cp's OEIS Frontend

A200127 Decimal expansion of greatest x satisfying 2*x^2 - 3*cos(x) = 4*sin(x).

%I A200127 #12 Feb 12 2025 13:01:15
%S A200127 1,4,6,5,2,3,5,3,8,6,1,4,2,6,3,1,8,5,6,9,4,5,9,2,6,8,3,0,5,7,2,6,9,4,
%T A200127 9,2,6,9,0,0,7,8,8,8,6,2,5,1,9,6,6,4,6,8,7,8,7,8,3,9,7,1,6,8,3,1,4,1,
%U A200127 7,3,5,2,9,3,5,6,5,7,7,2,4,5,6,1,7,8,8,7,7,2,4,7,3,1,0,3,9,9,1
%N A200127 Decimal expansion of greatest x satisfying 2*x^2 - 3*cos(x) = 4*sin(x).
%C A200127 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200127 G. C. Greubel, <a href="/A200127/b200127.txt">Table of n, a(n) for n = 1..10000</a>
%H A200127 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200127 least x: -0.530633047496848880166804175671064100...
%e A200127 greatest x: 1.4652353861426318569459268305726949...
%t A200127 a = 2; b = -3; c = 4;
%t A200127 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200127 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200127 r = x /. FindRoot[f[x] == g[x], {x, -.54, -.53}, WorkingPrecision -> 110]
%t A200127 RealDigits[r]  (* A200126 *)
%t A200127 r = x /. FindRoot[f[x] == g[x], {x, 1.46, 1.47}, WorkingPrecision -> 110]
%t A200127 RealDigits[r]  (* A200127 *)
%o A200127 (PARI) a=2; b=-3; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 01 2018
%Y A200127 Cf. A199949.
%K A200127 nonn,cons
%O A200127 1,2
%A A200127 _Clark Kimberling_, Nov 14 2011