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A195699
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Decimal expansion of arcsin(sqrt(1/8)) and of arccos(sqrt(7/8)).
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6
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3, 6, 1, 3, 6, 7, 1, 2, 3, 9, 0, 6, 7, 0, 7, 8, 0, 5, 5, 8, 9, 1, 8, 8, 6, 7, 6, 3, 2, 0, 6, 6, 6, 6, 8, 1, 0, 1, 2, 6, 0, 9, 2, 4, 3, 2, 1, 2, 2, 2, 0, 1, 3, 3, 8, 1, 3, 3, 7, 7, 0, 6, 6, 2, 9, 1, 8, 5, 3, 6, 9, 0, 9, 5, 7, 3, 1, 5, 1, 3, 2, 4, 8, 2, 4, 1, 3, 8, 0, 5, 4, 6, 9, 5, 5, 0, 6, 5, 1, 8
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals (1/2)*arccos(3/4) = arctan(sqrt(7)/7).
Equals sqrt(7)*Sum_{n >= 0} 1/((16*n + 8)*(2^n)*binomial(2*n,n)).
Equals sqrt(2)*Sum_{n >= 0} binomial(2*n,n)/((8*n + 4)*32^n). (End)
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EXAMPLE
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arcsin(sqrt(1/8)) = 0.3613671239067078055891886763206666...
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MATHEMATICA
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r = Sqrt[1/8];
N[ArcSin[r], 100]
N[ArcCos[r], 100]
N[ArcTan[r], 100]
N[ArcCos[-r], 100]
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PROG
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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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