初中三角函数详细数值表.docx

初中三角函数详细数值表.docx

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初中三角函数详细数值表

初中三角函数详细数值表

本篇是关于初中三角函数的速记与理解，皆来自于课本与网络，所以免费。

欢迎曾经与我一样不理解的初学者观阅~~~~~

本品仅用于学习交流，谢绝转载。

首先，我们先理解基础概念，如下：

SinA=

CosA=

TanA=

CotA=

还有一点很重要，

0

0

根据三角函数的定义，我们还可以得出

ＳｉｎＡ＊２＋ＣｏｓＡ＊２＝１

ＴａｎＡ　·　ＣｏｔＡ＝１

ＴａｎＡ＝ＳｉｎＡ／ＣｏｓＡ

ＣｏｔＡ＝ＣｏｓＡ／ＳｉｎＡ

ＴａｎＡ＝１／ＣｏｔＡ

sinA=cos（90-A）

tanA=cotA（90-A）

此为必背图表

　　角度

三角函数

０度

３０度

４５度

６０度

９０度

ｓｉｎ

０

１／２

１

ｃｏｓ

１

１／２

０

ｔａｎ

０

１

――

ｃｏｔ

――

１

０

相对应的示意图见下页～～～～～～～～～～～～～～～～～

＜Ａ＝３０度

＜Ａ＝４５度

＜Ａ＝６０度

如何用计算器计算函数值

（1）　求已知锐角的三角函数值

求sin63°52′41″的值．（精确到0．0001）

先用如下方法将角度单位状态设定为“度”：

SHIFT　MODE（SETUP）３　　显示Ｄ

依次键入　sin　　63　°　52　′　41　″　＝

得到结果；

求cot70°45′的值．（精确到0．0001）

在角度单位状态为“度”的情况下（屏幕显示），

按下列顺序依次按键：

１　÷　cot　　70　°　45　　′　＝　　

得到结果

（2）　由锐角三角函数值求锐角

已知tanx＝0．7410，求锐角x．（精确到1′）

在角度单位状态为“度”的情况下（屏幕显示），

按下列顺序依次按键：

SHIFT　tan　　（

）0　　·　７４１　＝　０

得到结果

再次键入　SHIFT　　o’’’　　　　完成

接下来如标题示，整理好的三角函数表

sin15=（√6-√2）/4,

sin75=（√6+√2）/2,

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

（上为特殊值）

sin1=0.01745

sin2=0.034899

sin3=0.052335

sin4=0.069756

sin5=0.087155

sin6=0.104528　

sin7=0.121869

sin8=0.139173

sin9=0.156434　　

sin10=0.17364

sin11=0.19080

sin12=0.20791　　

sin13=0.22495

sin14=0.24192

sin15=0.25881　

sin16=0.27563

sin17=0.29237

sin18=0.30901

sin19=0.32556

sin20=0.34202

sin21=0.35836　

sin22=0.37460

sin23=0.39073

sin24=0.40673　　

sin25=0.42261

sin26=0.43837

sin27=0.45399　　

sin28=0.46947

sin29=0.48480

sin30=0.49999　

sin31=0.51503

sin32=0.52991

sin33=0.54463　　

sin34=0.55919

sin35=0.57357

sin36=0.58778　

sin37=0.60181

sin38=0.61566

sin39=0.62932

sin40=0.64278

sin41=0.65605

sin42=0.66913　　

sin43=0.68199

sin44=0.69465

sin45=0.70710　　

sin46=0.71933

sin47=0.73135

sin48=0.74314　　

sin49=0.75470

sin50=0.76604

sin51=0.77714　

sin52=0.78801

sin53=0.79863

sin54=0.80901

sin55=0.81915

sin56=0.82903

sin57=0.83867

sin58=0.84804

sin59=0.85716

sin60=0.86602　

sin61=0.87461

sin62=0.88294

sin63=0.89100　　

sin64=0.89879

sin65=0.90630

sin66=0.91354　

sin67=0.92050

sin68=0.92718

sin69=0.93358

sin70=0.93969

sin71=0.94551

sin72=0.95105　　

sin73=0.95630

sin74=0.96126

sin75=0.96592　

sin76=0.97029

sin77=0.97437

sin78=0.97814　

sin79=0.98162

sin80=0.98480

sin81=0.98768　

sin82=0.99026

sin83=0.99254

sin84=0.99452　

sin85=0.99619

sin86=0.99756

sin87=0.99862　

sin88=0.99939

sin89=0.99984

sin90=1　　

cos1=0.99984

cos2=0.99939

cos3=0.99862　

cos4=0.99756

cos5=0.99619

cos6=0.99452

cos7=0.99254

cos8=0.99026

cos9=0.98768　

cos10=0.9848

cos11=0.9816

