cp's OEIS Frontend

A199733 Decimal expansion of least x satisfying x^2-4*x*cos(x)=3*sin(x).

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