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A200101 Decimal expansion of least x satisfying x^2 - 4*cos(x) = 2*sin(x), negated.

%I A200101 #11 Feb 12 2025 09:54:23
%S A200101 9,1,7,7,0,1,3,1,5,8,3,1,6,0,0,4,7,5,1,7,0,5,2,4,3,9,0,9,5,3,9,2,1,4,
%T A200101 8,7,7,1,8,1,9,6,1,1,6,8,5,9,0,0,5,7,1,1,5,1,0,0,4,8,9,0,0,2,2,4,8,9,
%U A200101 4,4,8,7,9,0,0,7,1,1,5,4,2,2,3,0,2,3,3,9,9,7,4,4,0,5,8,6,8,6,8
%N A200101 Decimal expansion of least x satisfying x^2 - 4*cos(x) = 2*sin(x), negated.
%C A200101 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200101 G. C. Greubel, <a href="/A200101/b200101.txt">Table of n, a(n) for n = 0..10000</a>
%H A200101 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200101 least x:  -0.91770131583160047517052439095392148771...
%e A200101 greatest x: 1.50407436560390845625770968131259727...
%t A200101 a = 1; b = -4; c = 2;
%t A200101 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200101 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200101 r = x /. FindRoot[f[x] == g[x], {x, -.92, -.91}, WorkingPrecision -> 110]
%t A200101 RealDigits[r]  (* A200101 *)
%t A200101 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A200101 RealDigits[r]  (* A200102 *)
%o A200101 (PARI) a=1; b=-4; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 25 2018
%Y A200101 Cf. A199949.
%K A200101 nonn,cons
%O A200101 0,1
%A A200101 _Clark Kimberling_, Nov 13 2011