A019810 -id:A019810 - cp's OEIS frontend

A019898 Decimal expansion of sine of 89 degrees.

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

Offset: 0

N. J. A. Sloane

Also decimal expansion of cosine of 1 degree. - Mohammad K. Azarian, Nov 17 2005
Equals sin(89*Pi/180). - Wesley Ivan Hurt, Sep 01 2014
An algebraic number of degree 48 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

			0.999847695156391239157011558813914851692740310583185939658320...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for algebraic numbers, degree 48

Cf. A019810.

Digits:=100: evalf(sin(89*Pi/180)); # Wesley Ivan Hurt, Sep 01 2014

RealDigits[N[Sin[89 Degree],6! ]][[1]] (*Vladimir Joseph Stephan Orlovsky, Jun 18 2009 *)

sin(89*Pi/180) \\ Charles R Greathouse IV, Aug 27 2017

Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar

A019812 Decimal expansion of sine of 3 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

An algebraic number of degree 16 and denominator 2. - Charles R Greathouse IV, Nov 02 2012
The minimal polynomial is p(x) = 65536*x^16 - 262144*x^14 + 430080*x^12 - 372736*x^10 + 182784*x^8 - 50176*x^6 + 7040*x^4 - 384*x^2 + 1 and p(x/2) = x^16 - 16*x^14 + 105*x^12 - 364*x^10 + 714*x^8 - 784*x^6 + 440*x^4 - 96*x^2 + 1. - Joerg Arndt, Apr 23 2024
The Fifteenth Century Persian mathematician Jamshid Al-Kashi 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 al-Watar wa'l Jaib. - Mohammad K. Azarian,Jan 14 2017

			0.052335956242943832722118629609...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Mohammad K. Azarian, A Study of Risa-la al-Watar wa'l Jaib ("The Treatise on the Chord and Sine"), Forum Geometricorum, Volume 15 (2015) 229-242. 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, Exact trigonometric values
Index entries for algebraic numbers, degree 16

Cf. A019896 (cosine), A019901 (tangent), A019985 (cotangent): for 3 degrees.

Cf. A019810, A019811, A019897, A019898.

First[RealDigits[Sin[Pi/60], 10, 100, -1]] (* Paolo Xausa, Jun 19 2024 *)

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

Equals cos(87 degrees) = cos(29*Pi/60) = sin(Pi/60) = sqrt(8-sqrt(3)-sqrt(15)-sqrt(10-2*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

A019814 Decimal expansion of sine of 5 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

An algebraic number of degree 12 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

			0.087155...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for algebraic numbers, degree 12

Cf. A019810, A019813, A019895, A019898.

Join[{0},RealDigits[Sin[5 Degree],10,120][[1]]] (* Harvey P. Dale, Jun 06 2018 *)

sin(Pi/36) \\ Charles R Greathouse IV, Aug 27 2017

Equals A019813 * A019898 + A019810 * A019895. - R. J. Mathar, Jan 27 2021
Equals sin(Pi/36) = cos(17*Pi/36). 2*this^2-1 = -A019889. - R. J. Mathar, Aug 29 2025
One of the 12 real-valued roots of 4096*x^12 -12288*x^10 +13824*x^8 -7168*x^6 +1680*x^4 -144*x^2 +1 =0. - R. J. Mathar, Aug 29 2025

Zero added in front by R. J. Mathar, Feb 05 2009

A110937 Decimal expansion of cosecant of 1 degree.

Original entry on oeis.org

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

Offset: 2

Mohammad K. Azarian, Jan 21 2006

An algebraic integer of degree 48. - Charles R Greathouse IV, Aug 27 2017

			57.298688498550183476612683735173...

Mohammad K. Azarian, Forty-Five Nested Equilateral Triangles and cosecant of 1 degree, Problem 813, College Mathematics Journal, Vol. 36, No. 5, November 2005, p. 413-414. Solution published in Vol. 37 , No. 5, November 2006, pp. 394-395.

Index entries for algebraic numbers, degree 48

Cf. A019810.

RealDigits[Csc[1 Degree],10,120][[1]] (* Harvey P. Dale, Aug 17 2012 *)

1/sin(Pi/180) \\ Charles R Greathouse IV, Aug 27 2017

A111474 Decimal expansion of the cube root of sine of 1 degree.

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, Nov 15 2005

An algebraic number of degree 144. - Charles R Greathouse IV, Apr 14 2014

			0.2593891...

Index entries for algebraic numbers, degree 144

Cf. A019810, A111460.

evalf(root[3](sin(Pi/180))) ; # R. J. Mathar, Oct 03 2011

RealDigits[N[Sin[Pi/180]^(1/3),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 04 2012 *)

sin(Pi/180)^(1/3) \\ Charles R Greathouse IV, Apr 14 2014

Cube root of A019810.

Offset to 0 by Mohammad K. Azarian, Dec 11 2008

A019816 Decimal expansion of sine of 7 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

An algebraic number of degree 48 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for algebraic numbers, degree 48

RealDigits[Sin[7 Degree],10,120][[1]] (* Harvey P. Dale, Mar 25 2016 *)

sin(7*Pi/180) \\ Charles R Greathouse IV, Aug 27 2017

Also cosine of 83 degrees. - Charles R Greathouse IV, Aug 27 2017

Equals A019815 * A019898 + A019810 * A019893. - R. J. Mathar, Jan 27 2021

A019820 Decimal expansion of sine of 11 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

An algebraic number of degree 48 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for algebraic numbers, degree 48.

Cf. A019810, A019819, A019889, A019898.

RealDigits[Sin[11*Pi/180],10,99][[1]] (* Stefano Spezia, Feb 09 2025 *)

sin(11*Pi/180) \\ Charles R Greathouse IV, Aug 27 2017

Equals A019819 * A019898 + A019810 * A019889. - R. J. Mathar, Jan 27 2021

A019811 Decimal expansion of sine of 2 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

An algebraic number of degree 12 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

			0.034899...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for algebraic numbers, degree 12

sin(Pi/90) \\ Charles R Greathouse IV, Aug 27 2017

Equals 2*A019810*A019898. - R. J. Mathar, Jan 17 2021

Zero added in front by R. J. Mathar, Feb 05 2009

A019822 Decimal expansion of sine of 13 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

An algebraic number of degree 48 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for algebraic numbers, degree 48

RealDigits[Sin[13 Degree],10,120][[1]] (* Harvey P. Dale, Sep 29 2013 *)

sin(13*Pi/180) \\ Charles R Greathouse IV, Aug 27 2017

Equals A019821 * A019898 + A019810 * A019887. - R. J. Mathar, Jan 27 2021

A019826 Decimal expansion of sine of 17 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

An algebraic number of degree 48 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for algebraic numbers, degree 48

sin(17*Pi/180) \\ Charles R Greathouse IV, Aug 27 2017

Equals A019825 * A019898 + A019810 * A019883. - R. J. Mathar, Jan 27 2021

cp's OEIS Frontend

A019898 Decimal expansion of sine of 89 degrees.

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A019812 Decimal expansion of sine of 3 degrees.

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A019814 Decimal expansion of sine of 5 degrees.

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A110937 Decimal expansion of cosecant of 1 degree.

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A111474 Decimal expansion of the cube root of sine of 1 degree.

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A019816 Decimal expansion of sine of 7 degrees.

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A019820 Decimal expansion of sine of 11 degrees.

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