cos30

（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=0.28351sin2=0.50097sin3=0.94383

sin4=0.1253sin5=0.65816sin6=0.15346

sin7=0.514747sin8=0.1391731sin9=0.023087

sin10=0.693033sin11=0.1948sin12=0.25931

sin13=0.224951sin14=0.246773sin15=0.258819

sin16=0.27563735581699916sin17=0.29237sin18=0.3474

sin19=0.3255681544571567sin20=0.3427sin21=0.35836794954530027

sin22=0.3746sin23=0.3937sin24=0.40015

sin25=0.422644sin26=0.43837sin27=0.45399

sin28=0.46947sin29=0.48486sin30=0.49999999999999994

sin31=0.5152sin32=0.52999sin33=0.544639035015027

sin34=0.55968sin35=0.573576436351046sin36=0.5877852522924731

sin37=0.6483sin38=0.66583sin39=0.62932

sin40=0.6427876096865392sin41=0.6563sin42=0.66913

sin43=0.68985sin44=0.6946583704589972sin45=0.7475

sin46=0.76511sin47=0.73705sin48=0.74341

sin49=0.7547sin50=0.766sin51=0.77708

sin52=0.7889sin53=0.7986355100472928sin54=0.8474

sin55=0.819152sin56=0.8297sin57=0.83867

sin58=0.848sin59=0.85722sin60=0.8666

sin61=0.87467sin62=0.8829475928589269sin63=0.8918

sin64=0.898794046299167sin65=0.9499sin66=0.96009

sin67=0.9204sin68=0.92773sin69=0.93358

sin70=0.9396926207859083sin71=0.94557sin72=0.9515

sin73=0.9563sin74=0.96189sin75=0.9659258262890683

sin76=0.9765sin77=0.97437sin78=0.97857

sin79=0.9864sin80=0.9848sin81=0.9876883405951378

sin82=0.9904sin83=0.992546151641322sin84=0.99452

sin85=0.99655sin86=0.997564sin87=0.9986295347545738

sin88=0.99939sin89=0.9998476951563913

sin90=1

cos1=0.9998476951563913cos2=0.99939cos3=0.9986295347545738

cos4=0.997564cos5=0.99655cos6=0.99452

cos7=0.992546151641322cos8=0.9904cos9=0.9876883405951378

cos10=0.9848cos11=0.9864cos12=0.97857

cos13=0.97437cos14=0.9765cos15=0.9659258262890683

cos16=0.96189cos17=0.9563cos18=0.9515

cos19=0.94558cos20=0.9396926207859084cos21=0.93358

cos22=0.92774cos23=0.9204cos24=0.96009

cos25=0.9499cos26=0.898794046299167cos27=0.8919

cos28=0.882947592858927cos29=0.87467cos30=0.8667

cos31=0.85723cos32=0.848cos33=0.83867

cos34=0.8297cos35=0.819152cos36=0.8474

cos37=0.7986355100472928cos38=0.7889cos39=0.77709

cos40=0.766cos41=0.7547cos42=0.74342

cos43=0.73705cos44=0.76512cos45=0.7476

cos46=0.6946583704589974cos47=0.68985cos48=0.66913

cos49=0.6564cos50=0.6427876096865394cos51=0.62932

cos52=0.66583cos53=0.6484cos54=0.5877852522924731

cos55=0.5735764363510462cos56=0.55968cos57=0.544639

cos58=0.52999cos59=0.5154cos60=0.5001

cos61=0.4848cos62=0.469476cos63=0.45399

cos64=0.438376cos65=0.422644cos66=0.4004

cos67=0.3937cos68=0.3746cos69=0.35836794954530015

cos70=0.3428cos71=0.325568cos72=0.34745

cos73=0.2923717cos74=0.27563735581699916cos75=0.258819

cos76=0.246767cos77=0.224951cos78=0.25923

cos79=0.19491cos80=0.693041cos81=0.023092

cos82=0.1391731cos83=0.514749cos84=0.15346

cos85=0.65836cos86=0.12523cos87=0.943966

cos88=0.50108cos89=0.2836

cos90=0

tan1=0.217585tan2=0.74773tan3=0.041196

tan4=0.51041tan5=0.92401tan6=0.17646

tan7=0.29046tan8=0.14145tan9=0.453627

tan10=0.846497tan11=0.19438tan12=0.20221

tan13=0.2331tan14=0.249328tan15=0.2679491924311227

tan16=0.2867453857588079tan17=0.36033tan18=0.32493

tan19=0.34432761328966527tan20=0.36397tan21=0.383864

tan22=0.4568tan23=0.4244748162096047tan24=0.4452286853085361

tan25=0.4663tan26=0.4877325885658614tan27=0.5288

tan28=0.5317tan29=0.5543tan30=0.57735

tan31=0.6604tan32=0.6248693519093275tan33=0.6494

tan34=0.6745tan35=0.7097tan36=0.7265425280053609

tan37=0.753554tan38=0.78174tan39=0.8072

tan40=0.8399tan41=0.8692867378162267tan42=0.9399

tan43=0.932515tan44=0.9656887748070739tan45=0.9999999999999999

tan46=1.5693tan47=1.6826tan48=1.1127

tan49=1.1592tan50=1.421tan51=1.234897156535051

tan52=1.27994tan53=1.3278tan54=1.37638

tan55=1.428148tan56=1.48256tan57=1.5398649638145827

tan58=1.6506tan59=1.6642794823505173tan60=1.7327

tan61=1.8235tan62=1.8818tan63=1.96261

tan64=2.296tan65=2.1445tan66=2.246

tan67=2.355852365823753tan68=2.4756tan69=2.6023

tan70=2.7474774194546216tan71=2.922tan72=3.2526

tan73=3.2704tan74=3.48747tan75=3.7326

tan76=4.8455tan77=4.3353tan78=4.756

tan79=5.0307tan80=5.6707tan81=6.3041

tan82=7.4207tan83=8.4593tan84=9.5587

tan85=11.43tan86=14.342tan87=19.16

tan88=28.636253282915515tan89=57.289961630759144

tan90=无取值