sin(x) in Wurzelschreibweise (Wertetabelle; >200 Exact Trigonometric values/constants)

   

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Exakte Sinuswerte
Winkel x sin(x) in Wurzelschreibweise (Exact trigonometric constants)
[°] [rad]  i = 0+1i = sqrt(-1) = (-1)^(1/2) = Wurzel(-1) =√(-1) = pow(-1,0.5)
0 0 0
45/1024=0.0439… Pi/4096 sqrt(2-sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2)))))))))))/2=0.0007669903187427045269385683579485…
45/512=0.087890625 Pi/2048 sqrt(2-sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2))))))))))/2=0.0015339801862847656123036971502640790799…
45/256=0.17578125 Pi/1024 sqrt(2-sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2)))))))))/2=0.0030679567629659762701453654909198425189446102134…
3/16=0.1875 Pi/960 sqrt(½-½sqrt(½+½sqrt(1-(sqrt(2+sqrt(2+sqrt(2)))(sqrt(½(5+sqrt(5)))/8-sqrt(3)(sqrt(5)-1)/16)-sqrt(2-sqrt(2+sqrt(2)))((sqrt(5)-1)/16+
sqrt(3/2(5+sqrt(5)))/8))²)))=0.003272486506526625459989844900576000217792029325656378279…
9/32=0.28125 Pi/640 sqrt(½-½sqrt(½+½sqrt(½+½sqrt(½+½sqrt(1+(sqrt(2(4+sqrt(2(5+sqrt(5)))))-4)/8)))))=0.0049087188079979905828775693506346970391518728…
45/128=0.3515625 Pi/512 sqrt(2-sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2))))))))/2=0.006135884649154475359640234590372580917057886317391329356…
3/8=0.375 Pi/480 sqrt(½-sqrt(1-(sqrt(2+sqrt(2+sqrt(2)))*(sqrt((5+sqrt(5))/2)/8-sqrt(3)/16(sqrt(5)-1))-sqrt(2-sqrt(2+sqrt(2)))((sqrt(5)-1)/16+sqrt(3/2(5+sqrt(5)))/8))²)/2)
=0.00654493796735185837307206889248063420567905677994080…
9/19=0.473684210.. Pi/380 ((-1)^(189/380)-(-1)^(191/380))/2=0.008267254911124917639466369170067325158275245910124001765…
1/2=0.5 Pi/360 ((-1)^(179/360)-(-1)^(181/360))/2=0.008726535498373934964888213973584423034027667688047014652…
9/16=0.5625 Pi/320 sqrt(½-½sqrt(½+½sqrt(½+½sqrt(1+(sqrt(2(4+sqrt(2(5+sqrt(5)))))-4)/8))))=0.009817319337149617498786319201510395858624983585722…
45/64=0.703125 Pi/256 sqrt(2-sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2)))))))/2=0.012271538285719926079408261951003212140372319591769250…
3/4 Pi/240 sqrt(2+sqrt(2+sqrt(2)))(sqrt((5+sqrt(5))/128)-sqrt(3)(sqrt(5)-1)/16)-sqrt(2-sqrt(2+sqrt(2)))((sqrt(5)-1)/16+sqrt(3/128(5+sqrt(5))))
1 Pi/180 (-1)^(89/180)*(1-(-1)^(1/90))/2=tan(1°)/sqrt(tan(1°)²+1)=0.017452406437283512819418978516316192472252720307139642683…
tan(1°)=(i*(sqrt(3)+i)*(x²+1)-(1+i*sqrt(3))*((x-i)*(x+i)²)^(2/3))/(2*((x-i)*(x+i)²)^(1/3))+x; x=tan(3°)=((2-sqrt(3))*(3+sqrt(5))-2)*(2-sqrt(2*(5-sqrt(5))))/4
9/8=1.125 Pi/160 sqrt(½-½ sqrt(½+½ sqrt(1+(sqrt(2 (4+sqrt(2 (5+sqrt(5)))))-4)/8)))=0.019633692460628302085477279238145208941416745894…
81/64=1.265625 Pi*9/1280 sqrt(½-½sqrt(½+½sqrt(½+½sqrt(½+½sqrt(½+¼sqrt(½(4+sqrt(2(4-sqrt(2(5+sqrt(5))))))))))))=0.02208752701857829050984635209793417499419…
21/16=1.3125 Pi*7/960 sqrt(½-½sqrt(½+½sqrt(1+(sqrt(2(4+sqrt(2(4+sqrt(7-sqrt(5)+sqrt(30-6sqrt(5)))))))-4)/8)))=0.022905443033697137893916949283617503205735804…
45/34=1.32352… Pi/136 sqrt(½-½sqrt(1+1/16(sqrt(2(17-sqrt(17)+sqrt(34-2sqrt(17))+sqrt(2(34+6 sqrt(17)-sqrt(578-34 sqrt(17))+sqrt(34-2sqrt(17))+8sqrt(2(17+sqrt(17)))))))-8)))
=1/(2sqrt(-2/(sqrt(8+sqrt(2(17-sqrt(17)+sqrt(34-2sqrt(17))+sqrt(2(34+6sqrt(17)-sqrt(578-34sqrt(17))+sqrt(34-2sqrt(17))+8sqrt(2(17+sqrt(17))))))))-4)))
45/32=1.40625 Pi/128 sqrt(2-sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2))))))/2=0.02454122852291228803173452945928292506546611923945147757…
1.5 Pi/120 sqrt(2+sqrt(2)) (sqrt(3) (1+sqrt(5))/16-sqrt((5-sqrt(5))/128))-sqrt(2-sqrt(2)) (sqrt(3/128 (5-sqrt(5)))+(1+sqrt(5))/16)
105/64=1.640625 Pi*7/768 sqrt(2-sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2-sqrt(2-sqrt(3))))))))/2=0.028630395210139003583763793993742419627031409589703…
