A377480 -id:A377480 - cp's OEIS frontend

A377479 Decimal expansion of the smallest positive real root of the equation cos(x) + x*sin(x) = 0.

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

Offset: 1

Stefano Spezia, Oct 29 2024

The absolute value of the x-coordinate of the tangent point between the cosine graph and the straight line through the origin.

			2.79838604578388713672024890313957...

Index entries for transcendental numbers

Cf. A003957, A115365, A197002, A377480, A377481.

ndigits=100; First[RealDigits[First[x/.NSolve[Cos[x]+x Sin[x]==0,x,ndigits]],10,ndigits]]
(* or *)
RealDigits[BesselJZero[-3/2, 1], 10, 100][[1]] (* Vaclav Kotesovec, Oct 31 2024 *)

\\ Note: besseljzero not guaranteed to work here since -3/2 < 0.
solve(x=2,3, cos(x)+x*sin(x)) \\ Charles R Greathouse IV, Jan 23 2025

A377481 Decimal expansion of sin(A377479).

Original entry on oeis.org

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

Offset: 0

Stefano Spezia, Oct 29 2024

The value of the slope of the straight line through the origin that is tangent to the cosine graph.

			0.3365084169183952916163198144073...

Cf. A377479, A377480.

ndigits=100; First[RealDigits[Sin[First[x/.NSolve[Cos[x]+x Sin[x]==0,x,ndigits+1]]],10,ndigits]]

cp's OEIS Frontend

A377479 Decimal expansion of the smallest positive real root of the equation cos(x) + x*sin(x) = 0.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI