Sin(10.0500°)= Sin(10°03'00")= 0.174507518326992Sin(10.0501°)= Sin(10°03'00")= 0.174509236875369Sin(10.0502°)= Sin(10°03'00")= 0.174510955423215Sin(10.0503°)= Sin(10°03'01")= 0.174512673970529Sin(10.0504°)= Sin(10°03'01")= 0.174514392517312Sin(10.0505°)= Sin(10°03'01")= 0.174516111063563Sin(10.0506°)= Sin(10°03'02")= 0.174517829609282Sin(10.0507°)= Sin(10°03'02")= 0.17451954815447Sin(10.0508°)= Sin(10°03'02")= 0.174521266699126Sin(10.0509°)= Sin(10°03'03")= 0.174522985243251}

《(完整版)三角函数特殊角值表》由会员分享，可在线阅读，更多相关《(完整版)三角函数特殊角值表（5页珍藏版）》请在人人文库网上搜索。
1、角度030456090120135150180270360函数角 a 的弧度0 /6/4 /3 /22 /33 /45 /63 /22sin01/2 2/23/21 3/2 2/21/20-10cos1 3/2 2/21/20-1/2- 2/2- 3/2-101tan0 3/313- 3-1- 3/3001、图示法：
借助于下面三个图形来记忆，即使有所遗忘也可根据图形重新推出：sin30 =cos60° °=1 ， sin45 °=cos45°=2 ， tan30 °=cot60 °=3 ， tan 45 °=cot45 &
2、#176;=122322123130?45?60?311正弦函数sin =y/r 余弦函数cos=x/r 正切函数tan =y/x余切函数cot =x/y 正割函数sec=r/x 余割函数csc =r/y2、列表法：说明：正弦值随角度变化，即0?30?45?60?90?变化；值从01231
变化，其余类似记忆2223、规律记忆法：观察表中的数值特征，可总结为下列记忆规律：有界性：（锐角三角函数值都是正值）即当0° 90°时，则 0 sin 1； 0 cos 1 ； tan 0 ； cot0。 增减性：（锐角的正弦、正切值随角度的增大而增大；余弦、余切值随角度的增大而减小），
3、即当 0 A B90°时，则 sinA sinB；tanA tanB；cosA cosB；cotA cotB；特别地：若0° 45°，则 sinA cosA； tanA cotA若 45° A 90°，则 sinAcosA； tanA cotA4、口决记忆法：观察表中的数值特征正弦、余弦值可表示为m 形式，正切、余切值可表示为m 形式，有关 m
的值可归纳成23顺口溜：一、二、三；三、二、一；三九二十七函数名 正弦余弦正切余切正割余割符号sin cos tan cot sec csc正弦函数sin（ A） =a/c余弦函数cos（A ）=b/c
4、正切函数tan（ A ） =a/b余切函数cot（ A ） =b/a其中 a 为对边， b 为邻边， c
为斜边三角函数对照表三角函数SINCOSTAN三角函数SINCOSTAN0°01090°10无1°0.01740.99980.017489°0.99980.017457.28992°0.03480.99930.034988°0.99930.034828.63623°0.05230.99860.052487°0.99860.052319.08114°0.06970.99750.069986°0
5、.99750.069714.30065°0.08710.99610.087485°0.99610.087111.43006°0.10450.99450.105184°0.99450.10459.51437°0.12180.99250.122783°0.99250.12188.14438°0.13910.99020.140582°0.99020.13917.11539°0.15640.98760.158381°0.98760.15646.313710°0.17360.98480.1763
6、80°0.98480.17365.671211°0.19080.98160.194379°0.98160.19085.144512°0.20790.97810.212578°0.97810.20794.704613°0.22490.97430.230877°0.97430.22494.331414°0.24190.97020.249376°0.97020.24194.010715°0.25880.96590.267975°0.96590.25883.732016°0.2756
7、0.96120.286774°0.96120.27563.487417°0.29230.95630.305773°0.95630.29233.270818°0.30900.95100.324972°0.95100.30903.077619°0.32550.94550.344371°0.94550.32552.904220°0.34200.93960.363970°0.93960.34202.747421°0.35830.93350.383869°0.93350.35832.605022
8、°0.37460.92710.404068°0.92710.37462.475023°0.39070.92050.424467°0.92050.39072.355824°0.40670.91350.445266°0.91350.40672.246025°0.42260.90630.466365°0.90630.42262.144526°0.43830.89870.487764°0.89870.43832.050327°0.45390.89100.509563°0.89100.
