%I #8 Jun 25 2018 22:53:35
%S 1,5,0,4,0,7,4,3,6,5,6,0,3,9,0,8,4,5,6,2,5,7,7,0,9,6,8,1,3,1,2,5,9,7,
%T 2,7,8,5,5,0,0,6,5,6,0,9,3,9,5,9,0,8,3,2,2,3,4,0,3,8,1,1,2,3,9,7,6,0,
%U 1,6,5,6,2,7,5,7,6,0,1,4,0,7,0,4,0,8,6,7,1,7,2,8,3,5,5,4,8,7,5
%N Decimal expansion of greatest x satisfying x^2 - 4*cos(x) = 2*sin(x).
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200102/b200102.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: -0.91770131583160047517052439095392148771...
%e greatest x: 1.50407436560390845625770968131259727...
%t a = 1; b = -4; c = 2;
%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.92, -.91}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200101 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200102 *)
%o (PARI) a=1; b=-4; c=2; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 25 2018
%Y Cf. A199949.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 13 2011