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

%I #8 Feb 08 2025 22:24:50

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

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

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

%N Decimal expansion of x>0 satisfying x^2-3*x*cos(x)=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 1.3569200623613718442251034863373965462473491...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, 1.35, 1.36}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199730 *)

%Y Cf. A199597.

%K nonn,cons,changed

%O 1,2

%A _Clark Kimberling_, Nov 09 2011