The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A019810 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A019810

Decimal expansion of sine of 1 degree.
(history; published version)

#45 by Alois P. Heinz at Wed Jul 10 20:12:12 EDT 2024

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proposed

approved

#44 by Robert C. Lyons at Wed Jul 10 19:53:02 EDT 2024

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editing

proposed

#43 by Robert C. Lyons at Wed Jul 10 19:52:59 EDT 2024

PROG

(PARI) real((I^(89/90) - I^(91/90))/2) // \\ (imaginary part is not exactly zero only because of finite precision) Rick L. Shepherd, Apr 12 2017

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approved

editing

#42 by Charles R Greathouse IV at Mon Aug 14 10:21:39 EDT 2023

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editing

approved

#41 by Charles R Greathouse IV at Mon Aug 14 10:21:37 EDT 2023

LINKS

<a href="/index/Al#algebraic_48">Index entries for algebraic numbers, degree 48</a>

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approved

editing

#40 by Charles R Greathouse IV at Sun Dec 16 02:17:34 EST 2018

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editing

approved

#39 by Charles R Greathouse IV at Sun Dec 16 02:17:32 EST 2018

CROSSREFS

Cf. A110937, A280188.

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approved

editing

#38 by N. J. A. Sloane at Wed Apr 12 23:27:45 EDT 2017

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proposed

approved

#37 by Rick L. Shepherd at Wed Apr 12 15:00:28 EDT 2017

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editing

proposed

#36 by Rick L. Shepherd at Wed Apr 12 14:57:04 EDT 2017

COMMENTS

The minimal polynomial is 281474976710656 x^48 - 3377699720527872 x^46 + 18999560927969280 x^44 - 66568831992070144 x^42 + 162828875980603392 x^40 - 295364007592722432 x^38 + 411985976135516160 x^36 - 452180272956309504 x^34 + 396366279591591936 x^32 - 280058255978266624 x^30 + 160303703377575936 x^28 - 74448984852135936 x^26 + 28011510450094080 x^24 - 8500299631165440 x^22 + 2064791072931840 x^20 - 397107008634880 x^18 + 59570604933120 x^16 - 6832518856704 x^14 + 583456329728 x^12 - 35782471680 x^10 + 1497954816 x^8 - 39625728 x^6 + 579456 x^4 - 3456 x^2 + 1 (WolframAlpha). - Rick L. Shepherd, Apr 12 2017

FORMULA

Equals sin(Pi/180) = cos(89*Pi/180) = (i^(89/90) - i^(91/90))/2 (the last from WolframAlpha, rearranged). - Rick L. Shepherd, Apr 12 2017

PROG

(PARI) real((I^(89/90) - I^(91/90))/2) // (imaginary part is not exactly zero only because of finite precision) Rick L. Shepherd, Apr 12 2017

STATUS

approved

editing