9/5=1.8 Pi/100 ((-1)^(49/100)-(-1)^(51/100))/2=0.031410759078128293839183673817829389757925705851337927822…
2 Pi/90 ((-1)^(22/45)-(-1)^(23/45))/2=0.03489949670250097164599518162533293735482457604329687142…
9/4=2.25 Pi/80 sqrt(½-½sqrt(1+(sqrt(2(4+sqrt(2(5+sqrt(5)))))-4)/8))=0.0392598157590686090208033637983335896801820…
81/32=2.53125 Pi*9/640 sqrt(½-½sqrt(½+½sqrt(½+½sqrt(½+¼sqrt(½(4+sqrt(2(4-sqrt(2(5+sqrt(5)))))))))))=0.04416427712706735994236374124388319861571…
18/7=2.5714285… Pi/70 ((-1)^(17/35)-(-1)^(18/35))/2 = 0.0448648303505149254580903368019609171338572943490410…
21/8=2.625 Pi*7/480 sqrt(½-½sqrt(1+(sqrt(2(4+sqrt(2(4+sqrt(7-sqrt(5)+sqrt(30-6sqrt(5)))))))-4)/8))=0.04579886693652076924387335224512474492…
45/17=2.647058823… Pi/68 sqrt(8-sqrt(2(17-sqrt(17)+sqrt(34-2sqrt(17))+sqrt(2(34+6sqrt(17)-sqrt(578-34sqrt(17))+sqrt(34-2sqrt(17))+8sqrt(2(17+sqrt(17))))))))/4=0.0461834…
45/16=2.8125 Pi/64 sqrt(2-sqrt(2+sqrt(2+sqrt(2+sqrt(2)))))/2=0.049067674327418014254954976942682658314745363…
3 Pi/60 (1-sqrt(3))*sqrt(5+sqrt(5))/8+sqrt(2)*(sqrt(5)-1)*(sqrt(3)+1)/16=0.052335956242943832722118629609…
105/32=3.28125 Pi*7/384 sqrt(2-sqrt(2+sqrt(2+sqrt(2+sqrt(2-sqrt(2-sqrt(3)))))))/2=0.0572373172875686255557583026508785741584635963586063…
10/3=3.33.. Pi/54 =((-1)^(13/27)-(-1)^(14/27))/2=0.058144828910475828538748016847071523634111413108164759…
3.515625 Pi*5/256 sqrt(2-sqrt(2+sqrt(2+sqrt(2+sqrt(2-sqrt(2-sqrt(2)))))))/2=0.0613207363022085777826145929172350071939802796769731…
18/5=3.6 Pi/50 ((-1)^(12/25)-(-1)^(13/25))/2=0.0627905195293133760761782245656311331224848319…
15/4=3.75 Pi/48 ((-1)^(23/48) - (-1)^(25/48))/2=sqrt(2-sqrt(2+sqrt(2+sqrt(3))))/2=0.06540312923014306681531555877517544144…
4 Pi/45 ((-1)^(43/90) - (-1)^(47/90))/2 =0.069756473744125300775958835194143328600903201652796…
45/11=4.0909… Pi/44 ((-1)^(21/44)-(-1)^(23/44))/2=0.071339183199232340327337752657837932765965152271970595548…
180/43=4.18604… Pi/43 ((-1)^(41/86)-(-1)^(45/86))/2=0.072995314660907525290078630655500235753400780773865381815…
30/7=4.28571… Pi/42 ((-1)^(10/21)-(-1)^(11/21))/2=0.074730093586424254290939745734766653373548755…
9/2=4.5 Pi/40 sqrt((4-sqrt(2*(4+sqrt(2*(5+sqrt(5))))))/2)/2=0.0784590957278449450329602459934596986819558771…
60/13=4.6153846… Pi/39 ((-1)^(37/78)-(-1)^(41/78))/2=0.080466568716725880436232835236050588144454832953483…
90/19=4.7368421… Pi/38 ((-1)^(9/19)-(-1)^(10/19))/2=0.0825793454723323246003439342374402276985836343395…
180/37=4.864864… Pi/37 ((-1)^(35/74)-(-1)^(39/74))/2=0.084805924475509191088501448331898288795307…
5 Pi/36 ((-1)^(17/36) - (-1)^(19/36))/2=0.0871557427476581735580642708374735513777011561497…
81/16=5.0625 Pi*9/320 sqrt(½-½sqrt(½+½sqrt(½+¼sqrt(½(4+sqrt(2(4-sqrt(2(5+sqrt(5))))))))))=0.08824237052036951313688274509922558441693358535834760299990…
36/7=5.1428571… Pi/35 ((-1)^(33/70)-(-1)^(37/70))/2=0.089639308903433499765470436845233008011125767525214568565…
5.25 Pi*7/240 1/(2sqrt(2/(4-sqrt(2(4+sqrt(2(4+sqrt(7-sqrt(5)+sqrt(30-6sqrt(5))))))))))=0.091501618663402385314002026414647086773215023…
90/17=5.294117… Pi/34 1/(4 sqrt(2/(15+sqrt(17)-sqrt(2(17-sqrt(17)))-sqrt(2(34+6sqrt(17)+sqrt(2(17-sqrt(17)))-sqrt(34(17-sqrt(17)))+8sqrt(2(17+sqrt(17))))))))
=0.092268359463301995239651107154506480363017283755823…
60/11=5.4545… Pi/33 ((-1)^(31/66)-(-1)^(35/66))/2=0.09505604330418266363210430415931109734405593750457…
45/8=5.625… Pi/32 sqrt(2-sqrt(2+sqrt(2+sqrt(2))))/2=0.0980171403295606019941955638886418458611366731675…
180/31=5.80645161… Pi/31 ((-1)^(29/62)-(-1)^(33/62))/2=0.1011683219874321777860407155854228233862112145…
6 Pi/30 (sqrt((5-sqrt(5))*6)-sqrt(5)-1)/8=0.104528463267653471399834154802498119080655869474593…
180/29=6.206896… Pi/29 ((-1)^(27/58)-(-1)^(31/58))/2=0.1081190184239417630308083269836870058626991245697…
