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

%I #12 Jun 24 2018 18:33:05

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

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

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

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

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

%H G. C. Greubel, <a href="/A200093/b200093.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.8029921542978842507203354534748712742...

%e greatest x: 1.492665923525132206969243059834936861...

%t a = 1; b = -3; 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, -.81, -.80}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200093 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.49, 1.50}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200094 *)

%o (PARI) a=1; b=-3; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 13 2011