A019887 -id:A019887 - cp's OEIS frontend

A019824 Decimal expansion of sine of 15 degrees.

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

Offset: 0

N. J. A. Sloane

Also the imaginary part of i^(1/6). - Stanislav Sykora, Apr 25 2012

			0.258819045102520762348898837624048328349068901319930513814003207315...

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Mark B. Villarino, Legendre's Singular Modulus, arXiv:2002.07250 [math.HO], 2020.
Wikipedia, Trigonometric constants expressed in real radicals
Index entries for algebraic numbers, degree 4

Cf. A002194, A020765, A101263.

RealDigits[ Sin[ Pi/12], 10, 111][[1]] (* Or *) RealDigits[(Sqrt[3] - 1)/(2 Sqrt[2]), 10, 111][[1]] (* Robert G. Wilson v *)
RealDigits[Sin[15 Degree],10,120][[1]] (* Harvey P. Dale, Jul 16 2016 *)

sin(Pi/12) \\ Charles R Greathouse IV, Apr 25 2012

Equals (sqrt(3)-1)/(2*sqrt(2)) = (A002194 -1) * A020765 = sin(Pi/12). - R. J. Mathar, Jun 18 2006
Equals 2F1(9/8,-1/8;1/2;3/4) / 2 = - 2F1(11/8,-3/8;1/2;3/4) / 2 = cos(5*Pi/12). - R. J. Mathar, Oct 27 2008
Equals sqrt(2 - sqrt(3))/2 = (1/2) * A101263. - Amiram Eldar, Aug 05 2020
Equals A019819 * A019894 + A019814 * A019889 = A019821 * A019896 + A019812 * A019887. - R. J. Mathar, Jan 27 2021
This^2 + A019884^2=1. - R. J. Mathar, Aug 31 2025
Smallest positive of the 4 real-valued roots of 16*x^4-16*x^2+1=0. - R. J. Mathar, Aug 31 2025
Equals 1/(4*A019884). - R. J. Mathar, Sep 05 2025

A019851 Decimal expansion of sine of 42 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

This sequence is also decimal expansion of cosine of 48 degrees. - Mohammad K. Azarian, Jun 29 2013

A quartic number with denominator 2. - Charles R Greathouse IV, Nov 05 2017

			0.6691306...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Wikipedia, Exact trigonometric constants
Index entries for algebraic numbers, degree 4

Cf. A019857, A019887, A019830, A019878.

sin(7/30*Pi) \\ Charles R Greathouse IV, Nov 05 2017

Equals cos(4*Pi/15) = (sqrt(5)-1)*(sqrt(3)*sqrt(5+2*sqrt(5))-1)/8 = 8*A019887^4 -8*A019887^2 + 1 = sqrt(1-A019857^2). - R. J. Mathar, Jun 18 2006
Equals 2*A019830*A019878. - R. J. Mathar, Jan 17 2021
A root of 16*x^4-8*x^3-16*x^2+8*x+1 =0. - R. J. Mathar, Aug 31 2025

A019875 Decimal expansion of sine of 66 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

A quartic number with denominator 2. - Charles R Greathouse IV, Aug 27 2017

			0.913545457...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Wikipedia, Exact trigonometric constants
Index entries for algebraic numbers, degree 4

Cf. A019821, A019842, A019866, A019887.

RealDigits[N[Cos[2*Pi/15], 110]][[1]] (* Wesley Ivan Hurt, Dec 27 2021 *)

cos(2*Pi/15) \\ Charles R Greathouse IV, Aug 27 2017

Equals cos(2*Pi/15) = 2*A019887^2 - 1 = 1 - 2*A019821^2. - R. J. Mathar, Jun 18 2006
Equals 2*A019842*A019866. - R. J. Mathar, Jan 17 2021
Largest of the 4 real-valued roots of 16*x^4-8*x^3-16*x^2+8*x+1=0. (Other A019851, -A019815, -A019887). - R. J. Mathar, Sep 04 2025

A019815 Decimal expansion of sine of 6 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Decimal expansion of 1/8 (-1 - sqrt(5) + sqrt(6*(5 - sqrt(5)))). - Artur Jasinski, Oct 28 2008

			sin(Pi/30) = 0.10452846...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Wikipedia, Exact trigonometric constants
Index entries for algebraic numbers, degree 4

First[RealDigits[1/8 (-1 - Sqrt[5] + Sqrt[6 (5 - Sqrt[5])]), 10, 100]] (* Artur Jasinski, Oct 28 2008 *)
RealDigits[Sin[6 Degree],10,120][[1]] (* Harvey P. Dale, Apr 27 2012 *)

sin(Pi/30) \\ Charles R Greathouse IV, Jan 30 2016

Equals cos(7*Pi/15) = -cos(8*Pi/15) = 2F1(6/5,-1/5;1/2;3/4) / 2 = -2F1(13/10,-3/10;1/2;3/4) / 2. - R. J. Mathar, Oct 27 2008
Equals 2*A019812*A019896. - R. J. Mathar, Jan 17 2021
Smallest positive of the 4 real-valued roots of 16*x^4+8*x^3-16*x^2-8*x+1=0. (Other A019887, -A019875, -A019851) - R. J. Mathar, Aug 31 2025
Equals A019821/(2*A019893). - R. J. Mathar, Sep 05 2025

