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A197003
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Decimal expansion of the slope of the line y=mx which meets the curve y=cos(x+Pi/4) orthogonally over the interval [0, 2*Pi] (as in A197002).
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2
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1, 0, 9, 3, 1, 6, 9, 7, 4, 4, 9, 8, 5, 0, 1, 6, 9, 2, 2, 0, 8, 8, 1, 5, 3, 2, 1, 4, 1, 6, 0, 5, 7, 9, 7, 1, 4, 4, 0, 4, 8, 9, 0, 6, 5, 9, 2, 9, 4, 8, 9, 8, 8, 8, 3, 5, 6, 3, 5, 1, 7, 5, 1, 3, 3, 2, 4, 9, 6, 0, 5, 3, 7, 6, 7, 0, 9, 4, 4, 7, 3, 6, 8, 3, 7, 6, 7, 0, 6, 7, 9, 9, 3, 4, 8, 1, 7, 9, 3, 4, 2
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OFFSET
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1,3
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COMMENTS
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See the Mathematica program for a graph.
xo=0.3695425666075803208276560438369...
yo=0.4039727532995172093189617400663...
m=1.09316974498501692208815321416057...
|OP|=0.54749949218543621432520415035...
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LINKS
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FORMULA
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MATHEMATICA
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c = Pi/4;
xo = x /. FindRoot[x == Sin[x + c] Cos[x + c], {x, .8, 1.2}, WorkingPrecision -> 100]
m = 1/Sin[xo + c]
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]
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PROG
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(PARI) my(d=solve(x=0, 1, cos(x)-x)); sqrt(2-2*sqrt(1-d^2))/d \\ Gleb Koloskov, Jun 16 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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