A335930 Decimal expansion of the arclength on y = sin(x) from (0,0) to (Pi,0).

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

Offset

1,1

Comments

Also the arclength between consecutive points of intersection of y = sin(x) and y = cos(x).

Links

Table of n, a(n) for n=1..90.

Formula

From Paolo Xausa, Nov 14 2024: (Start)

Equals Pi/A062539 + A062539 = A053004 + A062539.

Equals A010466*A257407. (End)

Equals A105419/2 = 2*A256667. - Hugo Pfoertner, Nov 14 2024

Example

3.8201977890277120179047620821714432919099676146...

Mathematica

r = NIntegrate[Sqrt[1 + Cos[t]^2], {t, 0, Pi}, WorkingPrecision -> 200]
RealDigits[r][[1]]
First[RealDigits[Sqrt[8]*EllipticE[1/2], 10, 100]] (* Paolo Xausa, Nov 14 2024 *)

Prog

(PARI) 2 * sqrt(2) * ellE(1/sqrt(2)) \\ Amiram Eldar, May 16 2026

Crossrefs

Cf. A335928, A335929, A335931, A335932.

Cf. A000796, A010466, A053004, A062539, A105419, A256667, A257407.

Sequence in context: A281416 A280567 A280835 * A386853 A195426 A202537

Adjacent sequences: A335927 A335928 A335929 * A335931 A335932 A335933

Keyword

nonn,cons

Author

Clark Kimberling, Jul 01 2020

Status

approved