cp's OEIS Frontend

A200223 Decimal expansion of least x satisfying 3*x^2 - cos(x) = 2*sin(x), negated.

%I A200223 #12 Feb 12 2025 13:03:02
%S A200223 3,2,3,1,1,4,3,3,3,8,8,6,2,2,6,2,8,4,5,3,5,6,3,7,0,4,9,2,3,1,1,7,1,4,
%T A200223 9,1,1,9,9,1,6,3,6,2,8,8,2,6,6,1,5,9,4,3,8,5,8,7,5,7,8,7,3,5,7,6,5,0,
%U A200223 5,3,8,8,8,6,0,1,7,1,0,9,8,2,8,0,4,8,2,3,7,4,7,7,2,7,6,2,7,0,6
%N A200223 Decimal expansion of least x satisfying 3*x^2 - cos(x) = 2*sin(x), negated.
%C A200223 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200223 G. C. Greubel, <a href="/A200223/b200223.txt">Table of n, a(n) for n = 0..10000</a>
%H A200223 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200223 least x: -0.3231143338862262845356370492311714...
%e A200223 greatest x: 0.84890518832952236173456381626613...
%t A200223 a = 3; b = -1; c = 2;
%t A200223 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200223 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200223 r = x /. FindRoot[f[x] == g[x], {x, -.33, -.32}, WorkingPrecision -> 110]
%t A200223 RealDigits[r]   (* A200223 *)
%t A200223 r = x /. FindRoot[f[x] == g[x], {x, .84, .85}, WorkingPrecision -> 110]
%t A200223 RealDigits[r]   (* A200224 *)
%o A200223 (PARI) a=3; b=-1; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 30 2018
%Y A200223 Cf. A199949.
%K A200223 nonn,cons
%O A200223 0,1
%A A200223 _Clark Kimberling_, Nov 14 2011