cp's OEIS Frontend

A200279 Decimal expansion of least x satisfying 3*x^2 - 4*cos(x) = 2*sin(x), negated.

%I A200279 #12 Feb 12 2025 14:32:54
%S A200279 7,3,5,6,3,8,0,7,6,4,4,4,6,8,2,0,8,6,1,4,7,7,6,9,5,5,6,1,2,3,1,1,6,8,
%T A200279 1,9,6,8,7,7,6,5,5,3,8,3,9,9,4,8,2,5,4,5,9,7,7,0,5,1,1,3,8,7,9,4,5,8,
%U A200279 4,1,7,8,0,7,1,9,1,9,7,3,5,5,2,8,4,2,2,0,3,5,6,5,9,2,8,5,8,5,3
%N A200279 Decimal expansion of least x satisfying 3*x^2 - 4*cos(x) = 2*sin(x), negated.
%C A200279 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200279 G. C. Greubel, <a href="/A200279/b200279.txt">Table of n, a(n) for n = 0..10000</a>
%H A200279 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200279 least x: -0.73563807644468208614776955612311...
%e A200279 greatest x: 1.096406992421267947221987681314...
%t A200279 a = 3; b = -4; c = 2;
%t A200279 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200279 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200279 r = x /. FindRoot[f[x] == g[x], {x, -.74, -.73}, WorkingPrecision -> 110]
%t A200279 RealDigits[r]  (* A200279 *)
%t A200279 r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
%t A200279 RealDigits[r]   (* A200280 *)
%o A200279 (PARI) a=3; b=-4; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 07 2018
%Y A200279 Cf. A199949.
%K A200279 nonn,cons
%O A200279 0,1
%A A200279 _Clark Kimberling_, Nov 15 2011