A277077 Decimal expansion of the root of cos(sin(x)) - x = 0.

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

Offset

0,1

Comments

The fixed point solution for the composite function y = cos(sin(x)).

The value A131691 is equal to the arccosine of this value and this value is equal to the arcsine of A131691.

Links

Table of n, a(n) for n=0..107.

Formula

Recursion: f(n) = cos(sin(f(n-1)) n->infinity.

Root of cos(sin(x)) - x = 0.

Example

0.76816915673679597746208623955865641813208731218273718569186715...

Mathematica

FindRoot[-x + Cos[Sin[x]] == 0, {x, 0.5, 1}, WorkingPrecision -> 265]

Prog

(PARI) solve(x=0.5, 1, cos(sin(x))-x) \\ Michel Marcus, Sep 29 2016

Crossrefs

Cf. A131691 (reversed form), A003957 (fixed point solution for cosine).

Sequence in context: A202345 A010512 A195370 * A196913 A091343 A196397

Adjacent sequences: A277074 A277075 A277076 * A277078 A277079 A277080

Keyword

nonn,easy,cons

Author

David D. Acker, Sep 27 2016

Status

approved