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