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Decimal expansion of x>0 satisfying 4*x^2-2*x*cos(x) = 3*sin(x).
2

%I #7 Jun 17 2022 14:37:23

%S 9,3,9,5,1,9,4,9,6,3,9,1,8,7,5,0,9,7,7,0,0,1,1,5,9,8,0,6,2,9,2,9,1,7,

%T 3,5,9,1,1,4,4,8,8,0,3,4,0,8,7,7,3,5,4,5,9,3,6,5,0,5,0,4,6,2,1,1,5,6,

%U 6,3,2,8,1,5,8,0,3,8,1,1,0,3,4,2,4,5,2,6,2,5,0,0,6,8,2,7,3,7,7

%N Decimal expansion of x>0 satisfying 4*x^2-2*x*cos(x) = 3*sin(x).

%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.

%e x = 0.93951949639187509770011598062929173591144880...

%t a = 4; b = -2; c = 3;

%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .93, .94}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199866 *)

%Y Cf. A199597.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 11 2011