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A199463 Decimal expansion of x>0 satisfying x^2-2*x*sin(x)=3*cos(x).

%I A199463 #9 Feb 08 2025 09:58:48
%S A199463 1,7,1,9,4,7,9,3,6,6,6,5,1,9,3,4,7,2,7,4,8,4,2,9,8,6,8,3,7,6,4,3,2,6,
%T A199463 5,8,7,2,0,0,7,1,1,8,4,3,8,3,2,9,8,2,1,6,7,8,0,0,7,0,5,4,3,4,0,4,3,2,
%U A199463 7,8,6,5,9,7,4,2,4,2,8,7,1,4,9,9,3,5,7,8,6,1,4,1,7,4,0,1,4,3,3
%N A199463 Decimal expansion of x>0 satisfying x^2-2*x*sin(x)=3*cos(x).
%C A199463 See A199429 for a guide to related sequences. The Mathematica program includes a graph.
%H A199463 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199463 1.719479366651934727484298683764326587200711843...
%t A199463 a = 1; b = -2; c = 3;
%t A199463 f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
%t A199463 Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
%t A199463 r = x /. FindRoot[f[x] == g[x], {x, 1.71, 1.72}, WorkingPrecision -> 110]
%t A199463 RealDigits[r]  (* A199463 *)
%Y A199463 Cf. A199429.
%K A199463 nonn,cons
%O A199463 1,2
%A A199463 _Clark Kimberling_, Nov 07 2011