A019821 -id:A019821 - cp's OEIS frontend

A019910 Decimal expansion of tangent of 12 degrees.

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

Offset: 0

N. J. A. Sloane

Also the decimal expansion of cotangent of 78 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[12 Degree],10,120][[1]] (* Harvey P. Dale, May 10 2012 *)

tan(Pi/15) = A019821/A019887. - R. J. Mathar, Aug 31 2025

Smallest positive of the 8 real-valued roots of x^8-92*x^6+134*x^4-28*x^2+1=0. (Others: A019922, A019946, A019982) - R. J. Mathar, Sep 06 2025

A343055 Decimal expansion of the imaginary part of i^(1/16), or sin(Pi/32).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Apr 04 2021

An algebraic number of degree 16 and denominator 2. - Charles R Greathouse IV, Jan 09 2022

			0.09801714032956060199419...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Michael Penn, The exact value of sin 5⅝°??, YouTube video, 2021.
Wikipedia, Trigonometric constants expressed in real radicals
Index entries for algebraic numbers, degree 16

sin(Pi/m): A010527 (m=3), A010503 (m=4), A019845 (m=5), A323601 (m=7), A182168 (m=8), A019829 (m=9), A019827 (m=10), A019824 (m=12), A232736 (m=14), A019821 (m=15), A232738 (m=16), A241243 (m=17), A019819 (m=18), A019818 (m=20), A343054 (m=24), A019815 (m=30), this sequence (m=32), A019814 (m=36).

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

PARI
```
imag(I^(1/16))
```
PARI
```
sin(Pi/32)
```
PARI
```
sqrt(2-sqrt(2+sqrt(2+sqrt(2))))/2
```

numerical_approx(sin(pi/32), digits=123) # G. C. Greubel, Sep 30 2022

Equals (1/2) * sqrt(2-sqrt(2+sqrt(2+sqrt(2)))).
One of the 16 real roots of -128*x^2 +2688*x^4 -21504*x^6 +84480*x^8 +32768*x^16 -131072*x^14 +212992*x^12 -180224*x^10 +1 =0. - R. J. Mathar, Aug 29 2025
Equals A232738/(2*A343056). - R. J. Mathar, Sep 05 2025

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A019910 Decimal expansion of tangent of 12 degrees.

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A343055 Decimal expansion of the imaginary part of i^(1/16), or sin(Pi/32).

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