A019893 -id:A019893 - cp's OEIS frontend

A019896 Decimal expansion of sine of 87 degrees.

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

Offset: 0

N. J. A. Sloane

Equals sin(29*Pi/60). - Wesley Ivan Hurt, Sep 01 2014

An algebraic number of degree 16 and denominator 2. - Charles R Greathouse IV, Aug 27 2017

			0.998629534754573873784492058439436580590952290767785532441441...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Raimundas Vidunas, Expressions for values of the gamma function, math.CA/0403510
Wikipedia, Trigonometric constants expressed in real radicals
Index entries for algebraic numbers, degree 16

Digits:=100: evalf(sin(29*Pi/60)); # Wesley Ivan Hurt, Sep 01 2014

RealDigits[Sin[87Degree], 10, 100][[1]] (* Alonso del Arte, Aug 31 2014 *)

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

Equals cos(Pi/60) = [5-sqrt(5)]*[1+sqrt(3)]*[2-sqrt(3)+sqrt{5+2*sqrt(5)}]/[8*sqrt(10)] = sqrt[(1+A019893)/2]. - R. J. Mathar, Jun 18 2006

Equals A019867 * A019870 + A019838 * A019841 = A019893 * A019896 + A019812 * A019815. - R. J. Mathar, Jan 27 2021

A019818 Decimal expansion of sine of 9 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Also the imaginary part of i^(1/10). - Stanislav Sykora, Apr 25 2012

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

			sin(Pi/20) = 0.1564344650402308690101053194671668923138...

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

Cf. A019812, A019815, A019893, A019896.

RealDigits[Sin[9 Degree],10,120][[1]] (* Harvey P. Dale, Sep 15 2014 *)

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

sqrt(8-2*sqrt(10+2*sqrt(5)))/4 = sqrt((1/2)*(1 - sqrt((1/8)*(5 + sqrt(5))))). - Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 13 2006
Equals A019815*A019896 + A019812*A019893. - R. J. Mathar, Jan 27 2021
This^2 + A019890^2=1. - R. J. Mathar, Aug 31 2025
Smallest positive of the 8 real-valued roots of 256*x^8 -512*x^6 +304*x^4 -48*x^2+1=0. - 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

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

A343056 Decimal expansion of the real part of i^(1/16), or cos(Pi/32).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Apr 04 2021

			0.9951847266721968862448369...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Leon D. Fairbanks, Powers of Cosine and Sine, arXiv:2308.04437 [math.GM], 2023. See p. 3.
Wikipedia, Trigonometric constants expressed in real radicals.
Index entries for algebraic numbers, degree 16

cos(Pi/m): A010503 (m=4), A019863 (m=5), A010527 (m=6), A073052 (m=7), A144981 (m=8), A019879 (m=9), A019881 (m=10), A019884 (m=12), A232735 (m=14), A019887 (m=15), A232737 (m=16), A210649 (m=17), A019889 (m=18), A019890 (m=20), A144982 (m=24), A019893 (m=30). this sequence (m=32), A019894 (m=36).

R:= RealField(127); Cos(Pi(R)/32); // G. C. Greubel, Sep 30 2022

RealDigits[Cos[Pi/32], 10, 100][[1]] (* Amiram Eldar, Apr 27 2021 *)

PARI
```
real(I^(1/16))
```
PARI
```
cos(Pi/32)
```
PARI
```
sqrt(2+sqrt(2+sqrt(2+sqrt(2))))/2
```

numerical_approx(cos(pi/32), digits=122) # G. C. Greubel, Sep 30 2022

Equals (1/2) * sqrt(2+sqrt(2+sqrt(2+sqrt(2)))).
Satisfies 32768*x^16 -131072*x^14 +212992*x^12 -180224*x^10 +84480*x^8 -21504*x^6 +2688*x^4 -128*x^2 +1 = 0. - R. J. Mathar, Aug 29 2025
Equals 2F1(-1/16,1/16;1/2;1/2). - R. J. Mathar, Aug 31 2025

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A019896 Decimal expansion of sine of 87 degrees.

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A019818 Decimal expansion of sine of 9 degrees.

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A019821 Decimal expansion of sine of 12 degrees.

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A019816 Decimal expansion of sine of 7 degrees.

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A343056 Decimal expansion of the real part of i^(1/16), or cos(Pi/32).

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