A019946 Decimal expansion of tangent of 48 degrees.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• changed

Comments

Also the decimal expansion of cotangent of 42 degrees. - Ivan Panchenko, Sep 01 2014

Examples

			tan(4*Pi/15) = 1.11061251482919287014348196416513553257695951039085904818440222...
		

Links

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

Crossrefs

Cf. A019857 (sine of 48 degrees).

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); Tan(4*Pi(R)/15); // G. C. Greubel, Nov 24 2018

Mathematica

RealDigits[Tan[48 Degree],10,120][[1]] (* Harvey P. Dale, Nov 26 2011 *)
RealDigits[Tan[4*Pi/15], 10, 100][[1]] (* G. C. Greubel, Nov 24 2018 *)

PARI

default(realprecision, 100); tan(4*Pi/15) \\ G. C. Greubel, Nov 24 2018

Sage

numerical_approx(tan(4*pi/15), digits=100) # G. C. Greubel, Nov 24 2018

Formula

Equals cot(7*Pi/30) = sqrt(23 - 10*sqrt(5) + 2*sqrt(3*(85 -38*sqrt(5)))). - G. C. Greubel, Nov 24 2018

Let r(n) = (n - 1)/(n + 1) if n mod 4 = 1, (n + 1)/(n - 1) otherwise; then this constant equals with Product_{n>=0} r(30*n+15) = (8/7) * (22/23) * (38/37) * (52/53) ... - Dimitris Valianatos, Sep 14 2019

Equals A019857 / A019851. - R. J. Mathar, Sep 06 2025