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A199446 Decimal expansion of x>0 satisfying 3*x^2+x*sin(x)=cos(x).

%I A199446 #8 Feb 08 2025 09:19:05
%S A199446 4,7,3,8,4,7,9,7,1,2,6,3,7,7,7,4,3,0,9,9,9,8,0,1,5,8,7,1,1,4,4,2,5,9,
%T A199446 8,5,9,1,1,6,7,1,8,0,1,2,0,4,5,3,1,8,9,1,0,6,3,0,9,0,7,5,6,5,3,7,7,8,
%U A199446 9,0,7,4,6,2,3,3,8,7,8,0,8,9,0,8,2,9,1,7,4,3,0,2,8,8,7,9,8,8,8
%N A199446 Decimal expansion of x>0 satisfying 3*x^2+x*sin(x)=cos(x).
%C A199446 See A199370 for a guide to related sequences. The Mathematica program includes a graph.
%H A199446 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199446 0.47384797126377743099980158711442598591167180120...
%t A199446 a = 3; b = 1; c = 1;
%t A199446 f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
%t A199446 Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
%t A199446 r = x /. FindRoot[f[x] == g[x], {x, .47, .48}, WorkingPrecision -> 110]
%t A199446 RealDigits[r] (* A199446 *)
%Y A199446 Cf. A199429.
%K A199446 nonn,cons
%O A199446 0,1
%A A199446 _Clark Kimberling_, Nov 06 2011