cos12=0.97814　　

cos13=0.9743

cos14=0.9702

cos15=0.9659　

cos16=0.9612

cos17=0.9563

cos18=0.9510　

cos19=0.9455

cos20=0.9396

cos21=0.9335　

cos22=0.9271

cos23=0.9205

cos24=0.9135

cos25=0.9063

cos26=0.8987

cos27=0.8910　　

cos28=0.8829

cos29=0.8746

cos30=0.8660　

cos31=0.8571

cos32=0.8480

cos33=0.8386　

cos34=0.8290

cos35=0.8191

cos36=0.8090　

cos37=0.7986

cos38=0.7880

cos39=0.7771　

cos40=0.7660

cos41=0.7547

cos42=0.7431

cos43=0.7313

cos44=0.7193

cos45=0.7071

cos46=0.6946

cos47=0.6819

cos48=0.6691

cos49=0.6560

cos50=0.6427

cos51=0.6293

cos52=0.6156

cos53=0.6018

cos54=0.5877　

cos55=0.5735

cos56=0.5592

cos57=0.5446　　

cos58=0.5299

cos59=0.5150

cos60=0.5000　

cos61=0.4848

cos62=0.4694

cos63=0.4539

cos64=0.4383

cos65=0.4226

cos66=0.4067

cos67=0.3907

cos68=0.3746

cos69=0.3583

cos70=0.3420

cos71=0.3255

cos72=0.3090　

cos73=0.2923

cos74=0.2756

cos75=0.2588

cos76=0.2419

cos77=0.2249

cos78=0.2079

cos79=0.1908

cos80=0.1736

cos81=0.1564　

cos82=0.1391

cos83=0.1218

cos84=0.1045

cos85=0.0871

cos86=0.06973

cos87=0.052　

cos88=0.0348

cos89=0.0174

cos90=0　　

tan1=0.017455

tan2=0.034920

tan3=0.052407　　

tan4=0.069926

tan5=0.087488

tan6=0.105104　

tan7=0.122784

tan8=0.140540

tan9=0.158384　

tan10=0.17632

tan11=0.19438

tan12=0.21255　　

tan13=0.23086

tan14=0.24932

tan15=0.26794　　

tan16=0.28674

tan17=0.30573

tan18=0.32491　　

tan19=0.34432

tan20=0.36397

tan21=0.38386　

tan22=0.40402

tan23=0.42447

tan24=0.44522　

tan25=0.46630

tan26=0.48773

an27=0.50952　　

tan28=0.53170

tan29=0.55430

tan30=0.57735　

tan31=0.60086

tan32=0.62486

tan33=0.64940　

tan34=0.67450

tan35=0.70020

tan36=0.72654

tan37=0.75355

tan38=0.78128

tan39=0.80978　

tan40=0.83909

tan41=0.86928

tan42=0.90040　

tan43=0.93251

tan44=0.96568

tan45=0.99999

tan46=1.03553

tan47=1.07236

tan48=1.11061　　

tan49=1.15036

tan50=1.19175

tan51=1.23489　　

tan52=1.27994

tan53=1.32704

tan54=1.3763

tan55=1.42814

tan56=1.48256

tan57=1.53986　

tan58=1.60033

tan59=1.66427

tan60=1.73205

tan61=1.80404

tan62=1.88072

tan63=1.96261

tan64=2.05030

tan65=2.14450

tan66=2.24603　　

tan67=2.35585

tan68=2.47508

tan69=2.60508　

tan70=2.74747

tan71=2.90421

tan72=3.07768

tan73=3.27085

tan74=3.48741

tan75=3.73205　

tan76=4.01078

tan77=4.33147

tan78=4.70463　

tan79=5.14455

tan80=5.67128

tan81=6.31375

tan82=7.11536

tan83=8.14434

tan84=9.51436

tan85=11.4300

tan86=14.3006

tan87=19.0811　

tan88=28.6362

tan89=57.2899

tan90=无取值

如果求精确度的话，还可以看下面

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=0.0174524064372