A199962 Decimal expansion of greatest x satisfying x^2 + 3*cos(x) = 4*sin(x).

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

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