三角函数值对照表常用的三角函数的值

三角函数值对照表常用的三角函数的值

三角函数是数学中属于初等函数中的超越函数的一类函数。它们的本质是任意角的集合与一个比值的集合的变量之间的映射。通常的三角函数是在平面直角坐标系中定义的，其定义域为整个实数域。另一种定义是在直角三角形中，但并不完全。

三角函数值表大全

角α0°30°45°60°90°120°135°150°180°270°360°弧度制oπ/6π/4π/3π/22π/33π/45π/6π3π/22πsinαo1/2√2/2√3/21√3/2√2/21/20-10cosα1√3/2√2/21/20-1/2-√2/2-√3/2-101tanαo√3/31√3__√3-1-√3/30-0

sin0=sin0°=0

cos0=cos0°=1

tan0=tan0°=0sin15=0.650；

sin15°=（√6-√2）/4

cos15=-0.759；cos15°=（√6+√2）/4

tan15=-0.855；tan15°=2-√3sin30=-0.988；

sin30°=1/2

cos30=0.154；cos30°=√3/2tan30=-6.405；

tan30°=√3/3sin45=0.851；

sin45°=√2/2cos45=0.525；

cos45°=sin45°=√2/2

tan45=1.620；tan45°=1

sin60=-0.305；sin60°=√3/2

cos60=-0.952；cos60°=1/2

tan60=0.320；tan60°=√3

sin75=-0.388；sin75°=cos15°

cos75=0.922；cos75°=sin15°

tan75=-0.421；tan75°=sin75°/cos75° =2+√3

sin90=0.894；sin90°=cos0°=1

cos90=-0.448；cos90°=sin0°=0

tan90=-1.995；tan90°不存在

sin105=-0.971；sin105°=cos15°

cos105=-0.241；cos105°=-sin15°

tan105=4.028；tan105°=-cot15°

sin120=0.581；sin120°=cos30°

cos120=0.814；cos120°=-sin30°

tan120=0.713；tan120°=-tan60°

sin135=0.088；sin135°=sin45°

cos135=-0.996；cos135°=-cos45°

tan135=-0.0887；tan135°=-tan45°

sin150=-0.7149；sin150°=sin30°

cos150=-0.699；cos150°=-cos30°

tan150=-1.022；tan150°=-tan30°

sin165=0.998；sin165°=sin15°

cos165=-0.066；cos165°=-cos15°

tan165=-15.041；tan165°=-tan15°

sin180=-0.801；sin180°=sin0°=0

cos180=-0.598；cos180°=-cos0°=-1

tan180=1.339；tan180°=0

sin195=0.219；sin195°=-sin15°

cos195=0.976；cos195°=-cos15°

tan195=0.225；tan195°=tan15°

sin360=0.959；sin360°=sin0°=0

cos360=-0.284；cos360°=cos0°=1

tan360=-3.380；tan360°=tan0°=0

cos72度=[√5-1]/4（利用黄金等腰三角形可得出）

sin1=0.0____ sin2=0.____7 sin3=0.____3

sin4=0.____ sin5=0.087__816 sin6=0.____6

sin7=0.12__4747 sin8=0.__006544 sin9=0.__0__

sin10=0.____ sin11=0.____ sin12=0.____1

sin13=0.____7 sin14=0.____3 sin15=0.____4

sin16=0.____6 sin17=0.____ sin18=0.3090__4

sin19=0.____ sin20=0.____ sin21=0.____7

sin22=0.____ sin23=0.____ sin24=0.____5

sin25=0.4226__44 sin26=0.____ sin27=0.____5

sin28=0.____ sin29=0.____6 sin30=0.____4

sin31=0.5__0542 sin32=0.____ sin33=0.____

sin34=0.____ sin35=0.____ sin36=0.____

sin37=0.60__483 sin38=0.6__6583 sin39=0.____

sin40=0.____ sin41=0.____ sin42=0.669__82

sin43=0.____ sin44=0.____ sin45=0.____

sin46=0.____ sin47=0.73__705 sin48=0.743__41

sin49=0.____ sin50=0.____ sin51=0.777__08

sin52=0.____ sin53=0.____ sin54=0.8090__4

sin55=0.819__18 sin56=0.____ sin57=0.____

sin58=0.____ sin59=0.857__22 sin60=0.____

sin61=0.____ sin62=0.____ sin63=0.____

sin64=0.____ sin65=0.____ sin66=0.9__6009

sin67=0.____ sin68=0.927__73 sin69=0.____

sin70=0.____ sin71=0.9455__7 sin72=0.____

sin73=0.____ sin74=0.____ sin75=0.____

sin76=0.____ sin77=0.____ sin78=0.978__57

sin79=0.98__64 sin80=0.____ sin81=0.____

sin82=0.____ sin83=0.____ sin84=0.____

sin85=0.____ sin86=0.____ sin87=0.____

sin88=0.____ sin89=0.____

sin90=1

cos1=0.____ cos2=0.____ cos3=0.____

cos4=0.____ cos5=0.____ cos6=0.____

cos7=0.____ cos8=0.____ cos9=0.____

cos10=0.____ cos11=0.98__64 cos12=0.978__57

cos13=0.____ cos14=0.____ cos15=0.____

cos16=0.____ cos17=0.____ cos18=0.____

cos19=0.9455__8 cos20=0.____ cos21=0.____