45/7=6.42857… Pi/28 ((-1)^(13/28) - (-1)^(15/28))/2=0.11196447610330785846870593527202420325819642296748…
105/16=6.5625 Pi*7/192 sqrt(2-sqrt(2+sqrt(2+sqrt(2-sqrt(2-sqrt(3))))))/2=0.114286964966846398117474961450939905318013970615076534…
20/3=6.666… Pi/27 ((-1)^(25/54)-(-1)^(29/54))/2=0.1160929141252302296756665233807114688534759…
6.75 Pi*3/80 sqrt(½-¼sqrt(½(4+sqrt(2(4+sqrt(2(5-sqrt(5))))))))=0.117537397457837644105568266840485623672373112095997672…
90/13=6.9230… Pi/26 ((-1)^(6/13)-(-1)^(7/13))/2 auch {0=64x6+32x5-80x4-32x³+24x²+6x-1; x=0.1205366802553230533490676874525435822736811592…}
7 Pi*7/180 sqrt(½-(x)^(1/3)/(8*2^(2/3))+(i sqrt(3)(x)^(1/3))/(8*2^(2/3))-1/(4(2(x))^(1/3))-(i sqrt(3))/(4(2(x))^(1/3)))=0.1218693434051474811128939192315251760…
; x=-sqrt(7-sqrt(5)+sqrt(6(5-sqrt(5))))+i sqrt(9+sqrt(5)-sqrt(6(5-sqrt(5))))
225/32=7.03125 Pi*5/128 sqrt(2-sqrt(2+sqrt(2+sqrt(2-sqrt(2-sqrt(2))))))/2=0.1224106751992161984987044741509457875752236090851…
36/5=7.2 Pi/25 ((-1)^(23/50)-(-1)^(27/50))/2
7.5 Pi/24 ((-1)^(11/24) - (-1)^(13/24))/2=sqrt(2-sqrt(2+sqrt(3)))/2
180/23=7.8260… Pi/23 ((-1)^(21/46)-(-1)^(25/46))/2
63/8=7.875 Pi*7/160 sqrt(½-½ sqrt(½+½ sqrt(1+(sqrt(8-2 sqrt(10-2 sqrt(5)))-4)/8)))=0.1370123416819680379002734968590146410977935668827552409…
8 Pi*2/45 sqrt(½-48/(½((x)+sqrt(((x))^2-y)))^(1/3)-1/768(½((x)+sqrt(((x))^2-y)))^(1/3)); x=1769472-1769472*sqrt(5)+1769472 sqrt(6(5+sqrt(5))); y=200385994162176; oder sqrt(½-48/(192*(-1)^(4/45))-1/768 (192*(-1)^(4/45)))=sqrt[2-(-1)^(4/45)+(-1)^(41/45)]/2
90/11=8.1818… Pi/22 ((-1)^(5/11)-(-1)^(6/11))/2 oder {0=32x^5-16x^4-32x³+12x²+6x-1; x=0.1423148382732851404437926686163696687910…}
60/7=8.5714285… Pi/21 ((-1)^(19/42)-(-1)^(23/42))/2
9 Pi/20 (sqrt(2)*(sqrt(5)+1)-2*sqrt(5-sqrt(5)))/8
180/19=9.47368421… Pi/19 ((-1)^(17/38)-(-1)^(21/38))/2=0.164594590280733894143652059087938419512172483359654123…
10 Pi/18 ((-1)^(4/9) - (-1)^(5/9))/2=cos(80°)=(((-i*sqrt(3)-1)/2)^(2/3)+((i*sqrt(3)-1)/2)^(2/3))/2 oder 0=8x³-6x+1; x=hyg2F1(7/6,-1/6;1/2;3/4)/2=Im(i^(1/9))
=AppellF1(7/6,1/1000,-503/3000,1/2,3/4,3/4)/2=0.173648177666930348851716626769314796000375677184069387236…
10.125 Pi*9/160 sqrt(½-½sqrt(½+¼sqrt(½(4+sqrt(2(4-sqrt(2(5+sqrt(5)))))))))=0.17579627993435450616338640896138801291928078113214638753…
10.5 Pi*7/120 sqrt(½-1/(4sqrt(2/(4+sqrt(7-sqrt(5)+sqrt(6(5-sqrt(5))))))))=0.18223552549214745660257337143740988295611962462751374…
180/17=10.588… Pi/17 sqrt(2)/8*sqrt(17-sqrt(17)-sqrt(2)*(sqrt(34+6*sqrt(17)+sqrt(2)*(sqrt(17)-1)*sqrt(17-sqrt(17))-8*sqrt(2)*sqrt(17+sqrt(17)))+sqrt(17-sqrt(17))))
45/4=11.25 Pi/16 ((-1)^(7/16)-(-1)^(9/16))/2=sqrt(2-sqrt(2+sqrt(2)))/2
12 Pi/15 (sqrt((5+sqrt(5))*2)-sqrt(3)*(sqrt(5)-1))/8=sin(1/3*atan(sqrt(5-2sqrt(5))))=sqrt(7-sqrt(5)-sqrt(6(5-sqrt(5))))/4=0.207911690817759337101742284405125…
90/7=12.8571… Pi/14 ((-1)^(3/7) - (-1)^(4/7))/2=0.222520933956314404288902564496794759466355568764544955311…
105/8=13.125 Pi*7/96 sqrt(2-sqrt(2+sqrt(2-sqrt(2-sqrt(3)))))/2=0.22707626303437320758569669257708808661570144348631699132…
27/2=13.5 Pi*3/40 sqrt(2-sqrt(2+sqrt((5-sqrt(5))/2)))/2=0.233445363855905411767744430202870848785741903887519600…
180/13=13.846… Pi/13 ((-1)^(11/26)*(1-(-1)^(1/13))*(1+(-1)^(1/13)))/2=((-1)^(11/26)-(-1)^(15/26))/2=0.239315…;sqrt{0=4096x^6-13312x^5+16640x^4-9984x³+2912x²-364x+13}
14 Pi*7/90 sqrt(2-sqrt(2+(-1)^(14/45)-(-1)^(31/45)))/2=0.2419218955996677225604423741003529652950079303987…
225/16=14.0625 Pi*5/64 sqrt(2-sqrt(2+sqrt(2-sqrt(2-sqrt(2)))))/2=0.242980179903263889948274162077471118320990783283832126…
15 Pi/12 (sqrt(3)-1)/sqrt(8)=sqrt(2-sqrt(3))/2=SIN(ARCTAN(1)/3)
15.75 Pi*7/80 sqrt(½-½sqrt(1+(sqrt(8-2sqrt(10-2sqrt(5)))-4)/8))=1/(2sqrt(2/(4-sqrt(2(4+sqrt(2(4-sqrt(2(5-sqrt(5))))))))))
