%I #8 Feb 08 2025 22:31:13

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

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

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

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

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e 1.236907149122441612859325763734515286117501...

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

%t f[x_] := a*x^2 + b*x*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, .90, .91}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199790 *)

%Y Cf. A199597.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 10 2011