cp's OEIS Frontend

A200297 Decimal expansion of least x satisfying 4*x^2-3*cos(x)=2*sin(x).

%I A200297 #12 Feb 12 2025 14:36:05
%S A200297 5,8,8,4,7,0,8,6,9,2,8,6,8,5,2,6,1,6,4,9,9,7,9,8,6,4,8,5,6,0,3,6,6,1,
%T A200297 8,8,2,9,8,3,2,9,5,4,3,1,0,7,1,1,9,3,6,5,0,0,9,1,7,5,7,7,4,4,8,9,7,9,
%U A200297 1,0,8,7,6,1,0,5,0,6,5,4,1,1,8,9,1,8,1,9,7,5,0,0,7,4,4,7,5,3,6
%N A200297 Decimal expansion of least x satisfying 4*x^2-3*cos(x)=2*sin(x).
%C A200297 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200297 G. C. Greubel, <a href="/A200297/b200297.txt">Table of n, a(n) for n = 0..10000</a>
%H A200297 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200297 least x: -0.58847086928685261649979864856036...
%e A200297 greatest x: 0.922697336548314794603906551791...
%t A200297 a = 4; b = -3; c = 2;
%t A200297 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200297 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200297 r = x /. FindRoot[f[x] == g[x], {x, -.59, -.58}, WorkingPrecision -> 110]
%t A200297 RealDigits[r]   (* A200297 *)
%t A200297 r = x /. FindRoot[f[x] == g[x], {x, .92, .93}, WorkingPrecision -> 110]
%t A200297 RealDigits[r]   (* A200298 *)
%o A200297 (PARI) a=4; b=-3; c=2; solve(x=-.59, -.58, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A200297 Cf. A199949.
%K A200297 nonn,cons
%O A200297 0,1
%A A200297 _Clark Kimberling_, Nov 15 2011