180/11=16.3636… Pi/11 ((-1)^(9/22) - (-1)^(13/22))/2 auch sqrt{ 0=1024x5-2816x4+2816x³-1232x²+220x-11;x=0.0793732…}=0.28173255684142969771141791534661…
16.5 Pi*11/120 sqrt(1/2-1/(4*sqrt(2/(4+sqrt(7+sqrt(5)-sqrt(6(5+sqrt(5))))))))=0.284015344703922617444389690699185350516107057310255223…
17 Pi*17/180 ((-1)^(73/180)-(-1)^(107/180))/2=0.2923717047227367280974686953771432526646871861826…
18 Pi/10 (sqrt(5)-1)/4=(√5-1)/4=0.30901699437494742410229341718281905886015458990288…
18.75 Pi*5/48 sqrt(2-sqrt(2+sqrt(2-sqrt(3))))/2=0.32143946530316158070105762407890158605846445800752915490…
19 Pi*19/180 sqrt(2-sqrt(2+sqrt(2-sqrt(2+(-1)^(14/45)-(-1)^(31/45)))))/2=0.325568154457156668714008935794721571798851606759123107215…
19.5 Pi*13/120 sqrt(1/2-1/(4*sqrt(2/(4+sqrt(7-sqrt(5)-sqrt(6*(5-sqrt(5))))))))=0.3338068592337709288283112855367461082971208424937535…
20 Pi/9 ((-1)^(7/18) (1-(-1)^(1/9)) (1 + (-1)^(1/9)))/2=(-1)^(7/18) (1-(-1)^(2/9))/2=sqrt(½-1/8(1-i*sqrt(3))(½(1+i*sqrt(3)))^(1/3)-1/4(½(1+i*sqrt(3)))^(2/3)) =(abs((i-sqrt(3))^(1/3)-(i+sqrt(3))^(1/3)))/(2^(4/3)) oder 64 x^6-96 x^4+36 x^2-3=0;x=0.342020…
20.25 Pi*9/80 sqrt(½-¼sqrt(½(4+sqrt(2(4-sqrt(2(5+sqrt(5))))))))=0.346117057077492976468214994928212505150789200683309434278…
21 Pi*7/60 1/(2*sqrt(2/(4-sqrt(7-sqrt(5)+sqrt(6*(5-sqrt(5)))))))=0.358367949545300273484137789413466834191544449460013795463…
360/17=21.17647… Pi*2/17 sqrt(8-sqrt(2(15+sqrt(17)+sqrt(2(17-sqrt(17)))-sqrt(2(34+6sqrt(17)-sqrt(2(17-sqrt(17)))+sqrt(34(17-sqrt(17)))-8sqrt(2(17+sqrt(17))))))))/4
22.5 Pi/8 sqrt(2-sqrt(2))/2=0.3826834323650897717284599840303988667613445624856270…
24 Pi*2/15 (sqrt(3)*(sqrt(5)+1)-sqrt(2)*sqrt(5-sqrt(5)))/8
25 Pi*5/36 (-1)^(13/36) (1 - (-1)^(5/18))/2=sqrt(½(4-2/(½(i-sqrt(3)))^(1/3)-2^(2/3)(i-sqrt(3))^(1/3)))/2=0.42261826174069943618697848964773…
25.5 Pi*17/120 sqrt(1/2-1/(4*sqrt(2/(4-sqrt(7-sqrt(5)-sqrt(6*(5-sqrt(5))))))))=0.430511096808295144376148356508279487640238425495…
180/7=25.71… Pi/7 ((-1)^(5/14) - (-1)^(9/14))/2 oder {64 x^6-112 x^4+56 x²-7=0} = 0.43388373911755812047576833284835875460999072778745987…
26 Pi*13/90 0=4096x^12-12288x^10-512x^9+13824x^8+1152x^7-7168x^6-864x^5+1680x^4+248x³-144x²-24x+1; x=0.438371146789077417452734540658265739…
26.25 Pi*7/48 sqrt(2-sqrt(2-sqrt(2-sqrt(3))))/2=0.442288690219001281995238977324244730156929205571162372150…
27 Pi*3/20 (2*sqrt(sqrt(5)+5)-sqrt(2)*(sqrt(5)-1))/8
28 Pi*7/45 sqrt(½-48/(192 (-1)^(14/45))-1/768 (192 (-1)^(14/45)))=sqrt(½ (1-sin((17 pi)/90)))=0.46947156278589077595946228822784329572321875671119680…
225/8=28.125 Pi*5/32 sqrt(2-sqrt(2-sqrt(2-sqrt(2))))/2=0.4713967368259976485563876259052543776574603189324806214…
28.5 Pi*19/120 sqrt(1/2-1/(4*sqrt(2/(4-sqrt(7+sqrt(5)-sqrt(6*(5+sqrt(5))))))))=0.477158760259608415048863008189386052534488779717814752…
29 Pi*29/180 sqrt(½-(-sqrt(7+sqrt(5)+sqrt(6(5+sqrt(5))))+i*sqrt(9-sqrt(5)-sqrt(6(5+sqrt(5)))))^(1/3)/(4 2^(2/3))-1/(2(2(-sqrt(7+sqrt(5)+ sqrt(6(5+sqrt(5))))+i*sqrt(9-sqrt(5)-sqrt(6(5+sqrt(5))))))^(1/3)))=0.484809620246337029075379622415776568276657476836866465797…
30 Pi/6 1/2
31.5 Pi*7/40 ½sqrt(½(4-sqrt(8-2 sqrt(10-2 sqrt(5)))))=0.5224985647159488649878978801782938234153871915232637…
32 Pi*8/45 sqrt(2-sqrt(2-(-1)^(13/45)+(-1)^(32/45)))/2=0.52991926423320495404678115181608666877201754995879996476…
33 Pi*11/60 1/(2*sqrt(2/(4-sqrt(7+sqrt(5)-sqrt(6*(5+sqrt(5)))))))
135/4=33.75 Pi*3/16 sqrt(2-sqrt(2-sqrt(2)))/2
34 Pi*17/90 ((-1)^(14/45)-(-1)^(31/45))/2=24/a+a/96=0.5591929034707468301604281399859892873066219403956694…
a=48*(-1)^(14/45)=24(1-sqrt(5)-sqrt(6*(5+sqrt(5)))+sqrt(2*(2*sqrt(5)-14-sqrt(6(5+sqrt(5)))+sqrt(30(5+sqrt(5))))))^(1/3)
34.5 Pi*23/120 sqrt(½-1/(4*sqrt(2/(4-sqrt(7-sqrt(5)+sqrt(6*(5-sqrt(5))))))))=0.56640623692483283182162505223376493251868845609981…
