cp's OEIS Frontend

A200015 Decimal expansion of greatest x satisfying x^2 - cos(x) = 3*sin(x).

%I A200015 #14 Feb 12 2025 04:52:45
%S A200015 1,6,9,0,7,7,9,7,3,8,9,6,9,8,1,5,3,3,4,9,5,7,5,0,4,8,5,7,5,5,8,8,0,9,
%T A200015 5,4,3,4,2,1,3,2,4,1,6,3,9,0,6,5,4,5,2,8,5,4,4,5,1,8,3,8,5,4,9,7,2,6,
%U A200015 1,2,8,7,2,5,7,1,9,9,7,4,5,7,7,4,3,1,6,6,2,4,6,8,3,9,3,9,2,8,1
%N A200015 Decimal expansion of greatest x satisfying x^2 - cos(x) = 3*sin(x).
%C A200015 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200015 G. C. Greubel, <a href="/A200015/b200015.txt">Table of n, a(n) for n = 1..10000</a>
%H A200015 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200015 least x:  -0.2943487723356863983696578902036195...
%e A200015 greatest x: 1.690779738969815334957504857558809...
%t A200015 a = 1; b = -1; c = 3;
%t A200015 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200015 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A200015 r = x /. FindRoot[f[x] == g[x], {x, -.3, -.29}, WorkingPrecision -> 110]
%t A200015 RealDigits[r]  (* A200014 *)
%t A200015 r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
%t A200015 RealDigits[r]   (* A200015 *)
%o A200015 (PARI) a=1; b=-1; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y A200015 Cf. A199949.
%K A200015 nonn,cons
%O A200015 1,2
%A A200015 _Clark Kimberling_, Nov 12 2011
%E A200015 a(88)-a(99) corrected by _G. C. Greubel_, Jun 23 2018