9、45391.962628°0.46940.88290.531762°0.88290.46941.880729°0.48480.87460.554361°0.87460.48481.804030°0.50000.86600.577360°0.86600.50001.732031°0.51500.85710.600859°0.85710.51501.664232°0.52990.84800.624858°0.84800.52991.600333°0.54460.83860.649457&#
10、176;0.83860.54461.539834°0.55910.82900.674556°0.82900.55911.482535°0.57350.81910.700255°0.81910.57351.428136°0.58770.80900.726554°0.80900.58771.376337°0.60180.79860.753553°0.79860.60181.327038°0.61560.78800.781252°0.78800.61561.279939°0.62930.77
11、710.809751°0.77710.62931.234840°0.64270.76600.839050°0.76600.64271.191741°0.65600.75470.869249°0.75470.65601.150342°0.66910.74310.900448°0.74310.66911.110643°0.68190.73130.932547°0.73130.68191.072344°0.69460.71930.965646°0.71930.69461.035545
12、6;0.70710.7071145°0.70710.70711同角基本关系式倒数关系商的关系平方关系tancot1sinsec22sincos1sincsc1tancsccos122cossec1coscsctansec22cotsecsin1cotcsc诱导公式sin()sincos()costan()tancot()cotsin()cossin()sin3cos()cossin(22cos()sintan()tan3cos(2cot()cot2tan()cottan(322cot()tancot(
322sin()cos2cos()sinsin()sinsin( 322cos()
13、costan()cotcos(3tan()tan22cot()tancot()cot3tan(223cot(两角和与差的三角函数公式sin()sincoscossinsin()sincoscossincos()coscossinsincos()coscossinsintan()tantan1tantantan()tantan1tantan)cossin(2)sincos(2)cos)sintan(2)tancot(2)cot)cot(其中
k Z)tan)cossin(2)sin)sincos(2)costan(2)tan)cotcot(2)cot)tan万能公式sin2 tan(/ 2)ta
14、n 2(/ 2)11tan 2(/ 2)costan 2(/ 2)1tan2 tan(/ 2)tan 2(/ 2)1半角的正弦、余弦和正切公式三角函数的降幂公式1cos21cos2sin()2sin22cos(1cos21cos2cos)222tan(1cos1 cossin)cossin1
cos21二倍角的正弦、余弦和正切公式三倍角的正弦、余弦和正切公式sin 22sincossin33sin4sin 3cos2cos2sin 22cos 21 1 2sin 2cos34cos33cos .tan 22 tantan33tantan313tan 21 tan
2三角函数的和差化积公式三角函数的积化和差公式sinsin2sincossincos1sin()sin()222sinsin2cossincossin1sin()sin()222coscos2coscoscoscos1cos()cos()222coscos2sinsinsinsin1cos
}

01
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。特殊三角函数值—般指在0、30°、45°、60°、90°、
180°角下的正余弦值。这些角度的三角函数值是经常用到的。利用两角和与差的三角函数公式，可以求出一些其他角度的三角函数值。
完整的三角函数值如下：
sin0=sin0°=0
cos0=cos0°=1
tan0=tan0°=0
sin15=0.650；sin15°=（√6-√2）/4
cos15=-0.759；cos15°=（√6+√2）/4
tan15=-0.855；tan15°=2-√3
sin30=-0.988；sin30°=1/2
cos30=0.154；cos30°=√3/2
tan30=-6.405；tan30°=√3/3
sin45=0.851；sin45°=√2/2
cos45=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=0.01745240643728351 sin2=0.03489949670250097 sin3=0.05233595624294383
sin4=0.0697564737441253 sin5=0.08715574274765816 sin6=0.10452846326765346
sin7=0.12186934340514747 sin8=0.13917310096006544 sin9=0.15643446504023087
sin10=0.17364817766693033 sin11=0.1908089953765448 sin12=0.20791169081775931
sin13=0.22495105434386497 sin14=0.24192189559966773 sin15=0.25881904510252074
sin16=0.27563735581699916 sin17=0.2923717047227367 sin18=0.3090169943749474
sin19=0.3255681544571567 sin20=0.3420201433256687 sin21=0.35836794954530027
sin22=0.374606593415912 sin23=0.3907311284892737 sin24=0.40673664307580015
sin25=0.42261826174069944 sin26=0.4383711467890774 sin27=0.45399049973954675
sin28=0.4694715627858908 sin29=0.48480962024633706 sin30=0.49999999999999994
