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A199605 Decimal expansion of least x satisfying x^2+3*x*cos(x)=sin(x).

%I A199605 #8 Feb 08 2025 10:08:11
%S A199605 9,3,0,4,9,5,0,0,2,6,3,5,9,7,0,1,0,9,7,6,3,3,4,1,0,2,4,0,2,5,4,7,8,5,
%T A199605 1,2,5,8,6,4,4,8,8,2,4,4,1,4,8,8,7,7,2,8,1,5,2,2,7,2,8,2,8,2,0,8,3,0,
%U A199605 6,9,2,4,0,1,9,7,5,5,2,4,2,5,1,0,1,9,2,8,9,1,3,1,7,8,3,6,8,9,9
%N A199605 Decimal expansion of least x satisfying x^2+3*x*cos(x)=sin(x).
%C A199605 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199605 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199605 least: -0.93049500263597010976334102402547851258644...
%e A199605 greatest:  3.01796308106862887266781443388576897037832...
%t A199605 a = 1; b = 3; c = 1;
%t A199605 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199605 Plot[{f[x], g[x]}, {x, -1.5, 3.5}, {AxesOrigin -> {0, 0}}]
%t A199605 r = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]
%t A199605 RealDigits[r]  (* A199605, least of 4 roots *)
%t A199605 r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision -> 110]
%t A199605 RealDigits[r]  (* A199606, greatest of 4 roots *)
%Y A199605 Cf. A199597.
%K A199605 nonn,cons
%O A199605 0,1
%A A199605 _Clark Kimberling_, Nov 08 2011