35 Pi*7/36 ((-1)^(11/36)-(-1)^(25/36))/2=0.573576436351046096108031912826157864620433371450986...
36 Pi/5 sqrt((5-sqrt(5))/8)=0.58778525229247312916870595463907276859765243764314599…
37.5 Pi*5/24 (sqrt(3(2+sqrt(2)))-sqrt(2-sqrt(2)))/4=sqrt(2-sqrt(2-sqrt(3)))/2
38 Pi*19/90 sqrt(2-sqrt(2-sqrt(2+(-1)^(14/45)-(-1)^(31/45))))/2=0.615661475325658279668811092843655628250930871515210…
270/7=38.571… Pi*3/14 cos(2*pi/7)=A116425/2-1={0=8x³+4x²-4x-1}=0.62348980185873353052500488400423981063227473…
39 Pi*13/60 1/(2*sqrt(2/(4-sqrt(7-sqrt(5)-sqrt(6*(5-sqrt(5)))))))=0.629320391049837452705902458279970426566862412129866…
40 Pi*2/9 (-1)^(5/18)*(1-(-1)^(4/9))/2=0.64278760968653932632264340990726343290755988420568…
40.5 Pi*9/40 sqrt(½(4-sqrt(8-2*sqrt(2(5+sqrt(5))))))/2=0.64944804833018365572632077089376287927750281217191397518…
41 Pi*41/180 ((-1)^(49/180)-(-1)^(131/180))/2=(-1)^(49/180)(1-(-1)^(41/90))/2=0.656059028990507284782495964023419247519401697870349…
42 Pi*7/30 (1-sqrt(5)+sqrt(6*(5+sqrt(5))))/8=(sqrt(6)*sqrt(5+sqrt(5))-sqrt(5)+1)/8=0.66913060635885821382627333068678047359958321895979…
43.5 Pi*29/120 sqrt(1/2-1/(4 sqrt(2/(4-sqrt(7+sqrt(5)+sqrt(6(5+sqrt(5))))))))=0.688354575693753984389256143419612293486469312096…
44 Pi*11/45 S=sin(pi/45);C=1-2sin(Pi/90)²;11S*C^10-S^11-165S³*C^8+462S^5*C^6-330S^7*C^4+55S^9*C²=0.6946583704589972866564062994226862299…
45 Pi/4 sqrt(2)/2=1/sqrt(2)=0.7071067811865475244008443621048490392848359376884740…
46 Pi*23/90 =cos(11Pi/45)={0=4096x12-12288x10+512x9+13824x8-1152x7-7168x6+864x5+1680x4-248x³-144x²+24x+1}=0.71933980033865113935605467445…
46.5 Pi*31/120 sqrt(1/2+1/(4*sqrt(2/(4-sqrt(7+sqrt(5)+sqrt(6*(5+sqrt(5))))))))=0.725374371012287637993284111189727442263439014961539…
48 Pi*4/15 cos(7pi/30)=sqrt(7-sqrt(5)+sqrt(6(5-sqrt(5))))/4=0.743144825477394235014697048974256977189113873498026…
48.59037789… A197260 3/4=0.75
49.5 Pi*11/40 cos(9pi/40)=sqrt((4+sqrt(2(4-sqrt(2(5+sqrt(5))))))/2)/2=0.76040596560003093817459436484490199988874706603899…
50 Pi*5/18 (-(½))(-1)^(7/9)(1+(-1)^(4/9))=cos(2Pi/9)=(-½ i (sqrt(3)-i))^(1/3)/2+(½ i (sqrt(3)+i))^(1/3)/2=0.766044443118978035202392650555416673935832457…
51 Pi*17/60 cos(13pi/60)=(W2(W3-1)*(W5+1)+2(W3+1)*sqrt(5-W5))/16=1/(2*sqrt(2/(4+sqrt(7-sqrt(5)-sqrt(6(5-sqrt(5)))))))=0.7771459614569708799799377436724…
380/7=51.428571… Pi*2/7 (-1)^(3/14)*(1-(-1)^(4/7))/2={0=64x6-112 x4+56 x²-7}=0.78183148246802980870844452667405775023233451870868752898…
52.5 Pi*7/24 (sqrt(3*(2-sqrt(2)))+sqrt(2+sqrt(2)))/4=sqrt(2+sqrt(2-sqrt(3)))/2=0.79335334029123516457977696150129927662867592105191…
54 Pi*3/10 (1+sqrt(5))/4=0.809016994374947424102293417182819058860154589902881431…
55.5 Pi*37/120 sqrt(1/2+1/(4*sqrt(2/(4-sqrt(7-sqrt(5)+sqrt(6*(5-sqrt(5))))))))0.824126188622015661729684903102312058134427949993…
225/4=56.25 Pi*5/16 cos(3Pi/16)=sqrt(2+sqrt(2-sqrt(2)))/2=0.8314696123025452370787883776179057567385608119872…
57 Pi*19/60 cos(11Pi/60)=1/(2sqrt(2/(4+sqrt(7+sqrt(5)-sqrt(6(5+sqrt(5)))))))=0.83867056794542402963759094180454789403950026509592…
630/11=57.2727… Pi*7/22 cos(2*pi/11)={0=32x5+16x4-32x³-12x²+6x+1}=0.8412535328311811688618116489193677175132924984205…
58.5 Pi*13/40 cos(7Pi/40)=1/(2sqrt(2/(4+sqrt(2(4-sqrt(2(5-sqrt(5))))))))=0.852640164354092221519383458130412135817266281929…
60 Pi/3 sqrt(3)/2 = 0.86602540378443864676372317075293618347140262690519…
61.5 Pi*41/120 sqrt(1/2+1/(4*sqrt(2/(4-sqrt(7+sqrt(5)-sqrt(6*(5+sqrt(5))))))))=0.878817112661965374129995143684524799610657309609109…
62 31Pi/90 ((-1)^(7/45)-(-1)^(38/45))/2=cos(7Pi/45)=0.8829475928589269420321713603157193860835366319995…
eine Nullstelle von 0=1+24x-144x²-248x^3+1680x^4+864x^5-7168x^6-1152x^7+13824x^8+512x^9-12288x^10+4096x^12
63 Pi*7/20 sqrt(½(4+sqrt(2(5-sqrt(5)))))/2=0.891006524188367862359709571413626312770518519036...
64 Pi*16/45 sqrt(½+48/(192*(-1)^(13/45))+1/768*(192*(-1)^(13/45)))=0.89879404629916699278229567669578535492997341381842...
