数学 百分网手机站

最常用三角函数值盘点

时间:2017-10-11 数学 我要投稿

  利用特殊角的三角函数值去求未知角的三角函数是高考中常见题型,本文是小编整理最常用三角函数值的资料,仅供参考。

  最常用三角函数值

  特殊角的三角函数

  角度a 0° 30° 45° 60° 90° 120° 180°

  1.sina 0 1/2 √2/2 √3/2 1 √3/2 0

  2.cosa 1 √3/2 √2/2 1/2 0 -1/2 -1

  3.tana 0 √3/3 1 √3 无限大 -√3 0

  4.cota / √3 1 √3/3 0 -√3/3 /

  函数名 正弦 余弦 正切 余切 正割 余割

  在平面直角坐标系xOy中,从点O引出一条射线OP,设旋转角为θ,设OP=r,P点的坐标为(x,y)有

  正弦函数 sinθ=y/r

  余弦函数 cosθ=x/r

  正切函数 tanθ=y/x

  余切函数 cotθ=x/y

  正割函数 secθ=r/x

  余割函数 cscθ=r/y

  正弦(sin):角α的对边比上斜边

  余弦(cos):角α的邻边比上斜边

  正切(tan):角α的对边比上邻边

  余切(cot):角α的邻边比上对边

  正割(sec):角α的斜边比上邻边

  余割(csc):角α的斜边比上对边

  三角函数值(附三角函数值表)

  (1)特殊角三角函数值

  sin0=0

  sin30=0.5

  sin45=0.7071 二分之根号2

  sin60=0.8660 二分之根号3

  sin90=1

  cos0=1

  cos30=0.866025404 二分之根号3

  cos45=0.707106781 二分之根号2

  cos60=0.5

  cos90=0

  tan0=0

  tan30=0.577350269 三分之根号3

  tan45=1

  tan60=1.732050808 根号3

  tan90=无

  cot0=无

  cot30=1.732050808 根号3

  cot45=1

  cot60=0.577350269 三分之根号3

  cot90=0

  (2)0°~90°的任意角的三角函数值,查三角函数表。(见下)

  (3)锐角三角函数值的变化情况

  (i)锐角三角函数值都是正值

  (ii)当角度在0°~90°间变化时,

  正弦值随着角度的增大(或减小)而增大(或减小)

  余弦值随着角度的增大(或减小)而减小(或增大)

  正切值随着角度的增大(或减小)而增大(或减小)

  余切值随着角度的增大(或减小)而减小(或增大)

  (iii)当角度在0°≤α≤90°间变化时,

  0≤sinα≤1, 1≥cosα≥0,

  当角度在0°<α<90°间变化时,

  tanα>0, cotα>0.

  “锐角三角函数”属于三角学,是《数学课程标准》中“空间与图形”领域的重要内容。从《数学课程标准》看,中学数学把三角学内容分成两个部分,第一部分放在义务教育第三学段,第二部分放在高中阶段。在义务教育第三学段,主要研究锐角三角函数和解直角三角形的内容,本套教科书安排了一章的内容,就是本章“锐角三角函数”。在高中阶段的三角内容是三角学的主体部分,包括解斜三角形、三角函数、反三角函数和简单的三角方程。无论是从内容上看,还是从思考问题的方法上看,前一部分都是后一部分的重要基础,掌握锐角三角函数的概念和解直角三角形的方法,是学习三角函数和解斜三角形的重要准备。

  附:三角函数值表

  sin0=0,

  sin15=(√6-√2)/4 ,

  sin30=1/2,

  sin45=√2/2,

  sin60=√3/2,

  sin75=(√6+√2)/2 ,

  sin90=1,

  sin105=√2/2*(√3/2+1/2)

  sin120=√3/2

  sin135=√2/2

  sin150=1/2

  sin165=(√6-√2)/4

  sin180=0

  sin270=-1

  sin360=0

  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

猜你喜欢:

1.特殊角度三角函数值表

2.高考数学解题技巧之常用公式

3.高考数学复习资料填空题答题方法

4.2018数学高考知识点

5.初三数学教学反思二(精选3篇)

6.2017广东高考数学诱导公式记忆口诀

7.教学反思集(2)数学(精选3篇)

博聚网