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A199793 Decimal expansion of x > 0 satisfying 3*x^2 - 2*x*cos(x) = sin(x).

%I A199793 #10 Feb 08 2025 22:36:14
%S A199793 7,7,6,4,4,3,1,0,8,9,0,3,8,3,8,1,0,1,9,0,9,6,6,9,9,4,9,1,6,2,9,8,2,8,
%T A199793 8,7,9,1,8,0,0,5,1,4,7,8,0,9,6,9,7,4,8,0,0,4,9,6,7,4,3,2,3,2,8,0,2,5,
%U A199793 3,5,0,0,9,6,6,9,9,4,8,0,5,6,9,3,4,9,4,0,5,2,8,4,9,8,9,3,2,7,5
%N A199793 Decimal expansion of x > 0 satisfying 3*x^2 - 2*x*cos(x) = sin(x).
%C A199793 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199793 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199793 0.77644310890383810190966994916298288791800514780...
%t A199793 a = 3; b = -2; c = 1;
%t A199793 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199793 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A199793 r = x /. FindRoot[f[x] == g[x], {x, .77, .78}, WorkingPrecision -> 110]
%t A199793 RealDigits[r]   (* A199793 *)
%Y A199793 Cf. A199597.
%K A199793 nonn,cons
%O A199793 0,1
%A A199793 _Clark Kimberling_, Nov 10 2011
%E A199793 a(96) onwards corrected by _Georg Fischer_, Aug 03 2021