A019890 Decimal expansion of sine of 81 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Also the real part of i^(1/10). - Stanislav Sykora, Apr 25 2012
Equals sin(9*Pi/20). - Wesley Ivan Hurt, Sep 01 2014
An algebraic number of degree 8 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

			0.98768834059513772619004024769343726075840686158988043492390480163...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Wikipedia, Trigonometric constants expressed in real radicals
Index entries for algebraic numbers, degree 8

Digits:=100: evalf(sin(9*Pi/20)); # Wesley Ivan Hurt, Sep 01 2014

RealDigits[Sin[81 Degree],10,120][[1]] (* Harvey P. Dale, Aug 11 2012 *)

sin(9*Pi/20) \\ Charles R Greathouse IV, Aug 27 2017

Equals cos(Pi/20) = sqrt((1+A019881)/2) = sqrt(1-A019818^2) = sqrt(5-sqrt(5))*(sqrt(5)+sqrt(5+2*sqrt(5)))/(4*sqrt(5)). - R. J. Mathar, Jun 18 2006
Equals A019863 * A019872 + A019836 * A019845 = A019887 * A019896 + A019812 * A019821. - R. J. Mathar, Jan 27 2021
Root of 256*x^8 -512*x^6 +304*x^4 -48*x^2+1=0. - R. J. Mathar, Aug 29 2025
Equals 2F1(-1/10,1/10;1/2;1/2). - R. J. Mathar, Aug 31 2025

A019821 Decimal expansion of sine of 12 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

An algebraic number of degree 8 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

			0.20791169...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Wikipedia, Exact trigonometric constants
Index entries for algebraic numbers, degree 8

Cf. A019815, A019887, A019893.

RealDigits[N[Sin[Pi/15], 110]][[1]] (* Wesley Ivan Hurt, Dec 27 2021 *)

sin(Pi/15) \\ Charles R Greathouse IV, Aug 27 2017

Equals sin(Pi/15) = sqrt(1-A019887^2) = (sqrt(5)-1)*(sqrt(5+2*sqrt(5)) - sqrt(3))/8. - R. J. Mathar, Jun 18 2006
Equals 2*A019815*A019893. - R. J. Mathar, Jan 17 2021
Smallest positive of the 8 real-valued roots of 256*x^8-448*x^6+224*x^4-32*x^2+1 =0. (Other A019893, A019833, A019857)- R. J. Mathar, Aug 31 2025

A019833 Decimal expansion of sine of 24 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

An algebraic number of degree 8 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Wikipedia, Exact trigonometric constants
Index entries for algebraic numbers, degree 8

sin(2*Pi/15) \\ Charles R Greathouse IV, Aug 27 2017

Equals sin(2*Pi/15) = sqrt(1-A019875^2) = 2*A019821*A019887. - R. J. Mathar, Jun 18 2006

One of the 8 real-valued roots of 256*x^8-448*x^6+224*x^4-32*x^2+1=0. - R. J. Mathar, Aug 31 2025

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

A019904 Decimal expansion of tangent of 6 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Also the decimal expansion of cotangent of 84 degrees. - Mohammad K. Azarian, Jun 30 2013
An algebraic integer of degree 8. - Charles R Greathouse IV, Nov 17 2017
Root of the polynomial 1-92*x^2+134*x^4-28*x^6+x^8=0. (Others: A019940, A019964, A019976). - R. J. Mathar, Sep 06 2025

			tan(Pi/30) = 0.105104235...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Wikipedia, Exact trigonometric constants
Index entries for algebraic numbers, degree 8

RealDigits[Tan[6 Degree],10,120][[1]] (* Harvey P. Dale, Jun 18 2024 *)

tan(Pi/30) \\ Charles R Greathouse IV, Nov 17 2017

Equals A019815 / A019839 = A019821/(1+A019887). - R. J. Mathar, Sep 06 2025

A019976 Decimal expansion of tangent of 78 degrees.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

Also the decimal expansion of cotangent of 12 degrees. - Ivan Panchenko, Sep 01 2014

An algebraic integer of degree 8. - Charles R Greathouse IV, Nov 05 2017

			tan(13*Pi/30) = 4.7046301...

Ivan Panchenko, Table of n, a(n) for n = 1..1000
Wikipedia, Exact trigonometric constants
Index entries for algebraic numbers, degree 8

1/tan(Pi/15) \\ Charles R Greathouse IV, Nov 05 2017

Equals A019887 / A019821 = A019833/(1-A019875) . - R. J. Mathar, Sep 06 2025

cp's OEIS Frontend

A019824 Decimal expansion of sine of 15 degrees.

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A019851 Decimal expansion of sine of 42 degrees.

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A019875 Decimal expansion of sine of 66 degrees.

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A019815 Decimal expansion of sine of 6 degrees.

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A019890 Decimal expansion of sine of 81 degrees.

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A019821 Decimal expansion of sine of 12 degrees.

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A019833 Decimal expansion of sine of 24 degrees.

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