cp's OEIS Frontend

A199617 Decimal expansion of least x satisfying x^2+4*x*cos(x)=3*sin(x).

%I A199617 #9 Feb 08 2025 10:14:04
%S A199617 5,5,3,5,4,3,3,8,1,7,8,6,0,3,3,6,2,8,7,0,2,0,3,4,4,9,0,5,9,1,1,8,1,6,
%T A199617 9,3,0,4,0,6,3,2,5,8,0,1,1,9,4,8,5,5,2,5,1,2,7,6,2,5,4,7,5,2,7,1,3,8,
%U A199617 3,1,4,4,4,4,6,9,3,7,3,9,8,3,1,0,6,3,4,6,4,5,4,9,0,8,8,0,0,8,6
%N A199617 Decimal expansion of least x satisfying x^2+4*x*cos(x)=3*sin(x).
%C A199617 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199617 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199617 least: -0.5535433817860336287020344905911816930...
%e A199617 greatest:  3.4822676247861932090867036675576803...
%t A199617 a = 1; b = 4; c = 3;
%t A199617 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199617 Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
%t A199617 r = x /. FindRoot[f[x] == g[x], {x, -.56, -.55}, WorkingPrecision -> 110]
%t A199617 RealDigits[r]  (* A199617, least of 4 roots *)
%t A199617 r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
%t A199617 RealDigits[r]  (* A199618, greatest of 4 roots *)
%Y A199617 Cf. A199597.
%K A199617 nonn,cons
%O A199617 0,1
%A A199617 _Clark Kimberling_, Nov 08 2011