

A199962


Decimal expansion of greatest x satisfying x^2 + 3*cos(x) = 4*sin(x).


3



2, 2, 3, 5, 8, 0, 9, 2, 8, 2, 0, 6, 4, 5, 6, 9, 1, 2, 1, 1, 1, 5, 2, 6, 4, 1, 4, 8, 3, 1, 7, 0, 1, 9, 8, 4, 4, 2, 4, 8, 0, 4, 9, 2, 0, 3, 9, 2, 6, 5, 3, 9, 0, 4, 0, 4, 3, 4, 1, 5, 0, 9, 1, 3, 0, 2, 6, 0, 5, 2, 4, 8, 0, 6, 1, 5, 1, 6, 5, 3, 9, 7, 5, 3, 5, 0, 8, 8, 3, 7, 8, 7, 4, 1, 9, 3, 2, 6, 9
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OFFSET

1,1


COMMENTS

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


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000


EXAMPLE

least x: 0.7589622035176968518571982860561050925949...
greatest x: 2.23580928206456912111526414831701984424...


MATHEMATICA

a = 1; b = 3; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, 1, 3}, {AxesOrigin > {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .75, .76}, WorkingPrecision > 110]
RealDigits[r] (* A199961 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.2, 2.3}, WorkingPrecision > 110]
RealDigits[r] (* A199962 *)


PROG

(PARI) a=1; b=3; c=4; solve(x=2, 3, a*x^2 + b*cos(x)  c*sin(x)) \\ G. C. Greubel, Jun 23 2018


CROSSREFS

Cf. A199949.
Sequence in context: A337745 A253853 A127678 * A114990 A241421 A157176
Adjacent sequences: A199959 A199960 A199961 * A199963 A199964 A199965


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Nov 12 2011


STATUS

approved



