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A200303 Decimal expansion of least x satisfying 4*x^2 - 3*cos(x) = 4*sin(x), negated.

%I A200303 #12 Feb 12 2025 14:37:08
%S A200303 4,6,7,6,4,3,6,3,2,2,2,9,0,5,6,5,3,4,2,0,3,5,4,0,0,4,9,4,7,7,1,6,5,0,
%T A200303 1,3,9,2,4,1,6,9,8,1,7,2,2,4,0,2,6,3,5,7,1,6,8,7,3,2,8,1,2,7,5,7,8,8,
%U A200303 0,9,5,9,8,2,5,0,6,1,3,9,9,5,1,3,0,2,3,8,8,9,3,3,8,9,3,9,4,0,3
%N A200303 Decimal expansion of least x satisfying 4*x^2 - 3*cos(x) = 4*sin(x), negated.
%C A200303 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200303 G. C. Greubel, <a href="/A200303/b200303.txt">Table of n, a(n) for n = 0..10000</a>
%H A200303 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200303 least x: -0.4676436322290565342035400494771...
%e A200303 greatest x: 1.10881188297172762185849535228...
%t A200303 a = 4; b = -3; c = 4;
%t A200303 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200303 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A200303 r = x /. FindRoot[f[x] == g[x], {x, -.47, -.46}, WorkingPrecision -> 110]
%t A200303 RealDigits[r]   (* A200303 *)
%t A200303 r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
%t A200303 RealDigits[r]   (* A200304 *)
%o A200303 (PARI) a=4; b=-3; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y A200303 Cf. A199949.
%K A200303 nonn,cons
%O A200303 0,1
%A A200303 _Clark Kimberling_, Nov 15 2011