cos22=0.927__74 cos23=0.____ cos24=0.9__6009

cos25=0.____ cos26=0.____ cos27=0.____

cos28=0.____ cos29=0.____ cos30=0.____

cos31=0.857__23 cos32=0.____ cos33=0.____

cos34=0.____ cos35=0.819__18 cos36=0.8090__4

cos37=0.____ cos38=0.____ cos39=0.777__09

cos40=0.____ cos41=0.____ cos42=0.743__42

cos43=0.73__705 cos44=0.____ cos45=0.____

cos46=0.____ cos47=0.____ cos48=0.669__82

cos49=0.____ cos50=0.____ cos51=0.____

cos52=0.6__6583 cos53=0.60__484 cos54=0.____

cos55=0.____ cos56=0.____ cos57=0.____

cos58=0.____ cos59=0.5__0544 cos60=0.____

cos61=0.____ cos62=0.____6 cos63=0.____

cos64=0.____ cos65=0.4226__44 cos66=0.____

cos67=0.____ cos68=0.____ cos69=0.____5

cos70=0.____ cos71=0.____ cos72=0.3090__45

cos73=0.____7 cos74=0.____6 cos75=0.____4

cos76=0.____7 cos77=0.____4 cos78=0.____3

cos79=0.____1 cos80=0.____ cos81=0.__0__

cos82=0.__006546 cos83=0.12__4749 cos84=0.____6

cos85=0.087__836 cos86=0.____3 cos87=0.____66

cos88=0.____8 cos89=0.0__2836

tan1=0.0____ tan2=0.____3 tan3=0.____96

tan4=0.____1 tan5=0.____1 tan6=0.____6

tan7=0.____ tan8=0.____ tan9=0.____

tan10=0.____ tan11=0.____8 tan12=0.____

tan13=0.____ tan14=0.____8 tan15=0.____

tan16=0.____ tan17=0.____3 tan18=0.____

tan19=0.____7 tan20=0.____4 tan21=0.____

tan22=0.____ tan23=0.____ tan24=0.____

tan25=0.____ tan26=0.____ tan27=0.____

tan28=0.53__788 tan29=0.____ tan30=0.____

tan31=0.____ tan32=0.____ tan33=0.____

tan34=0.____ tan35=0.____ tan36=0.____

tan37=0.____ tan38=0.____ tan39=0.____

tan40=0.____ tan41=0.____ tan42=0.____

tan43=0.9325__8 tan44=0.____ tan45=0.____

tan46=1.____ tan47=1.____ tan48=1.____

tan49=1.____ tan50=1.19__1 tan51=1.____

tan52=1.____ tan53=1.____ tan54=1.____

tan55=1.428__44 tan56=1.____ tan57=1.____

tan58=1.____ tan59=1.____ tan60=1.____

tan61=1.____ tan62=1.____ tan63=1.____

tan64=2.____ tan65=2.____ tan66=2.____

tan67=2.____ tan68=2.____ tan69=2.____

tan70=2.____ tan71=2.____ tan72=3.____

tan73=3.____ tan74=3.4874__7 tan75=3.____

tan76=4.____ tan77=4.33__53 tan78=4.____

tan79=5.__0307 tan80=5.____ tan81=6.3__041

tan82=7.1__207 tan83=8.__4593 tan84=9.5__587

tan85=11.____ tan86=14.____ tan87=19.081__

tan88=28.____ tan89=57.____

tan90=无取值范围

三角函数十组诱导公式

公式一公式二sin（2kπ+α）=sin αcos（2kπ+α）=cos αtan（2kπ+α）=tan αcot（2kπ+α）=cot αsec（2kπ+α）=sec αcsc（2kπ+α）=csc αsin（π+α）=-sin αcos（π+α）=-cos αtan（π+α）=tan αcot（π+α）=cot αsec（π+α）=-sec αcsc（π+α）=-csc α公式三公式四sin（-α）=-sin αcos（-α）=cos αtan（-α）=-tan

αcot（-α）=-cot αsec（-α）=sec αcsc（-α）=-csc αsin（π-α）=sin αcos（π-α）=-cos αtan（π-α）=-tan αcot（π-α）=-cot

αsec（π-α）=-sec αcsc（π-α）=csc α公式五公式六 sin（α-π）=-sin αcos（α-π）=-cos αtan（α-π）=tan αcot（α-π）=cot

αsec（α-π）=-sec αcsc（α-π）=-csc αsin（2π-α）=-sin αcos（2π-α）=cos αtan（2π-α）=-tan αcot（2π-α）=-cot αsec（2π-α）=sec αcsc（2π-α）=-csc α公式七公式八sin（π/2+α）=cosαcos（π/2+α）=−sinαtan（π/2+α）=-cotαcot（π/2+α）=-tanαsec（π/2+α）=-cscαcsc（π/2+α）=secαsin（π/2-α）=cosαcos（π/2-α）=sinαtan（π/2-α）=cotαcot（π/2-α）=tanαsec（π/2-α）=cscαcsc（π/2-α）=secα公式九公式十sin（3π/2+α）=-cosαcos（3π/2+α）=sinαtan（3π/2+α）=-cotαcot（3π/2+α）=-tanαsec（3π/2+α）=cscαcsc（3π/2+α）=-secαsin（3π/2-α）=-cosαcos

（3π/2-α）=-sinαtan（3π/2-α）=cotαcot（3π/2-α）=tanαsec（3π/2-α）=-cscαcsc（3π/2-α）=-secα