cp's OEIS Frontend

A199734 Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=3*sin(x).

%I A199734 #8 Feb 08 2025 22:12:15
%S A199734 1,6,2,5,2,7,8,3,8,3,3,7,8,4,4,8,6,4,3,9,3,3,0,0,3,2,2,6,2,4,6,8,3,6,
%T A199734 1,0,6,0,8,6,5,5,9,6,7,1,6,5,8,5,7,2,8,1,5,4,4,7,5,9,5,5,8,3,7,9,3,6,
%U A199734 1,2,3,7,9,4,4,8,6,8,8,1,9,7,7,8,7,3,1,5,2,5,4,9,3,4,0,9,1,8,2
%N A199734 Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=3*sin(x).
%C A199734 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199734 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199734 least: -3.746168565528221340687013560527596978856...
%e A199734 greatest:  1.625278383378448643933003226246836106...
%t A199734 a = 1; b = -4; c = 3;
%t A199734 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199734 Plot[{f[x], g[x]}, {x, -4, 2}, {AxesOrigin -> {0, 0}}]
%t A199734 r = x /. FindRoot[f[x] == g[x], {x, -3.8, -3.7}, WorkingPrecision -> 110]
%t A199734 RealDigits[r]   (* A199733 least root *)
%t A199734 r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
%t A199734 RealDigits[r]   (* A199734 greatest root *)
%Y A199734 Cf. A199597.
%K A199734 nonn,cons
%O A199734 1,2
%A A199734 _Clark Kimberling_, Nov 09 2011