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A200004 Decimal expansion of least x satisfying 2*x^2 + cos(x) = 4*sin(x).

%I A200004 #13 Feb 12 2025 04:49:04
%S A200004 2,8,4,1,5,5,4,2,5,1,7,7,1,4,8,1,4,9,1,6,8,0,5,3,6,2,8,8,7,3,5,4,4,3,
%T A200004 3,1,0,5,0,2,6,1,5,3,6,0,2,5,8,1,3,5,3,6,8,0,9,3,6,7,6,7,1,4,5,7,3,3,
%U A200004 4,3,5,2,2,1,4,0,1,8,7,8,6,5,4,8,3,5,5,8,2,8,9,0,5,2,9,2,9,0,6
%N A200004 Decimal expansion of least x satisfying 2*x^2 + cos(x) = 4*sin(x).
%C A200004 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200004 G. C. Greubel, <a href="/A200004/b200004.txt">Table of n, a(n) for n = 0..10000</a>
%H A200004 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200004 least x:  0.2841554251771481491680536288735443310...
%e A200004 greatest x: 1.36083225539066890467183928569132636...
%t A200004 a = 2; b = 1; c = 4;
%t A200004 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200004 Plot[{f[x], g[x]}, {x, -.1, 2}, {AxesOrigin -> {0, 0}}]
%t A200004 r = x /. FindRoot[f[x] == g[x], {x, .28, .29}, WorkingPrecision -> 110]
%t A200004 RealDigits[r]   (* A200004 *)
%t A200004 r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
%t A200004 RealDigits[r]   (* A200005 *)
%o A200004 (PARI) a=2; b=1; c=4; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y A200004 Cf. A199949.
%K A200004 nonn,cons
%O A200004 0,1
%A A200004 _Clark Kimberling_, Nov 12 2011