64.5 Pi*43/120 sqrt(1/2 + 1/(4 sqrt(2/(4 - sqrt(7 - sqrt(5) - sqrt(6 (5 - sqrt(5))))))))=0.9025852843498606067626451490957717568163838270992085…
66 Pi*11/30 cos(2Pi/15)=(1+sqrt(5)+sqrt(6(5-sqrt(5))))/8=0.913545457642600895502127571985317177940810459377474…
135/2=67.5 Pi*3/8 sqrt(2+sqrt(2))/2
1170/17=68.8235… Pi*13/34 [sqrt(17)-1+sqrt(34-2sqrt(17))+sqrt{68+12sqrt(17)+2(sqrt(17)-1)sqrt(34-2sqrt(17))-16sqrt(34+2sqrt(17))}]/16=0.932472229404355804573115891821…
=cos(2Pi/17)=Nullstelle von 256x8+128x7-448x6-192x5+240x4+80x3-40x²-8x+1 Wikipedia: 17-Eck
69 Pi*23/60 cos(7Pi/60)=1/(2sqrt(2/(4+sqrt(7-sqrt(5)+sqrt(6(5-sqrt(5)))))))=0.933580426497201748990043063139570741405965268537466…
70 Pi*7/18 cos(Pi/9)={0=8x³-6x-1}=1/(2^(2/3)(k=1+i*sqrt(3))^(1/3))+(k/2)^(1/3)/2=0.939692620785908384054109277324731469936208134264464…
70.5 Pi*47/120 sqrt(1/2+1/(4 sqrt(2/(4+sqrt(7-sqrt(5)-sqrt(6 (5-sqrt(5))))))))=0.9426414910921783947771677362823118828448666906665…
72 Pi*2/5 sqrt((5+sqrt(5))/8)=0.9510565162951535721164393333793821434056986341257502…
73.5 Pi*49/120 sqrt(1/2 + 1/(4 sqrt(2/(4 + sqrt(7 + sqrt(5) - sqrt(6 (5 + sqrt(5))))))))=0.95881973486819304976102854139259829104918091884905898…
75 Pi*5/12 (1+sqrt(3))/sqrt(8)
76 Pi*19/45 sqrt(2+sqrt(2+(-1)^(14/45)-(-1)^(31/45)))/2=0.970295726275996472306377874033990377632260852443082915…
76.5 Pi*17/40 cos(3Pi/40)=sqrt(½(4+sqrt(2(4+sqrt(2(5-sqrt(5)))))))/2=0.972369920397676601833645834118797644002576369406261…
540/7=77.142857… Pi*3/7 cos(Pi/14)=(-1)^(1/14)*(1-(-1)^(6/7))/2={0=64x6-112 x4+56 x²-7}=0.974927912181823607018131682993931217232785800619997…
78 Pi*13/30 cos(Pi/15)=(sqrt(5)-1+sqrt(6(5+sqrt(5))))/8=0.978147600733805637928566747869599532459737808862677…
315/4=78.75 Pi*7/16 sqrt(2+sqrt(2+sqrt(2)))/2
79.5 Pi*53/120 sqrt(1/2+1/(4 sqrt(2/(4+sqrt(7-sqrt(5)+sqrt(6 (5-sqrt(5))))))))=0.9832549075639545845546320564305089875746236546656674825…
80 Pi*4/9 (-1)^(1/18)*(1-(-1)^(8/9))/2
81 Pi*9/20 sqrt(½(4+sqrt(2(5+sqrt(5)))))/2=0.98768834059513772619004024769343726075840686158988043492…
82.5 Pi*11/24 sqrt(2+sqrt(2+sqrt(3)))/2
84 Pi*7/15 cos(pi/30)=sqrt(7+sqrt(5)+sqrt(6 (5+sqrt(5))))/4=0.994521895368273336922691944980570381520792088709319…
85.5 Pi*19/40 cos(pi/40)=½sqrt(½(4+sqrt(2(4+sqrt(2(5+sqrt(5)))))))=sqrt(2+sqrt(2+sqrt(½(5+sqrt(5)))))/2=0.9969173337331279761977734087420444201589268815…
87 Pi*29/60 cos(pi/60)=1/(2sqrt(2/(4+sqrt(7+sqrt(5)+sqrt(6(5+sqrt(5)))))))=0.998629534754573873784492058439436580590952290767785…
88.5 Pi*59/120 (sqrt(30-9sqrt(10))+sqrt(30+3sqrt(10))-sqrt(10+3sqrt(10))+sqrt(10-sqrt(10))+sqrt(30-15sqrt(2))+sqrt(10+5sqrt(2))+sqrt(6-3sqrt(2))+sqrt(2+sqrt(2)))/16
=((-1)^(1/120) - (-1)^(119/120))/2=0.9996573249755572800367608883676798759498759712410784612…
90 Pi/2 1
100 Pi*5/9 -(-1)^(17/18)*(1+(-1)^(1/9))/2
720/7=102.8571… Pi*4/7 -(-1)^(13/14)*(1+(-1)^(1/7))/2
105 Pi*7/12 (1+sqrt(3))/sqrt(8)
108 Pi*3/5 sqrt((5+sqrt(5))/8)=sin(Pi*2/5)=0.9510565162951535721164393333793821434056986341257502…
112.5 Pi*5/8 sqrt(2+sqrt(2))/2
120 Pi*2/3 sqrt(3)/2
126 Pi*7/10 (1+sqrt(5))/4=sin(Pi*3/10)=0.809016994374947424102293417182819058860154589902881431…
900/7=128.571… Pi*5/7 -(-1)^(11/14)*(1 + (-1)^(3/7))/2
135 Pi*3/4 sqrt(2)/2=1/sqrt(2)=sin(Pi/4)=0.7071067811865475244008443621048490392848359376884740…
144 Pi*4/5 sqrt((5-sqrt(5))/8)=sin(Pi/5)=0.58778525229247312916870595463907276859765243764314599…
