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A200307 Decimal expansion of least x satisfying 4*x^2 - 4*cos(x) = 3*sin(x), negated.

%I A200307 #12 Feb 12 2025 14:37:13
%S A200307 6,1,7,4,0,6,5,1,4,4,2,0,1,3,2,1,3,1,6,8,8,2,9,8,4,3,5,0,7,2,3,0,9,8,
%T A200307 1,2,5,7,3,1,3,9,1,2,9,5,5,9,8,2,5,4,5,5,5,4,4,5,8,1,9,7,6,3,6,4,4,3,
%U A200307 7,4,4,1,0,8,2,0,8,0,0,5,4,9,4,6,8,7,4,7,3,9,7,8,1,1,1,8,0,5,9
%N A200307 Decimal expansion of least x satisfying 4*x^2 - 4*cos(x) = 3*sin(x), negated.
%C A200307 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200307 G. C. Greubel, <a href="/A200307/b200307.txt">Table of n, a(n) for n = 0..10000</a>
%H A200307 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200307 least x: -0.6174065144201321316882984350723098...
%e A200307 greatest x: 1.06740848569359172383926056700706...
%t A200307 a = 4; b = -4; c = 3;
%t A200307 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200307 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200307 r = x /. FindRoot[f[x] == g[x], {x, -.62, -.63}, WorkingPrecision -> 110]
%t A200307 RealDigits[r]   (* A200307 *)
%t A200307 r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
%t A200307 RealDigits[r]   (* A200308 *)
%o A200307 (PARI) a=4; b=-4; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 10 2018
%Y A200307 Cf. A199949.
%K A200307 nonn,cons
%O A200307 0,1
%A A200307 _Clark Kimberling_, Nov 16 2011