A348294 Decimal expansion of y-coordinate of the intersection of y = sin(x) and y = arctan(x) in the first quadrant.

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

Offset

0,1

Comments

Also positive root of arcsin(x) = tan(x).

The equation arcsin(x) = tan(x) has a unique positive root x_0. Note that arcsin(x) < tan(x) for x in [-1, -x_0) U (0, x_0) and arcsin(x) > tan(x) for x in (-x_0, 0) U (x_0, 1].

Links

Table of n, a(n) for n=0..89.

Example

sin(1.5570858155...) = arctan(1.5570858155...) = 0.9999060124...

Mathematica

RealDigits[x /. FindRoot[Tan[x] == ArcSin[x], {x, 0.99}, WorkingPrecision -> 100], 10, 90][[1]] (* Amiram Eldar, Oct 10 2021 *)

Prog

(PARI) solve(x=0.99, 1, tan(x)-asin(x))

Crossrefs

Cf. A348293 (x-coordinate).

Sequence in context: A258815 A114054 A347220 * A018938 A292888 A111659

Adjacent sequences: A348291 A348292 A348293 * A348295 A348296 A348297

Keyword

nonn,cons

Author

Jianing Song, Oct 10 2021

Status

approved