150 Pi*5/6 1/2
152 Pi*38/45 sin(28°)=sin(pi*7/45) siehe oben
157.5 Pi*7/8 sqrt(2-sqrt(2))/2=sin(Pi/8)=0.3826834323650897717284599840303988667613445624856270…
162 Pi*9/10 (sqrt(5)-1)/4
165 Pi*11/12 (sqrt(3)-1)/sqrt(8)
170 Pi*17/18 sin(10°)=cos(80°)=((-1)^(4/9)-(-1)^(5/9))/2=0.173648177666930348851716626769314796000…
180 Pi 0
195 Pi*13/12 (1-sqrt(3))/sqrt(8)
198 Pi*11/10 (1-sqrt(5))/4
200 Pi*10/9 ((-1)^(11/18)-(-1)^(7/18))/2=-sin(Pi/9)=-0.34202014332566873304409961468225958076308336751416062…
202.5 Pi*9/8 -sqrt(2-sqrt(2))/2=((-1)^(5/8)-(-1)^(3/8))/2=-sin(Pi/8)=-0.382683432365089771728459984030398866761344562485627…
1440/7=205.71428… Pi*8/7 ((-1)^(9/14)-(-1)^(5/14))/2=-sin(Pi/7)=-0.43388373911755812047576833284835875460999072778745987…
210 Pi*7/6 -1/2
216 Pi*6/5 -sqrt((5-sqrt(5))/8)=-sin(Pi/5)=-0.58778525229247312916870595463907276859765243764314599…
220 Pi*11/9 (-1)^(5/18)*((-1)^(4/9)-1)/2=((-1)^(13/18)-(-1)^(5/18))/2=-sin(Pi*2/9)=-0.6427876096865393263226434099072634329075598842…
225 Pi*5/4 -sqrt(2)/2
1620/7=231.42857.. Pi*9/7 ((-1)^(11/14)-(-1)^(3/14))/2=-cos(Pi*3/14)=-0.7818314824680298087084445266740577502323345187…
234 Pi*13/10 -(sqrt(5)+1)/4
240 Pi*4/3 -sqrt(3)/2
247.5 Pi*11/8 -sqrt(2+sqrt(2))/2
252 Pi*7/5 -sqrt((5+sqrt(5))/8)=-sin(Pi*2/5)=-0.9510565162951535721164393333793821434056986341257502…
255 Pi*17/12 (-1-sqrt(3))/sqrt(8)=-0.96592582628906828674974319972889736763390483900840455…
1800/7=257.142857.. Pi*10/7 2*sin(pi/28)²-1=-cos(Pi/14)=((-1)^(13/14)-(-1)^(1/14))/2=-0.97492791218182360701813168299393121723278580061999…
260 Pi*13/9 -cos(Pi/18)=((-1)^(17/18)-(-1)^(1/18))/2=-0.98480775301220805936674302458952301367064325…
270 Pi*3/2 -1
280 Pi*14/9 -cos(Pi/18)=((-1)^(17/18)-(-1)^(1/18))/2=-0.98480775301220805936674302458952301367064325…
1980/7=282.857.. Pi*11/7 =-cos(Pi/14)=((-1)^(13/14)-(-1)^(1/14))/2=-0.97492791218182360701813168299393121723278580061999…
285 Pi*19/12 -(1+sqrt(3))/(2 sqrt(2))
288 Pi*8/5 -sqrt((5+sqrt(5))/8)=-sin(Pi*2/5)=-0.9510565162951535721164393333793821434056986341257502…
292.5 Pi*13/8 -cos(Pi/8)=-sqrt(2+sqrt(2))/2=-0.923879532511286756128183189396788286822416625863642486…
300 Pi*5/3 -sqrt(3)/2=-0.8660254037844386467637231707529361834714026269051903140…
306 Pi*17/10 -(1+sqrt(5))/4=-sin(Pi*3/10)=-0.809016994374947424102293417182819058860154589902881431…
315 Pi*7/4 -1/sqrt(2)=-sin(Pi/4)=-0.7071067811865475244008443621048490392848359376884740…
324 Pi*9/5 -sqrt((5-sqrt(5))/8)=-sin(Pi/5)=-0.58778525229247312916870595463907276859765243764314599…
337.5 Pi*15/8 -sqrt(2-sqrt(2))/2=-sin(Pi/8)=-0.3826834323650897717284599840303988667613445624856270…
342 Pi*19/10 (1-sqrt(5))/4=-0.3090169943749474241022934171828190588601545899028814310…
345 Pi*23/12 -sqrt(2-sqrt(3))/2=(1-sqrt(3))/sqrt(8)=-0.258819045102520762348898837624048328349068901319930513…
350 Pi*35/18 ((-1)^(5/9)-(-1)^(4/9))/2=-sin(Pi/18)=-0.173648177666930348851716626769314796000375677184069387236…
357 Pi*119/60 -sin(Pi/60)=(sqrt(3)-1)*sqrt(5+sqrt(5))/8-sqrt(2)*(sqrt(5)-1)*(sqrt(3)+1)/16=-0.052335956242943832722118629609078418731…
360 Pi*2 0
3960/Pi=1260.5.. 22 -sin(22-7Pi)=2cos(11)*sin(11)=3sin(22/3)-4sin(22/3)³=sin(22 rad) 14400 digits
cos(x)=sin(x+pi/2)=sin(pi/2-x)=1-2sin(x/2)²=(exp(-x*i)+exp(x*i))/2=(sin(y+x)+sin(y-x))/(2sin(y))
cos(x)=sgn(sin(x+Pi/2))*sqrt(1-sin(x)²)   ;    sgn(cos(x+PI/2))=sgn(((abs(x)%(2*PI))-PI)*x)=SquareWave(-x/Pi/2)
