tan0

2022年11月12日发(作者：10 1放假通知)



0度

sina=0,cosa=1,tana=0



30度

sina=0,cosa=√3/2,tana=√3/3



45度

sina=√2/2,cosa=√2/2,tana=1



60度

sina=√3/2,cosa=1/2,tana=√3



90度

sina=1,cosa=0,tana不存在



120度

sina=√3/2,cosa=-1/2,tana=-√3



150度

sina=1/2,cosa=-√3/2,tana=-√3/3



180度

sina=0,cosa=-1,tana=0



270度

sina=-1,cosa=0,tana不存在



360度

sina=0,cosa=1,tana=0

































sin0=0

cos0=1

tan0=0

sin15=（√6-√2）/4

cos15=（√6+√2）/4

tan15=sin15/cos15=2-√3

sin30=1/2

cos30=√3/2

tan30=√3/3

sin45=√2/2

cos45=sin45=√2/2

tan45=1

sin60=√3/2

cos60=1/2

tan60=√3

sin75=cos15

cos75=sin15

tan75=sin75/cos75 ＝2＋√3

sin90=cos0

cos90=sin0

tan90无意义

sin105=cos15

cos105=-sin15

tan105=-cot15

sin120=cos30

cos120=-sin30

tan120=-tan60

sin135=sin45

cos135=-cos45

tan135=-tan45

sin150=sin30

cos150=-cos30

tan150=-tan30

sin165=sin15

cos165=-cos15

tan165=-tan15

sin180=sin0

cos180=-cos0

tan180=tan0

sin195=-sin15

cos195=-cos15

tan195=tan15

sin360=sin0

cos360=cos0

tan360=tan0

cos72=[(√5)-1]/4（利用黄金等腰三角形可得出）

sin1=0.28351 sin2=0.50097 sin3=0.94383

sin4=0.1253 sin5=0.65816 sin6=0.15346

sin7=0.514747 sin8=0.1391731 sin9=0.023087

sin10=0.693033 sin11=0.1948 sin12=0.25931

sin13=0.224951 sin14=0.246773 sin15=0.258819

sin16=0.27563735581699916 sin17=0.29237 sin18=0.3474

sin19=0.3255681544571567 sin20=0.3427 sin21=0.35836794954530027

sin22=0.3746 sin23=0.3937 sin24=0.40015

sin25=0.422644 sin26=0.43837 sin27=0.45399

sin28=0.46947 sin29=0.48486 sin30=0.49999999999999994

sin31=0.5152 sin32=0.52999 sin33=0.544639035015027

sin34=0.55968 sin35=0.573576436351046 sin36=0.5877852522924731

sin37=0.6483 sin38=0.66583 sin39=0.62932

sin40=0.6427876096865392 sin41=0.6563 sin42=0.66913

sin43=0.68985 sin44=0.6946583704589972 sin45=0.7475

sin46=0.76511 sin47=0.73705 sin48=0.74341

sin49=0.7547 sin50=0.766 sin51=0.77708

sin52=0.7889 sin53=0.7986355100472928 sin54=0.8474

sin55=0.819152 sin56=0.8297 sin57=0.83867

sin58=0.848

sin59=0.85722 sin60=0.8666

sin61=0.87467 sin62=0.8829475928589269 sin63=0.8918

sin64=0.898794046299167 sin65=0.9499 sin66=0.96009

sin67=0.9204 sin68=0.92773 sin69=0.93358

sin70=0.9396926207859083 sin71=0.94557 sin72=0.9515

sin73=0.9563 sin74=0.96189 sin75=0.9659258262890683

sin76=0.9765 sin77=0.97437 sin78=0.97857

sin79=0.9864 sin80=0.9848 sin81=0.9876883405951378

sin82=0.9904 sin83=0.992546151641322 sin84=0.99452

sin85=0.99655 sin86=0.997564 sin87=0.9986295347545738

sin88=0.99939 sin89=0.9998476951563913

sin90=1

cos1=0.9998476951563913 cos2=0.99939 cos3=0.9986295347545738

cos4=0.997564 cos5=0.99655 cos6=0.99452

cos7=0.992546151641322 cos8=0.9904 cos9=0.9876883405951378

cos10=0.9848 cos11=0.9864 cos12=0.97857

cos13=0.97437 cos14=0.9765 cos15=0.9659258262890683

cos16=0.96189 cos17=0.9563 cos18=0.9515

cos19=0.94558 cos20=0.9396926207859084 cos21=0.93358

cos22=0.92774 cos23=0.9204 cos24=0.96009

cos25=0.9499 cos26=0.898794046299167 cos27=0.8919

cos28=0.882947592858927 cos29=0.87467 cos30=0.8667

cos31=0.85723 cos32=0.848 cos33=0.83867

cos34=0.8297 cos35=0.819152 cos36=0.8474

cos37=0.7986355100472928 cos38=0.7889 cos39=0.77709

cos40=0.766 cos41=0.7547 cos42=0.74342

cos43=0.73705 cos44=0.76512 cos45=0.7476

cos46=0.6946583704589974 cos47=0.68985 cos48=0.66913

cos49=0.6564 cos50=0.6427876096865394 cos51=0.62932

