A348294 -id:A348294

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A348293

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

+10
1

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

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OFFSET

1,2

COMMENTS

The equation sin(x) = arctan(x) has a unique positive root x_0. Note that arctan(x) < sin(x) for x in (-oo, -x_0) U (0, x_0) and arctan(x) > sin(x) for x in (-x_0, 0) U (x_0, +oo).

LINKS

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

EXAMPLE

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

MATHEMATICA

RealDigits[x /. FindRoot[Sin[x] == ArcTan[x], {x, 3/2}, WorkingPrecision -> 100], 10, 90][[1]] (* Amiram Eldar, Oct 10 2021 *)

PROG

(PARI) solve(x=1.55, 1.57, atan(x)-sin(x))

CROSSREFS

Cf. A348294 (y-coordinate).

KEYWORD

nonn,cons

AUTHOR

Jianing Song, Oct 10 2021

STATUS

approved

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