|
%I #8 Jun 22 2018 23:24:52
%S 1,9,9,0,5,0,3,4,6,1,6,6,8,4,9,3,8,3,5,5,8,1,8,7,6,0,2,2,2,0,4,4,1,2,
%T 4,7,6,3,6,9,4,5,1,1,6,7,7,1,8,2,5,3,6,2,0,8,9,8,8,7,5,4,8,8,9,7,0,7,
%U 6,6,2,2,9,2,7,5,9,1,9,6,3,0,3,2,0,2,8,2,0,8,9,2,5,5,7,4,8,1,0
%N Decimal expansion of greatest x satisfying x^2+3*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="/A199960/b199960.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: 1.046472542540093403618073553786437093400...
%e greatest x: 1.9905034616684938355818760222044124763...
%t a = 1; b = 3; 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, 1.0, 1.1}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199959 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.99, 2.0}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199960 *)
%o (PARI) a=1; b=3; c=3; solve(x=1.9, 2, 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
|
