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A197000 Decimal expansion of xo, where P=(xo,yo) is the point nearest O=(0,0) in which a line y=mx meets the curve y=1+cos(x) orthogonally. 15

%I

%S 1,2,4,8,8,0,1,4,3,6,7,2,1,5,5,0,8,5,6,0,4,7,5,1,2,5,0,2,0,1,2,8,3,8,

%T 1,5,3,5,5,8,7,6,1,4,3,0,3,6,0,8,2,1,6,3,4,1,4,6,0,2,5,0,2,0,4,4,2,0,

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

%N Decimal expansion of xo, where P=(xo,yo) is the point nearest O=(0,0) in which a line y=mx meets the curve y=1+cos(x) orthogonally.

%C See the Mathematica program for a graph.

%C xo=1.2488014367215508560475125020128381535587614...

%C yo=1.3164595537507515212878992732671186100622603...

%C m=1.05417844265684217515747734305673483746142104...

%C |OP|=1.81454423617045980814297669595599066552030...

%t c = 1;

%t xo = x /.

%t FindRoot[x == Sin[x] (c + Cos[x]), {x, 1, 1.3}, WorkingPrecision -> 100]

%t RealDigits[xo] (* A197000 *)

%t m = 1/Sin[xo]

%t RealDigits[m] (* A197001 *)

%t yo = m*xo

%t d = Sqrt[xo^2 + yo^2]

%t Show[Plot[{c + Cos[c*x], yo - (1/m) (x - xo)}, {x, 0, Pi}], ContourPlot[{y == m*x}, {x, 0, Pi}, {y, 0, 2}], PlotRange -> All, AspectRatio -> Automatic, AxesOrigin -> Automatic]

%Y Cf. A197001, A196996, A197002.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 09 2011

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Last modified February 25 10:21 EST 2020. Contains 332222 sequences. (Running on oeis4.)