot[{f[x], g[x]}, {x, -1.5, 3.5}, {AxesOrigin -> {0, 0}}]
%t A199606 r = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]
%t A199606 RealDigits[r]  (* A199605, least of 4 roots *)
%t A199606 r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision -> 110]
%t A199606 RealDigits[r]  (* A199606, greatest of 4 roots *)
%Y A199606 Cf. A199597.
%K A199606 nonn,cons
%O A199606 1,1
%A A199606 _Clark Kimberling_, Nov 08 2011