A199735 - OEIS

%I #8 Feb 08 2025 13:26:39

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

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

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

%N Decimal expansion of least x satisfying x^2-4*x*cos(x)=2*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 least: -3.69221424543584046112101682937268753850...

%e greatest:  1.519514926470401221585705162098148990...

%t a = 1; b = -4; c = 2;

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

%t Plot[{f[x], g[x]}, {x, -4, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -3.7, -3.6}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A199735 least root *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A199736 greatest root *)

%Y Cf. A199597.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Nov 09 2011