A200231 - OEIS

%I #8 Jun 22 2018 07:57:39

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

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

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

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

%C See A199949 for a guide to related sequences.  The Mathematica program includes a graph.

%H G. C. Greubel, <a href="/A200231/b200231.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.508066683701868134653059484203509821...

%e greatest x: 0.9632913766196791046556418296641642...

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

%t f[x_] := a*x^2 + b*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, -.51, -.50}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200231 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .96, .97}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200232 *)

%o (PARI) a=3; b=-2; c=2; solve(x=-.51, -.50, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 14 2011