The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A348294 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A348294

Decimal expansion of y-coordinate of the intersection of y = sin(x) and y = arctan(x) in the first quadrant.
(history; published version)

#10 by N. J. A. Sloane at Mon Oct 11 18:48:43 EDT 2021

STATUS

editing

approved

#9 by N. J. A. Sloane at Mon Oct 11 18:48:36 EDT 2021

NAME

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

STATUS

proposed

editing

Discussion

Mon Oct 11

18:48

N. J. A. Sloane: It is important to say "Decimal expansion of ..." to make it clear that this is not some function of n.

#8 by Amiram Eldar at Sun Oct 10 13:15:52 EDT 2021

STATUS

editing

proposed

#7 by Amiram Eldar at Sun Oct 10 13:15:48 EDT 2021

MATHEMATICA

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

STATUS

proposed

editing

#6 by Jianing Song at Sun Oct 10 11:47:08 EDT 2021

STATUS

editing

proposed

#5 by Jianing Song at Sun Oct 10 11:46:50 EDT 2021

CROSSREFS

Cf. A348294 A348293 (x-coordinate).

#4 by Jianing Song at Sun Oct 10 11:46:29 EDT 2021

EXAMPLE

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

CROSSREFS

Cf. A348294 (x-coordinate).

#3 by Jianing Song at Sun Oct 10 11:44:05 EDT 2021

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].

#2 by Jianing Song at Sun Oct 10 10:52:21 EDT 2021

NAME

allocated for Jianing Songy-coordinate of the intersection of y = sin(x) and y = arctan(x) in the first quadrant.

DATA

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

PROG

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

KEYWORD

allocated

nonn,cons

AUTHOR

Jianing Song, Oct 10 2021

STATUS

approved

editing

#1 by Jianing Song at Sun Oct 10 10:48:36 EDT 2021

NAME

allocated for Jianing Song

KEYWORD

allocated

STATUS

approved