A019881 -id:A019881 - cp's OEIS frontend

A019893 Decimal expansion of sine of 84 degrees.

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

Offset: 0

N. J. A. Sloane

Equals sin(7*Pi/15). - Wesley Ivan Hurt, Sep 01 2014

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

			0.9945218953682733369226919449805703815207920887093194273665588...

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

Digits:=100: evalf(sin(7*Pi/15)); # Wesley Ivan Hurt, Sep 01 2014

RealDigits[ Cos[Pi/30], 10, 111] (* Robert G. Wilson v *)
RealDigits[Sin[84 Degree],10,120][[1]] (* Harvey P. Dale, May 14 2022 *)

cos(Pi/30) \\ Charles R Greathouse IV, Aug 27 2017

Equals cos(Pi/30) = 2F1(11/20,9/20;1/2;3/4) / 2. - R. J. Mathar, Oct 27 2008
Equals 2*A019851*A019857. - R. J. Mathar, Jan 17 2021
Root of 256*x^8 -448*x^6 +224*x^4 -32*x^2 +1 = 0. - R. J. Mathar, Aug 29 2025
4*this^3 -3*this = A019881. - R. J. Mathar, Aug 29 2025
Equals 2F1(-1/20,1/20;1/2;3/4). - R. J. Mathar, Aug 31 2025

A179593 Decimal expansion of the volume of pentagonal rotunda with edge length 1.

Original entry on oeis.org

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 19 2010

Pentagonal rotunda: 20 vertices, 35 edges, and 17 faces.

			6.91776296812470206991299603070264133354087600944966144271710443099823...

Wolfram Alpha, Johnson solid 6
Index entries for algebraic numbers, degree 2.

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A019881, A179587, A179588, A179589, A179590, A179591, A179592.

Mathematica
```
RealDigits[N[(45+17*Sqrt[5])/12,200]]
```

Digits of (45+17*sqrt(5))/12.

A232737 Decimal expansion of the real part of I^(1/8), or cos(Pi/16).

Original entry on oeis.org

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

Offset: 0

Stanislav Sykora, Nov 29 2013

The corresponding imaginary part is in A232738.

			0.9807852804032304491261822361342390369739337308933360950029160885453...

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

Cf. A232738 (imaginary part), A010503 (real(I^(1/2))), A010527 (real(I^(1/3))), A144981 (real(I^(1/4))), A019881 (real(I^(1/5))), A019884 (real(I^(1/6))), A232735 (real(I^(1/7))), A019889 (real(I^(1/9))), A019890 (real(I^(1/10))).

RealDigits[Cos[Pi/16], 10, 120][[1]] (* Amiram Eldar, Jun 29 2023 *)

real(I^(1/8)) \\ Seiichi Manyama, Apr 04 2021

cos(Pi/16) \\ Seiichi Manyama, Apr 04 2021

sqrt(2+sqrt(2+sqrt(2)))/2 \\ Seiichi Manyama, Apr 04 2021

Equals (1/2) * sqrt(2+sqrt(2+sqrt(2))). - Seiichi Manyama, Apr 04 2021
Root of 128*x^8 -256*x^6 +160*x^4 -32*x^2 +1 = 0. - R. J. Mathar, Aug 29 2025
2*this^2 -1 = A144981. - R. J. Mathar, Aug 29 2025
Equals 2F1(-1/8,1/8;1/2;1/2). - R. J. Mathar, Aug 31 2025

A019836 Decimal expansion of sine of 27 degrees.

Original entry on oeis.org

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

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, Trigonometric constants expressed in real radicals
Index entries for algebraic numbers, degree 8

RealDigits[Sin[27 Degree],10,120][[1]] (* Harvey P. Dale, Nov 09 2014 *)

cos(7*Pi/20) \\ Charles R Greathouse IV, Aug 27 2017

Equals A019827 * A019890 + A019818 * A019881 = A019833 * A019896 + A019812 * A019875. - R. J. Mathar, Jan 27 2021

Equals cos(7*Pi/20). 2*this^2-1 = -A019845. - R. J. Mathar, Aug 29 2025

A138370 Count of post-period decimal digits up to which the rounded n-th convergent to 4sin(2Pi/5) agrees with the exact value.

Original entry on oeis.org

2, 3, 4, 5, 5, 6, 6, 8, 9, 10, 11, 12, 12, 13, 14, 15, 15, 17, 18, 17, 19, 21, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 33, 34, 35, 36, 37, 38, 38, 40, 41, 42, 41, 42, 43, 45, 44, 46, 44, 47, 49, 49, 50, 52, 53, 54, 55, 57, 59, 60, 61, 63, 62, 65, 67, 67, 68, 70, 69, 70, 70, 71

Offset: 2

Artur Jasinski, Mar 17 2008

The computation of A138369 is repeated for 4*sin(2*Pi/5) = sqrt(2)*sqrt(5+sqrt(5))
= 3.80422606518061.. = 4*A019881.
The convergents are 19/5 (n=2), 175/46 (n=3), 544/143 (n=4), 719/189 (n=5), 2701/710 (n=6) etc.

			a(6)=5 because 2701/710 = 3.80422535... agrees with 3.8042260651.. if both are rounded up to 5 decimal digits (3.80423 = 3.80423), but disagrees at the level of rounding to 6 decimal digits (3.804226 <> 3.804225) or more.

