login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A175288 Decimal expansion of the constant x satisfying (cos(x))^2 = sin(x). 5
6, 6, 6, 2, 3, 9, 4, 3, 2, 4, 9, 2, 5, 1, 5, 2, 5, 5, 1, 0, 4, 0, 0, 4, 8, 9, 5, 9, 7, 7, 7, 9, 2, 7, 2, 0, 6, 6, 7, 4, 9, 0, 1, 3, 8, 7, 2, 5, 9, 4, 7, 8, 4, 2, 8, 3, 1, 4, 7, 3, 8, 4, 2, 8, 0, 3, 9, 7, 8, 9, 8, 9, 3, 7, 9, 0, 5, 9, 2, 8, 1, 7, 0, 7, 9, 0, 6, 8, 3, 1, 1, 6, 9, 5, 8, 1, 1, 3, 5, 2, 5, 9, 7, 7, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This is the angle (in radians) at which the modified loop curve x^4=x^2*y-y^2 returns to the origin. Writing the curve in (r,phi) circular coordinates, r = sin(phi) * (cos^2(phi)-sin(phi)) /cos^4(phi), the two values of r=0 are phi=0 and the value of phi defined here. The equivalent angle of the Bow curve is Pi/4.

Also the minimum positive solution to tan(x) = cos(x). - Franklin T. Adams-Watters, Jun 17 2014

LINKS

Table of n, a(n) for n=0..104.

Eric Weisstein's World of Mathematics, Bow.

FORMULA

x = arcsin(A094214). cos(x)^2 = sin(x) = 0.618033988... = A094214.

From Amiram Eldar, Feb 07 2022: (Start)

Equals Pi/2 - A195692.

Equals arccos(1/sqrt(phi)).

Equals arctan(1/sqrt(phi)) = arccot(sqrt(phi)). (End)

Root of the equation cos(x) = tan(x). - Vaclav Kotesovec, Mar 06 2022

EXAMPLE

x = 0.66623943.. = 38.1727076... degrees.

MATHEMATICA

r = 1/GoldenRatio;

N[ArcSin[r], 100]

RealDigits[%] (* A175288 *)

RealDigits[x/.FindRoot[Cos[x]^2==Sin[x], {x, .6}, WorkingPrecision->120]] [[1]] (* Harvey P. Dale, Nov 08 2011 *)

RealDigits[ ArcCos[ Sqrt[ (Sqrt[5] - 1)/2]], 10, 105] // First (* Jean-François Alcover, Feb 19 2013 *)

CROSSREFS

Cf. A019669, A094214, A001622, A195692, A352151.

Sequence in context: A019103 A272619 A172360 * A349187 A153509 A248093

Adjacent sequences: A175285 A175286 A175287 * A175289 A175290 A175291

KEYWORD

cons,easy,nonn

AUTHOR

R. J. Mathar, Mar 23 2010, Mar 29 2010

EXTENSIONS

Disambiguated the curve here from the Mathworld bow curve - R. J. Mathar, Mar 29 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 15:38 EST 2022. Contains 358644 sequences. (Running on oeis4.)