A199956 - OEIS

%I #10 Jun 22 2018 23:23:16

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

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

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

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

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

%H G. C. Greubel, <a href="/A199956/b199956.txt">Table of n, a(n) for n = 1..10000</a>

%e least x:  0.74080336819413223759642692454702162091742...

%e greatest x: 1.854778410356751774141939581736998761204...

%t a = 1; b = 2; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .74, .75}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199955 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.8, 1.9}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199956 *)

%o (PARI) a=1; b=2; c=3; solve(x=.5, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018

%Y Cf. A199949.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 12 2011