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%I #11 Jun 24 2018 08:57:58
%S 1,3,6,0,8,3,2,2,5,5,3,9,0,6,6,8,9,0,4,6,7,1,8,3,9,2,8,5,6,9,1,3,2,6,
%T 3,6,8,8,2,5,4,9,7,9,2,6,2,5,5,0,8,5,8,3,1,1,0,7,4,1,3,2,6,7,8,2,0,6,
%U 1,0,6,2,3,0,1,3,9,9,4,2,4,7,4,6,2,9,0,5,6,4,0,9,9,1,4,8,2,9,9
%N Decimal expansion of greatest x satisfying 2*x^2 + cos(x) = 4*sin(x).
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200005/b200005.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: 0.2841554251771481491680536288735443310...
%e greatest x: 1.36083225539066890467183928569132636...
%t a = 2; b = 1; c = 4;
%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -.1, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, .28, .29}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200004 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200005 *)
%o (PARI) a=2; b=1; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y Cf. A199949.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 12 2011
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