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

%I #13 Feb 08 2025 09:40:34

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

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

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

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

%C See A199429 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 1.384358289135175432171140921123786477989432717720...

%t a = 1; b = -1; c = 3;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, 1.38, 1.39}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199456 *)

%Y Cf. A199429.

%K nonn,cons,changed

%O 1,2

%A _Clark Kimberling_, Nov 06 2011