sin31=0.5150380749100542 sin32=0.5299192642332049 sin33=0.544639035015027
sin34=0.5591929034707468 sin35=0.573576436351046 sin36=0.5877852522924731
sin37=0.6018150231520483 sin38=0.6156614753256583 sin39=0.6293203910498375
sin40=0.6427876096865392 sin41=0.6560590289905073 sin42=0.6691306063588582
sin43=0.6819983600624985 sin44=0.6946583704589972 sin45=0.7071067811865475
sin46=0.7193398003386511 sin47=0.7313537016191705 sin48=0.7431448254773941
sin49=0.7547095802227719 sin50=0.766044443118978 sin51=0.7771459614569708
sin52=0.7880107536067219 sin53=0.7986355100472928 sin54=0.8090169943749474
sin55=0.8191520442889918 sin56=0.8290375725550417 sin57=0.8386705679454239
sin58=0.848048096156426 sin59=0.8571673007021122 sin60=0.8660254037844386
sin61=0.8746197071393957 sin62=0.8829475928589269 sin63=0.8910065241883678
sin64=0.898794046299167 sin65=0.9063077870366499 sin66=0.9135454576426009
sin67=0.9205048534524404 sin68=0.9271838545667873 sin69=0.9335804264972017
sin70=0.9396926207859083 sin71=0.9455185755993167 sin72=0.9510565162951535
sin73=0.9563047559630354 sin74=0.9612616959383189 sin75=0.9659258262890683
sin76=0.9702957262759965 sin77=0.9743700647852352 sin78=0.9781476007338057
sin79=0.981627183447664 sin80=0.984807753012208 sin81=0.9876883405951378
sin82=0.9902680687415704 sin83=0.992546151641322 sin84=0.9945218953682733
sin85=0.9961946980917455 sin86=0.9975640502598242 sin87=0.9986295347545738
sin88=0.9993908270190958 sin89=0.9998476951563913
sin90=1
cos1=0.9998476951563913 cos2=0.9993908270190958 cos3=0.9986295347545738
cos4=0.9975640502598242 cos5=0.9961946980917455 cos6=0.9945218953682733
cos7=0.992546151641322 cos8=0.9902680687415704 cos9=0.9876883405951378
cos10=0.984807753012208 cos11=0.981627183447664 cos12=0.9781476007338057
cos13=0.9743700647852352 cos14=0.9702957262759965 cos15=0.9659258262890683
cos16=0.9612616959383189 cos17=0.9563047559630355 cos18=0.9510565162951535
cos19=0.9455185755993168 cos20=0.9396926207859084 cos21=0.9335804264972017
cos22=0.9271838545667874 cos23=0.9205048534524404 cos24=0.9135454576426009
cos25=0.9063077870366499 cos26=0.898794046299167 cos27=0.8910065241883679
cos28=0.882947592858927 cos29=0.8746197071393957 cos30=0.8660254037844387
cos31=0.8571673007021123 cos32=0.848048096156426 cos33=0.838670567945424
cos34=0.8290375725550417 cos35=0.8191520442889918 cos36=0.8090169943749474
cos37=0.7986355100472928 cos38=0.7880107536067219 cos39=0.7771459614569709
cos40=0.766044443118978 cos41=0.754709580222772 cos42=0.7431448254773942
cos43=0.7313537016191705 cos44=0.7193398003386512 cos45=0.7071067811865476
cos46=0.6946583704589974 cos47=0.6819983600624985 cos48=0.6691306063588582
cos49=0.6560590289905074 cos50=0.6427876096865394 cos51=0.6293203910498375
cos52=0.6156614753256583 cos53=0.6018150231520484 cos54=0.5877852522924731
cos55=0.5735764363510462 cos56=0.5591929034707468 cos57=0.5446390350150272
cos58=0.5299192642332049 cos59=0.5150380749100544 cos60=0.5000000000000001
