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A019812
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Decimal expansion of sine of 3 degrees.
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19
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0, 5, 2, 3, 3, 5, 9, 5, 6, 2, 4, 2, 9, 4, 3, 8, 3, 2, 7, 2, 2, 1, 1, 8, 6, 2, 9, 6, 0, 9, 0, 7, 8, 4, 1, 8, 7, 3, 1, 0, 1, 8, 2, 5, 3, 9, 4, 0, 1, 6, 4, 9, 2, 0, 4, 8, 3, 5, 0, 9, 3, 8, 1, 5, 9, 9, 8, 5, 7, 1, 0, 4, 6, 4, 1, 7, 5, 4, 5, 4, 6, 8, 6, 4, 4, 6, 4, 5, 9, 8, 8, 1, 1, 8, 8, 6, 9, 3, 9, 8
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OFFSET
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0,2
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COMMENTS
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The minimal polynomial is p(x) = 65536*x^16 - 262144*x^14 + 430080*x^12 - 372736*x^10 + 182784*x^8 - 50176*x^6 + 7040*x^4 - 384*x^2 + 1 and p(x/2) = x^16 - 16*x^14 + 105*x^12 - 364*x^10 + 714*x^8 - 784*x^6 + 440*x^4 - 96*x^2 + 1. - Joerg Arndt, Apr 23 2024
The Fifteenth Century Persian mathematician Jamshid Al-Kashi was the first to calculate the value of sine of one degree correct to ten sexagesimal places (17 decimal digits) from sine of 3 degrees in his Risala al-Watar wa'l Jaib. - Mohammad K. Azarian,Jan 14 2017
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LINKS
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FORMULA
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Equals cos(87 degrees) = cos(29*Pi/60) = sin(Pi/60) = sqrt(8-sqrt(3)-sqrt(15)-sqrt(10-2*sqrt(5)))/4 (an intermediate calculation by Dr. Rob - see Math Forum link). - Rick L. Shepherd, Jul 03 2006
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EXAMPLE
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0.052335956242943832722118629609...
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MATHEMATICA
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Join[{0}, First[RealDigits[Sin[Pi/60], 10, 100]]] (* Paolo Xausa, Apr 23 2024 *)
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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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