OFFSET
0,1
COMMENTS
See the Mathematica program for a graph.
xo=0.36954256660758032082765604383693...
yo=0.40397275329951720931896174006631...
m=1.093169744985016922088153214160579...
|OP|=0.547499492185436214325204150357...
FORMULA
Equals d/2 = A003957/2, where d is the Dottie number. - Gleb Koloskov, Jun 16 2021
MAPLE
evalf(solve(cos(x)=x, x)/2, 140); # Alois P. Heinz, Feb 20 2024
MATHEMATICA
c = Pi/4;
xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
RealDigits[xo] (* A197002 *)
m = 1/Sin[xo + c]
RealDigits[m] (* A197003 *)
yo = m*xo
d = Sqrt[xo^2 + yo^2]
Show[Plot[{Cos[x + c], yo - (1/m) (x - xo)}, {x, -Pi/4, 1}], ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 1}], PlotRange -> All, AspectRatio -> Automatic, AxesOrigin -> Automatic]
PROG
(PARI) solve(x=0, 1, cos(x)-x)/2 \\ Gleb Koloskov, Jun 16 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 09 2011
STATUS
approved