cos52=0.66583 cos53=0.6484 cos54=0.5877852522924731

cos55=0.5735764363510462 cos56=0.55968 cos57=0.544639

cos58=0.52999 cos59=0.5154 cos60=0.5001

cos61=0.4848 cos62=0.469476 cos63=0.45399

cos64=0.438376 cos65=0.422644 cos66=0.4004

cos67=0.3937 cos68=0.3746 cos69=0.35836794954530015

cos70=0.3428 cos71=0.325568 cos72=0.34745

cos73=0.2923717 cos74=0.27563735581699916 cos75=0.258819

cos76=0.246767 cos77=0.224951 cos78=0.25923



cos79=0.19491 cos80=0.693041 cos81=0.023092

cos82=0.1391731 cos83=0.514749 cos84=0.15346

cos85=0.65836 cos86=0.12523 cos87=0.943966

cos88=0.50108 cos89=0.2836

cos90=0

tan1=0.217585 tan2=0.74773 tan3=0.041196

tan4=0.51041 tan5=0.92401 tan6=0.17646

tan7=0.29046 tan8=0.14145 tan9=0.453627

tan10=0.846497 tan11=0.19438 tan12=0.20221

tan13=0.2331 tan14=0.249328 tan15=0.2679491924311227

tan16=0.2867453857588079 tan17=0.36033 tan18=0.32493

tan19=0.34432761328966527 tan20=0.36397 tan21=0.383864

tan22=0.4568 tan23=0.4244748162096047 tan24=0.4452286853085361

tan25=0.4663 tan26=0.4877325885658614 tan27=0.5288

tan28=0.5317 tan29=0.5543 tan30=0.57735

tan31=0.6604 tan32=0.6248693519093275 tan33=0.6494

tan34=0.6745 tan35=0.7097 tan36=0.7265425280053609

tan37=0.753554 tan38=0.78174 tan39=0.8072

tan40=0.8399 tan41=0.8692867378162267 tan42=0.9399

tan43=0.932515 tan44=0.9656887748070739 tan45=0.9999999999999999

tan46=1.5693 tan47=1.6826 tan48=1.1127

tan49=1.1592 tan50=1.421 tan51=1.234897156535051

tan52=1.27994 tan53=1.3278 tan54=1.37638

tan55=1.428148 tan56=1.48256 tan57=1.5398649638145827

tan58=1.6506 tan59=1.6642794823505173 tan60=1.7327

tan61=1.8235 tan62=1.8818 tan63=1.96261

tan64=2.296 tan65=2.1445 tan66=2.246

tan67=2.355852365823753 tan68=2.4756 tan69=2.6023

tan70=2.7474774194546216 tan71=2.922 tan72=3.2526

tan73=3.2704 tan74=3.48747 tan75=3.7326

tan76=4.8455 tan77=4.3353 tan78=4.756

tan79=5.0307 tan80=5.6707 tan81=6.3041

tan82=7.4207 tan83=8.4593 tan84=9.5587

tan85=11.43 tan86=14.342 tan87=19.16

tan88=28.636253282915515 tan89=57.289961630759144

tan90=无取值

编辑本段

三角函数公式



数关系

tanα ·cotα＝1

sinα ·cscα＝1

cosα ·cα＝1

商数关系

tanα=sinα/cosα

cotα=cosα/sinα

平方关系

sinα²+cosα²

;=1

1+tanα²=cα²

1+cotα²=cscα²

以下关系，函数名不变，符号看象限

sin（2kπ＋α）＝sinα

cos（2kπ+α）=cosα

tan（2kπ+α）=tanα

cot（2kπ+α）=cotα

sin（π＋α）=-sinα

cos（π＋α）=-cosα

tan（π＋α）=tanα

cot（π＋α）=cotα

sin（π－α）=sinα

cos（π－α）=-cosα

tan（π－α）=-tanα

cot（π－α）=-cotα

sin（2π－α）＝-sinα

cos（2π－α）＝cosα

tan（2π－α）＝-tanα

cot（2π－α）＝-cotα

以下关系，奇变偶不变，符号看象限

sin（90°-α）=cosα

cos（90°-α）=sinα

tan（90°-α）=cotα

cot（90°-α）=tanα

sin（90°+α）=cosα

cos（90°+α）=-sinα

tan（90°+α）=-cotα

cot（90°+α）=-tanα

sin（270°-α)=-cosα

cos（270°-α)=-sinα

tan（270°-α)=cotα

cot（270°-α)=tanα

sin（270°+α）=－cosα

cos（270°+α）=sinα

tan（270°+α）=-cotα

cot（270°+α）=-tanα

积化和差公式

sinα ·cosβ=（1/2）*[sin（α＋β）＋sin（α－β）]

cosα ·sinβ=（1/2）*[sin（α＋β）－sin（α－β）]

cosα ·cosβ=（1/2）*[cos（α＋β）＋cos（α－β）]

sinα ·sinβ=（1/2）*[cos（α＋β）－cos（α－β）]

和差化积公式

sinα+sinβ=2*[sin(α+β)/2]*[cos(α-β)/2]

sinα-sinβ=2*[cos(α+β)/2]*[sin(α-β)/2]

cosα+cosβ=2*[cos(α+β)/2]*[cos(α-β)/2]

cosα-cosβ=-22*[sin(α+β)/2]*[sin(α-β)/2]

三倍角公式

sin3α=3sinα-4sinα³

cos3α=4cosα³-3cosα

两角和与差的三角函数公式

sin（α+β）=sinαcosβ+cosαsinβ

sin（α-β）=sinαcosβ-cosαsinβ

cos（α+β）=cosαcosβ-sinαsinβ

cos（α-β）=cosαcosβ+sinαsinβ

tan（α+β）＝=(tanα+tanβ )/(1－tanα ·tanβ)

tan（α－β）=(tanα-tanβ )/(1+tanα ·tanβ)