标题：三角函数值
应用
三角函数在复数中有较为重要的应用。在物理学中，三角函数也是常用的工具。 
它有六种基本函数： 
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 
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
三角函数值表
sin0=sin0°=0 
cos0=cos0°=1
tan0=tan0°=0
sin15=0.65028784015711686582974027098887；sin15°=（√6-√2）/4 
cos15=-0.75968791285882127384814640363328；cos15°=（√6+√2）/4 
tan15=-0.85599340090851876402619277823803；tan15°=2-√3 
sin30=-0.98803162409286178998774890729446；sin30°=1/2
cos30=0.15425144988758405071866214661421；cos30°=√3/2 
tan30=-6.405331196646275784896075505668；tan30°=√3/3 
sin45=0.85090352453411842486237967761804；sin45°=√2/2
cos45=0.52532198881772969604746440482356；cos45°=sin45°=√2/2
tan45=1.6197751905438615499827965173949；tan45°=1 
sin60=-0.30481062110221670562564946547843；sin60°=√3/2 
cos60=-0.95241298041515629269381659599293；cos60°=1/2
tan60=0.32004038937956297493818761970571；tan60°=√3
sin75=-0.38778163540943043773094219282288；sin75°=cos15°
cos75=0.92175126972474931639229684521414；cos75°=sin15°
tan75=-0.42070095062112435384419621180484；tan75°=sin75°/cos75° =2+√3 
sin90=0.89399666360055789051826949840421；sin90°=cos0°=1
cos90=-0.44807361612917015236547731439964；cos90°=sin0°=0
tan90=-1.9952004122082420252873530763796；tan90°不存在
sin105=-0.9705352835374847209338032056452；sin105°=cos15°
cos105=-0.24095904923620141814219566395281；cos105°=-sin15°
tan105=4.0278017638844193492341772197301；tan105°=-cot15°
sin120=0.58061118421231428928240695979069；sin120°=cos30°
cos120=0.81418097052656176790578986177889；cos120°=-sin30°
tan120=0.71312300978590911614556745464875；tan120°=-tan60°
sin135=0.088368686104001433036970666416798；sin135°=sin45°
cos135=-0.99608783514118495835764440142782；cos135°=-cos45°
tan135=-0.088715756770060446136984268003075；tan135°=-tan45°
sin150=-0.71487642962916463143638609739663；sin150°=sin30°
cos150=0.69925080647837513141645161882553；cos150°=-cos30°
tan150=-1.0223462354365875649863661852619；tan150°=-tan30°
sin165=0.99779727944989076515961268295525；sin165°=sin15°
cos165=-0.066336936335623731837538732255201；cos165°=-cos15°
tan165=-15.041353046538895371867886988769；tan165°=-tan15°
sin180=-0.80115263573383047774673111582099；sin180°=sin0°=0
cos180=-0.5984600690578581389679486481597；cos180°=-cos0°=-1
tan180=1.3386902103511543616808987449579；tan180°=0 
sin195=0.21945466799406361597859718309894；sin195°=-sin15°
cos195=0.97562269791944432311811100484535；cos195°=-cos15°
tan195=0.22493805080802215296340937063051；tan195°=tan15°
sin360=0.95891572341430650775887594775378；sin360°=sin0°=0
cos360=-0.28369109148652733463742432444589；cos360°=cos0°=1
tan360=-3.3801404139609579824775356112668；tan360°=tan0°=0
cos72=[(√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 
cos90=0 
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
数学方程式
数关系tanα ·cotα=1 
sinα ·cscα=1 
cosα ·secα=1
商数关系tanα=sinα/cosα cotα=cosα/sinα
平方关系sinα&sup2;+cosα&sup2;=1 
1+tanα&sup2;=secα&sup2; 
1+cotα&sup2=cscα&sup2; 
以下关系，函数名不变，图像看象限. 
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
积化合差公式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sin α+sinβ=2sin[(α+β)/2]·cos[(α-β)/2]
sin α-sin β=2cos[(α+β)/2]·sin[(α-β)/2]
cos α+cos β=2cos[(α+β)/2]·cos[(α-β)/2]
cos α-cos β=-2sin[(α+β)/2]·sin[(α-β)/2]
三倍角公式sin3α=3sinα-4sinα&sup3; 
cos3α=4cosα&sup3;-3cosα
两角和与差的三角函数关系
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)
正弦二倍角公式：sin2α = 2cosαsinα 
推导：sin2A=sin(A+A)=sinAcosA+cosAsinA=2sinAcosA 
拓展公式：sin2A=2sinAcosA=2tanAcos^2A=2tanA/[1+tan^2A] 
1+sin2A=(sinA+cosA)^2
余弦二倍角公式：余弦二倍角公式有三组表示形式，三组形式等价： 
1.Cos2a=Cos^2a-Sin^2a=[1-tan^2a]/[1+tan^2a] 
2.Cos2a=1-2Sin^2a 
3.Cos2a=2Cos^2a-1 
推导：cos2A=cos(A+A)=cosAcosA-sinAsinA=cos^2A-sin^2A=2cos^2A-1 
=1-2sin^2A
正切二倍角公式：tan2α=2tanα/[1-tan^2α] 
推导：tan2A=tan(A+A)=(tanA+tanA)/(1-tanAtanA)=2tanA/[1-tan^2A]
降幂公式：cosA^2=[1+cos2A]/2 
sinA^2=[1-cos2A]/2 
tanA^2=[1-cos2A]/[1+cos2A] 
变式：
sin2α=sin^2(α+π/4)-cos^2(α+π/4)=2sin^2(a+π/4)-1=1-2cos^2(α+π/4);　cos2α=2sin(α+π/4)cos(α+π/4)
余弦定理：　
a^2=b^2+c^2-2bc cosA
b^2=c^2+a^2-2ca cosB
c^2=a^2+b^2-2ab cosC