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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.
1
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].
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
KEYWORD
nonn,cons
AUTHOR
Jianing Song, Oct 10 2021
STATUS
approved