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A200287 Decimal expansion of least x satisfying 4*x^2 - cos(x) = 2*sin(x), negated.

%I A200287 #12 Feb 12 2025 14:33:55
%S A200287 3,0,0,9,3,1,8,8,5,4,2,1,9,0,2,3,7,0,0,3,1,0,0,6,2,4,0,7,1,7,5,1,4,9,
%T A200287 5,6,3,1,9,8,7,9,8,0,3,3,2,2,2,6,8,8,4,5,0,8,3,5,0,3,3,3,7,2,3,5,3,1,
%U A200287 6,0,8,9,4,3,2,6,1,3,9,1,9,2,8,1,6,6,5,7,1,9,5,2,0,1,6,2,3,0,2
%N A200287 Decimal expansion of least x satisfying 4*x^2 - cos(x) = 2*sin(x), negated.
%C A200287 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200287 G. C. Greubel, <a href="/A200287/b200287.txt">Table of n, a(n) for n = 0..10000</a>
%H A200287 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200287 least x: -0.300931885421902370031006240717514956...
%e A200287 greatest x: 0.7193842604598758321075524115913806...
%t A200287 a = 4; b = -1; c = 2;
%t A200287 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200287 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A200287 r = x /. FindRoot[f[x] == g[x], {x, -.31, -.30}, WorkingPrecision -> 110]
%t A200287 RealDigits[r]    (* A200287 *)
%t A200287 r = x /. FindRoot[f[x] == g[x], {x, .71, .72}, WorkingPrecision -> 110]
%t A200287 RealDigits[r]   (* A200288 *)
%o A200287 (PARI) a=4; b=-1; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 07 2018
%Y A200287 Cf. A199949.
%K A200287 nonn,cons
%O A200287 0,1
%A A200287 _Clark Kimberling_, Nov 15 2011