cos61=0.4848096202463371 cos62=0.46947156278589086 cos63=0.4539904997395468
cos64=0.43837114678907746 cos65=0.42261826174069944 cos66=0.4067366430758004
cos67=0.3907311284892737 cos68=0.3746065934159122 cos69=0.35836794954530015
cos70=0.3420201433256688 cos71=0.32556815445715675 cos72=0.30901699437494745
cos73=0.29237170472273677 cos74=0.27563735581699916 cos75=0.25881904510252074
cos76=0.24192189559966767 cos77=0.22495105434386514 cos78=0.20791169081775923
cos79=0.19080899537654491 cos80=0.17364817766693041 cos81=0.15643446504023092
cos82=0.13917310096006546 cos83=0.12186934340514749 cos84=0.10452846326765346
cos85=0.08715574274765836 cos86=0.06975647374412523 cos87=0.052335956242943966
cos88=0.03489949670250108 cos89=0.0174524064372836
tan1=0.017455064928217585 tan2=0.03492076949174773 tan3=0.052407779283041196
tan4=0.06992681194351041 tan5=0.08748866352592401 tan6=0.10510423526567646
tan7=0.1227845609029046 tan8=0.14054083470239145 tan9=0.15838444032453627
tan10=0.17632698070846497 tan11=0.19438030913771848 tan12=0.2125565616700221
tan13=0.2308681911255631 tan14=0.24932800284318068 tan15=0.2679491924311227
tan16=0.2867453857588079 tan17=0.30573068145866033 tan18=0.3249196962329063
tan19=0.34432761328966527 tan20=0.36397023426620234 tan21=0.3838640350354158
tan22=0.4040262258351568 tan23=0.4244748162096047 tan24=0.4452286853085361
tan25=0.4663076581549986 tan26=0.4877325885658614 tan27=0.5095254494944288
tan28=0.5317094316614788 tan29=0.554309051452769 tan30=0.5773502691896257
tan31=0.6008606190275604 tan32=0.6248693519093275 tan33=0.6494075931975104
tan34=0.6745085168424265 tan35=0.7002075382097097 tan36=0.7265425280053609
tan37=0.7535540501027942 tan38=0.7812856265067174 tan39=0.8097840331950072
tan40=0.8390996311772799 tan41=0.8692867378162267 tan42=0.9004040442978399
tan43=0.9325150861376618 tan44=0.9656887748070739 tan45=0.9999999999999999
tan46=1.0355303137905693 tan47=1.0723687100246826 tan48=1.1106125148291927
tan49=1.1503684072210092 tan50=1.19175359259421 tan51=1.234897156535051
tan52=1.2799416321930785 tan53=1.3270448216204098 tan54=1.3763819204711733
tan55=1.4281480067421144 tan56=1.4825609685127403 tan57=1.5398649638145827
tan58=1.6003345290410506 tan59=1.6642794823505173 tan60=1.7320508075688767
tan61=1.8040477552714235 tan62=1.8807264653463318 tan63=1.9626105055051503
tan64=2.050303841579296 tan65=2.1445069205095586 tan66=2.246036773904215
tan67=2.355852365823753 tan68=2.4750868534162946 tan69=2.6050890646938023
tan70=2.7474774194546216 tan71=2.904210877675822 tan72=3.0776835371752526
tan73=3.2708526184841404 tan74=3.4874144438409087 tan75=3.7320508075688776
tan76=4.0107809335358455 tan77=4.331475874284153 tan78=4.704630109478456
tan79=5.144554015970307 tan80=5.671281819617707 tan81=6.313751514675041
tan82=7.115369722384207 tan83=8.144346427974593 tan84=9.514364454222587
tan85=11.43005230276132 tan86=14.300666256711942 tan87=19.08113668772816
tan88=28.636253282915515 tan89=57.289961630759144
tan90=无取值范围
}