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A200012 Decimal expansion of least x satisfying x^2 - cos(x) = 2*sin(x) (negated).

%I A200012 #16 Feb 12 2025 04:51:36
%S A200012 3,9,4,1,2,4,1,9,2,8,5,8,9,7,5,9,6,0,0,9,9,7,0,5,3,9,9,3,5,4,5,9,0,0,
%T A200012 9,8,5,3,6,9,2,2,4,9,6,1,9,3,9,1,2,2,9,7,9,2,1,9,8,4,8,1,1,6,8,5,3,1,
%U A200012 1,8,7,4,1,7,6,0,2,4,8,1,7,9,3,5,8,3,4,5,6,0,3,0,7,1,7,9,2,1,5
%N A200012 Decimal expansion of least x satisfying x^2 - cos(x) = 2*sin(x) (negated).
%C A200012 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200012 G. C. Greubel, <a href="/A200012/b200012.txt">Table of n, a(n) for n = 0..10000</a>
%H A200012 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200012 least x:  -0.3941241928589759600997053993545900...
%e A200012 greatest x: 1.450938449634974431128285576690357738...
%t A200012 a = 1; b = -1; c = 2;
%t A200012 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200012 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A200012 r = x /. FindRoot[f[x] == g[x], {x, -.4, -.3}, WorkingPrecision -> 110]
%t A200012 RealDigits[r]   (* A200012 *)
%t A200012 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200012 RealDigits[r]   (* A200013 *)
%o A200012 (PARI) a=1; b=-1; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y A200012 Cf. A199949.
%K A200012 nonn,cons
%O A200012 0,1
%A A200012 _Clark Kimberling_, Nov 12 2011