

A019812


Decimal expansion of sine of 3 degrees.


19



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

0,2


COMMENTS

An algebraic number of degree 16 and denominator 2.  Charles R Greathouse IV, Nov 02 2012
The Fifteenth Century Persian mathematician Jamshid AlKashi was the first to calculate the value of sine of one degree correct to ten sexagesimal places (17 decimal digits) from sine of 3 degrees in his Risala alWatar wa'l Jaib.  Mohammad K. Azarian,Jan 14 2017


LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Mohammad K. Azarian, A Study of Risala alWatar wa'l Jaib ("The Treatise on the Chord and Sine"), Forum Geometricorum, Volume 15 (2015) 229242. Mathematical Reviews, MR 3418854 (Reviewed), Zentralblatt MATH, Zbl 1328.01015.
Dr. Rob, The Math Forum at Drexel, The Exact Value of the Sine of 1 Degree
Scott Surgent, Exact values of the sine and cosine functions in increments of 3 degrees, 2012
Wikipedia, Trigonometric constants expressed in real radicals


FORMULA

Equals cos(87 degrees) = cos(29*Pi/60) = sin(Pi/60) = sqrt(8sqrt(3)sqrt(15)sqrt(102*sqrt(5)))/4 (an intermediate calculation by Dr. Rob  see Math Forum link).  Rick L. Shepherd, Jul 03 2006
Equals A019811*A019898 + A019810*A019897.  R. J. Mathar, Jan 27 2021


EXAMPLE

0.052335956242943832722118629609...


PROG

(PARI) sin(Pi/60) \\ Charles R Greathouse IV, Aug 27 2017


CROSSREFS

Cf. A019896 (cosine), A019901 (tangent), A019985 (cotangent): for 3 degrees.
Cf. A019810, A019811, A019897, A019898.
Sequence in context: A071216 A069483 A011226 * A222222 A071544 A031285
Adjacent sequences: A019809 A019810 A019811 * A019813 A019814 A019815


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane


STATUS

approved



