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A199603 Decimal expansion of least x satisfying x+3*cos(x)=0.

%I A199603 #8 Feb 07 2025 19:49:51
%S A199603 1,1,7,0,1,2,0,9,5,0,0,0,2,6,2,6,0,5,3,7,0,6,0,4,3,0,1,1,8,5,8,9,7,1,
%T A199603 0,8,1,9,9,9,4,0,2,0,2,5,9,5,5,5,1,5,6,4,7,4,1,6,8,1,9,7,4,4,3,7,0,0,
%U A199603 2,4,9,2,4,7,7,1,7,3,0,8,4,2,6,4,7,9,9,0,8,0,1,1,0,0,7,0,8,0,5
%N A199603 Decimal expansion of least x satisfying x+3*cos(x)=0.
%C A199603 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199603 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199603 least: -1.1701209500026260537060430118589710...
%e A199603 greatest:  2.9381003939708118076581364784259...
%t A199603 a = 1; b = 3; c = 0;
%t A199603 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199603 Plot[{f[x], g[x]}, {x, -1.5, 3.5}, {AxesOrigin -> {0, 0}}]
%t A199603 r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t A199603 RealDigits[r]  (* A199603 least of 4 roots *)
%t A199603 r = x /. FindRoot[f[x] == g[x], {x, 2.93, 2.94}, WorkingPrecision -> 110]
%t A199603 RealDigits[r]  (* A199604 greatest of 4 roots *)
%Y A199603 Cf. A199597.
%K A199603 nonn,cons
%O A199603 1,3
%A A199603 _Clark Kimberling_, Nov 08 2011