tan(x)=sgn(cos(x))*sin(x)/sqrt(1-sin(x)²) ;    sgn(cos(x))=sgn(((abs(x)+3*PI/2)%(2*PI))-PI)=SquareWave(x/2/PI+1/4)
cot(x)=sgn(cos(x))*sqrt(1-sin(x)²)/sin(x)
sin(13x)=13*sin(x) - 364*sin(x)^3 + 2912*sin(x)^5 - 9984*sin(x)^7 +16640*sin(x)^9 - 13312*sin(x)^11 + 4096*sin(x)^13
sin(11x)=11*sin(x) - 220*sin(x)^3 + 1232*sin(x)^5 - 2816*sin(x)^7 +2816*sin(x)^9 - 1024*sin(x)^11
sin(7x) = 7*sin(x)-56*sin(x)³+112*sin(x)^5-64*sin(x)^7
sin(5x)=sin(x)*(5-20*sin(x)²+16*sin(x)^4)
sin(3x)=3*sin(x)-4*sin(x)³
tan(3x)=(3tan(x)-tan(x)³)/(1-3tan(x)²)
sin(2x)=2*sin(x)*cos(x)=2*sin(x)*sqrt(1-sin(x)²)=sqrt(4*sin(x)²*(1-sin(x)²)) {0...Pi/2}
sin(x)=3sin(x/3)-4sin(x/3)³=sqrt(4*sin(x/2)²*(1-sin(x/2)²))=sqrt(½-sqrt(1-sin(2*x)²)/2) {0…Pi/2}
sin(x/2)=3sin(x/6)-4sin(x/6)³=sqrt(4*sin(x/4)²*(1-sin(x/4)²))=sqrt(½-sqrt(1-sin(x)²)/2) {0…Pi/2}
sin(1/3*atan(1))=(sqrt(3)-1)/(2 sqrt(2))=sqrt(2-sqrt(3))/2
sin(1/3*atan(sqrt(5-2 sqrt(5))))=sqrt(7-sqrt(5)-sqrt(6 (5-sqrt(5))))/4
sin(½*atan(x))=x/(sqrt(2)*sqrt(x²+1)*sqrt(1/sqrt(x²+1)+1))
sin(atan(x))=x/sqrt(x²+1)
sin(2*atan(x))=(2 x)/(x²+1)
sin(3*atan(x))=(3 x-x³)/(x²+1)^(3/2)
sin(4*atan(x))=(4 (x-x³))/(x²+1)²
sin(5*atan(x)) = (5 x-10 x^3+x^5)/(1+x²)^(5/2)
sin(6*atan(x)) =((6 x-20 x^3+6 x^5))/(1+x²)^(6/2)
sin(7*atan(x)) =(7 x-35 x^3+21 x^5-x^7)/(1+x²)^(7/2)
(pi+i)^(1/3) = (1+pi²)^(1/6)*cos(1/3*atan(1/pi))+i*(1+pi²)^(1/6)*sin(1/3*atan(1/pi))
dgms+((x^3+x)²+(x²+1)²)^(1/3) cos(1/3 atan(1/x))² = x²+1
atan(x)=2*atan((sqrt(x²+1)-1)/x)=atan(y)+atan((x-y)/(x*y+1))
tan(3*asin(x))=(4 x³-3 x)/(sqrt(1-x) sqrt(1+x) (-1+4*x²))
atan(1/tan(1/(x)))/3=pi/6-1/(3*x) für x>1/3
sin(pi/x)=((-1)^((x/2-1)/x) - (-1)^((x/2+1)/x))/2
sin(x+y) = sin(x)*cos(y) + cos(x)*sin(y) = sin(x)*sqrt(1-sin(y)²) + sqrt(1-sin(x)²)*sin(y) wenn -Pi/2 <= x <= Pi/2
cos(x+y)*cos(x-y)=cos(y)²-sin(x)²=cos(y)²+cos(x)²-1=1-sin(x)²-sin(y)²
n*sin(x)+k*cos(x) = sqrt(n²+k²)*sin(x+atan(k/n))
sin(x-y) = sin(x)*cos(y) - cos(x)*sin(y) = sin(x)*sqrt(1-sin(y)²) - sqrt(1-sin(x)²)*sin(y)
atan(1/sqrt(x²-1)) = sgn(-x)*acos(1/x)+sgn(x)*(PI/2) für |x|>1
Pi=2*(acos(1/x)+atan(1/sqrt(x*x-1))) |x|>1; x=13/5 ist Pi=(acos(5/13)+atan(5/12))*2
[cos(x)+ i * sin(x)]^n = e^(i*x)^n=e^(i*nx) = cos(n*x)+ i * sin(n*x) Satz von de Moivre mit Eulerformel

sin(22)=sin(7Pi-22)=2cos(11)*sin(11)=2sin(1)*cos(1)*(2cos(2)-2cos(4)+2cos(6)-2cos(8)+2cos(10)-1)(1+2cos(2)+2cos(4)+2cos(6)+2cos(8)+2cos(10))
mit cos(10)=1-2sin(5)²=(cos(1)-sin(1))(sin(1)+cos(1))(2cos(4)-1-2sin(2))(2sin(2)+2cos(4)-1)
und sin(5) =sin(1)(1+2cos(2)+2cos(4))=sin(1)*(5-20*sin(1)²+16*sin(1)^4)=16*sin(1)^5-20*sin(1)³+5*sin(1)
und cos(8) =(cos(4)-sin(4))(sin(4)+cos(4))=1-2sin(4)²
und cos(4) =(cos(2)-sin(2))(sin(2)+cos(2))=1-2sin(2)²=1-8*sin(1)²*cos(1)²


sin(x) mit Grundrechenarten berechnen per online Iterationsrechner
Hinweis: Die Werte auf dieser Seite sind alle exakt. Gute Näherungswerte unter Fast ganzzahlig (Almost Integer).

Interessant: bei sin(1°)=((-1)^(89/180)-(-1)^(91/180))/2, sin(41°)=((-1)^(49/180)-(-1)^(131/180))/2
also 1°, 7° ,11° ,13°, 17°, 19°, 23°, 29°, 31°, 37°, 41°,43°, 47°, 49°, 53°, 59°, 61°, 67°, 71°, 73°, 77°, 79°, 83° und 89°
tauchen die Ergebnisse auch in den Nullstellen folgenden Polynoms auf:
0=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 x28-74448984852135936 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

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