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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 (list; constant; graph; refs; listen; history; text; internal format)
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: A103597 A253853 A127678 * A114990 A241421 A157176

Adjacent sequences:  A199959 A199960 A199961 * A199963 A199964 A199965

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 12 2011

STATUS

approved

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Last modified August 23 00:50 EDT 2019. Contains 326211 sequences. (Running on oeis4.)