sin(3°) (3 Mrd. Stellen; accurate to 3 billion digits)

  

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a) Calc sin(3°) with Sqrt[5]=√5 :


sin[3°] = (Sqrt[3] Sin[(11 Pi)/60]-Cos[(11 Pi)/60])/2 = (Sqrt[3]*(1/(2Sqrt[2/(4-Sqrt[7+Sqrt[5]-Sqrt[6(5+Sqrt[5])]])]))-Sqrt[2+Sqrt[7+Sqrt[5]-Sqrt[6(5+Sqrt[5])]]/2]/2)/2

cfg file for y-cruncher: sin(3°) - Lamprecht(2024i).cfg
Validation file: sin(3Deg) - 20241124-140507.txt

b) Calc sin(3°) with Sqrt[3]=√3 and Sqrt[5]=√5 :



My formula: sin[3°] = (1 - Sqrt[3]) (Sqrt[5 + Sqrt[5]]/8) + Sqrt[2] (Sqrt[5] - 1) (Sqrt[3] + 1)/16

cfg file for y-cruncher: sin(3°) - Lamprecht(2024).cfg
Validation file: sin(3Deg) - 20241124-135759.txt
y-cruncher Screenshot: a)                                                 b)










Gerd Lamprecht, Deutschland 24.11.2024





Date Announced Date Completed: Source: Who: Constant: Decimal Digits: Time: Computer:
Dec 03, 2024 Dec 03, 2024 Source Gerd Lamprecht sin(1°) 1,000,000,000 Compute:  85 s YMP
Verify: -		 Intel Core i9 7900X
32 GB
November 26, 2024 November 26, 2024 Source Gerd Lamprecht sin(10°) 1,000,000,000 Compute:  28.6 min
Verify: 1.2 min		 Intel Core i9 7900X
32 GB
November 24, 2024 November 24, 2024 Source Gerd Lamprecht sin(3°) 3,000,000,000 Compute:  37 s
Verify: 28 s		 Intel Core i9 7900X
32 GB
November 13, 2024 November 13, 2024 Source Gerd Lamprecht Gamma(1/10) 3,000,000,000 Compute:  46 minutes
Not Verified		 Intel Core i9 7900X
32 GB
November 10, 2024 November 10, 2024 Source Gerd Lamprecht Gamma(1/24) 3,000,000,000 Compute:  17 minutes
Not Verified		 Intel Core i9 7900X
32 GB
November 07, 2024 November 07, 2024 Source Gerd Lamprecht Gamma(1/8) 4,000,000,000 Compute:  28 minutes
Verify: 17 min		 Intel Core i9 7900X
32 GB
October 20, 2024 October 19, 2024 Source Gerd Lamprecht Gamma(1/5) 3,000,000,010 Compute:  48.5 minutes
Verified by Alexander Yee		 Intel Core i9 7900X
32 GB

Links:
03.11.2024: ExotischeGammawerte-Gamma1d5 (3 Mrd. Stellen {3 bio digits})
07.11.2024: New-formula-Gamma1d8 (4 Mrd. Stellen {4 bio digits})
10.11.2024: https: Liste-mathematische-Rekorde
10.11.2024: http: Liste-mathematische-Rekorde
10.11.2024: y-cruncher/records