Cf. A138335, A138336, A138337, A138339, A138343, A138366, A138367, A138369.

Definition and values replaced as defined via continued fractions - R. J. Mathar, Oct 01 2009

A179592 Decimal expansion of the circumradius of pentagonal cupola with edge length 1.

Original entry on oeis.org

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 19 2010

Pentagonal cupola: 15 vertices, 25 edges, and 12 faces.

			2.232950509415690049500415383249682772934080730579181647457441260...

Wolfram Alpha, Johnson solid 5
Index entries for algebraic numbers, degree 4.

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A019881, A179587, A179588, A179589, A179590, A179591.

Mathematica
```
RealDigits[N[Sqrt[11+4*Sqrt[5]]/2,200]]
```

Digits of sqrt(11+4*sqrt(5))/2.

A165954 Decimal expansion of sqrt(10 + 2sqrt(5))/(2Pi).

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Oct 04 2009

The ratio of the volume of a regular icosahedron to the volume of the circumscribed sphere (with circumradius a*sqrt(10 + 2*sqrt(5))/4 = a*A019881, where a is the icosahedron's edge length; see MathWorld link). For similar ratios for other Platonic solids, see A165922, A049541, A165952, and A165953. A063723 shows the order of these by size.

			0.6054613829125255833862652051280444903008454088014288933200935000838295683...

Eric Weisstein's World of Mathematics, Icosahedron.
Index entries for transcendental numbers.

Cf. A000796, A002163, A165922, A049541, A165952, A165953, A063723, A019881, A019694, A060294.

RealDigits[Sqrt[10+2Sqrt[5]]/(2Pi),10,120][[1]] (* Harvey P. Dale, Aug 27 2013 *)

PARI
```
sqrt(10+2*sqrt(5))/(2*Pi)
```

sqrt(10 + 2*sqrt(5))/(2*Pi) = sqrt(10 + 2*A002163)/(2*A000796) = 2*sin(2*Pi/5)/Pi = 2*sin(A019694)/A000796 = 2*sin(72 deg)/Pi = 2*A019881/A000796 = 2*A019881*A049541 = (2/Pi)*sin(72 deg) = A060294*A019881.

A340721 Decimal expansion of Gamma(3/5).

Original entry on oeis.org

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

Offset: 1

R. J. Mathar, Jan 17 2021

			1.489192248812817102..

DLMF, Gamma function properties, DLMF section 5.5.
Eric Weisstein's World of Mathematics, Gamma Function.
Wikipedia, Particular values of the Gamma function.
Index to sequences related to gamma function.

Cf. A019881, A175380, A246745, A256191.

Maple
```
evalf(GAMMA(3/5),120) ;
```

RealDigits[Gamma[3/5], 10, 120][[1]] (* Amiram Eldar, May 29 2023 *)

this * A246745 = Pi/A019881. [DLMF (5.5.3)]

this * A256191 *2^(7/10)/sqrt(2*Pi) = 2*A175380 [DLMF (5.5.5)]

A019830 Decimal expansion of sine of 21 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Wikipedia, Trigonometric constants expressed in real radicals

Cf. A019812, A019816, A019823, A019827, A019881, A019892, A019885, A019896.

RealDigits[Sin[21 Degree],10,120][[1]] (* Harvey P. Dale, Apr 06 2016 *)

sin(7*Pi/60) \\ Charles R Greathouse IV, Jan 30 2016

Equals A019823*A019892 + A019816*A019885 = A019827*A019896 + A019812*A019881. - R. J. Mathar, Jan 27 2021

A019907 Decimal expansion of tangent of 9 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Also the decimal expansion of cotangent of 81 degrees. - Mohammad K. Azarian, Jun 30 2013

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

RealDigits[Tan[9 Degree],10,120][[1]] (* Harvey P. Dale, Aug 23 2020 *)

Equals tan(Pi/20) = A019818/A019890. - R. J. Mathar, Aug 29 2025
Smallest positive of the 8 real-valued roots of x^8-44*x^6+166*x^4-44*x^2+1=0. (Others A019925, A019961, A019979). - R. J. Mathar, Aug 31 2025
Equals A019827/(1+A019881). - R. J. Mathar, Sep 06 2025

cp's OEIS Frontend

A019893 Decimal expansion of sine of 84 degrees.

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A179593 Decimal expansion of the volume of pentagonal rotunda with edge length 1.

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A232737 Decimal expansion of the real part of I^(1/8), or cos(Pi/16).

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A019836 Decimal expansion of sine of 27 degrees.

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A138370 Count of post-period decimal digits up to which the rounded n-th convergent to 4*sin(2*Pi/5) agrees with the exact value.

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A179592 Decimal expansion of the circumradius of pentagonal cupola with edge length 1.

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Mathematica

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A165954 Decimal expansion of sqrt(10 + 2*sqrt(5))/(2*Pi).

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Mathematica

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A340721 Decimal expansion of Gamma(3/5).

A138370 Count of post-period decimal digits up to which the rounded n-th convergent to 4sin(2Pi/5) agrees with the exact value.

A165954 Decimal expansion of sqrt(10 + 2sqrt(5))/(2Pi).