cp's OEIS Frontend

A200096 Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = 3*sin(x).

%I A200096 #12 Feb 12 2025 09:53:27
%S A200096 1,6,5,4,6,9,9,7,8,2,2,9,3,9,0,1,0,7,1,1,3,1,6,8,6,6,8,1,8,3,0,8,0,0,
%T A200096 6,3,5,4,6,5,9,6,8,5,5,6,7,0,3,5,0,6,3,0,7,5,3,8,7,7,2,4,0,1,0,7,0,3,
%U A200096 8,7,2,6,4,8,7,7,0,4,0,0,3,7,8,7,1,8,7,6,8,5,2,5,7,6,2,3,7,1,4
%N A200096 Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = 3*sin(x).
%C A200096 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200096 G. C. Greubel, <a href="/A200096/b200096.txt">Table of n, a(n) for n = 1..10000</a>
%H A200096 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200096 least x:  -0.677119411697943130184179520098917021...
%e A200096 greatest x: 1.6546997822939010711316866818308006354...
%t A200096 a = 1; b = -3; c = 3;
%t A200096 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200096 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200096 r = x /. FindRoot[f[x] == g[x], {x, -.88, -.67}, WorkingPrecision -> 110]
%t A200096 RealDigits[r]  (* A200095 *)
%t A200096 r = x /. FindRoot[f[x] == g[x], {x, 1.65, 1.66}, WorkingPrecision -> 110]
%t A200096 RealDigits[r]  (* A200096 *)
%o A200096 (PARI) a=1; b=-3; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018
%Y A200096 Cf. A199949.
%K A200096 nonn,cons
%O A200096 1,2
%A A200096 _Clark Kimberling_, Nov 13 2011