解直角三角形的函数值列举2.docx
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解直角三角形的函数值列举2.docx
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解直角三角形的函数值列举2
∙
概念:
在直角三角形中,除直角外,一共有五个元素,即三条边和两个锐角,由直角三角形中除直角外的已知元素,求出所有未知元素的过程叫做解直角三角形。
解直角三角形的边角关系:
在Rt△ABC中,∠C=90°,∠A,∠B,∠C所对的边分别为a,b,c,
(1)三边之间的关系:
(勾股定理);
(2)锐角之间的关系:
∠A+∠B=90°;
(3)边角之间的关系:
。
∙解直角三角形的函数值:
锐角三角函数:
sinA=a/c,cosA=b/c,tanA=a/b,cotA=b/a
(1)互余角的三角函数值之间的关系:
若∠A+∠B=90°,那么sinA=cosB或sinB=cosA
(2)同角的三角函数值之间的关系:
①sin2A+cos2A=1
②tanA=sinA/cosA
③tanA=1/tanB
④a/sinA=b/sinB=c/sinC
(3)锐角三角函数随角度的变化规律:
锐角∠A的tan值和sin值随着角度的增大而增大,cos值随着角度的增大而减小。
∙解直角三角形的应用:
一般步骤是:
(1)将实际问题抽象为数学问题(画图,转化为直角三角形的问题);
(2)根据题目的条件,适当选择锐角三角函数等去解三角形;
(3)得到数学问题的答案;
(4)还原为实际问题的答案。
∙解直角三角形的函数值列举:
sin1=0.01745240643728351sin2=0.03489949670250097sin3=0.05233595624294383
sin4=0.0697564737441253sin5=0.08715574274765816sin6=0.10452846326765346
sin7=0.12186934340514747sin8=0.139********006544sin9=0.156********023087
sin10=0.173********693033sin11=0.1908089953765448sin12=0.20791169081775931
sin13=0.22495105434386497sin14=0.24192189559966773sin15=0.25881904510252074
sin16=0.27563735581699916sin17=0.2923717047227367sin18=0.3090169943749474
sin19=0.3255681544571567sin20=0.3420201433256687sin21=0.35836794954530027
sin22=0.374606593415912sin23=0.3907311284892737sin24=0.40673664307580015
sin25=0.42261826174069944sin26=0.4383711467890774sin27=0.45399049973954675
sin28=0.4694715627858908sin29=0.48480962024633706sin30=0.49999999999999994
sin31=0.5150380749100542sin32=0.5299192642332049sin33=0.544639035015027
sin34=0.5591929034707468sin35=0.573576436351046sin36=0.5877852522924731
sin37=0.6018150231520483sin38=0.6156614753256583sin39=0.6293203910498375
sin40=0.6427876096865392sin41=0.6560590289905073sin42=0.6691306063588582
sin43=0.6819983600624985sin44=0.6946583704589972sin45=0.7071067811865475
sin46=0.7193398003386511sin47=0.7313537016191705sin48=0.7431448254773941
sin49=0.7547095802227719sin50=0.766044443118978sin51=0.7771459614569708
sin52=0.7880107536067219sin53=0.7986355100472928sin54=0.8090169943749474
sin55=0.8191520442889918sin56=0.8290375725550417sin57=0.8386705679454239
sin58=0.848048096156426sin59=0.8571673007021122sin60=0.8660254037844386
sin61=0.8746197071393957sin62=0.8829475928589269sin63=0.8910065241883678
sin64=0.898794046299167sin65=0.9063077870366499sin66=0.9135454576426009
sin67=0.9205048534524404sin68=0.9271838545667873sin69=0.9335804264972017
sin70=0.9396926207859083sin71=0.9455185755993167sin72=0.9510565162951535
sin73=0.9563047559630354sin74=0.9612616959383189sin75=0.9659258262890683
sin76=0.9702957262759965sin77=0.9743700647852352sin78=0.9781476007338057
sin79=0.981627183447664sin80=0.984807753012208sin81=0.9876883405951378
sin82=0.9902680687415704sin83=0.992546151641322sin84=0.9945218953682733
sin85=0.9961946980917455sin86=0.9975640502598242sin87=0.9986295347545738
sin88=0.9993908270190958sin89=0.9998476951563913
sin90=1
cos1=0.9998476951563913cos2=0.9993908270190958cos3=0.9986295347545738
cos4=0.9975640502598242cos5=0.9961946980917455cos6=0.9945218953682733
cos7=0.992546151641322cos8=0.9902680687415704cos9=0.9876883405951378
cos10=0.984807753012208cos11=0.981627183447664cos12=0.9781476007338057
cos13=0.9743700647852352cos14=0.9702957262759965cos15=0.9659258262890683
cos16=0.9612616959383189cos17=0.9563047559630355cos18=0.9510565162951535
cos19=0.9455185755993168cos20=0.9396926207859084cos21=0.9335804264972017
cos22=0.9271838545667874cos23=0.9205048534524404cos24=0.9135454576426009
cos25=0.9063077870366499cos26=0.898794046299167cos27=0.8910065241883679
cos28=0.882947592858927cos29=0.8746197071393957cos30=0.8660254037844387
cos31=0.8571673007021123cos32=0.848048096156426cos33=0.838670567945424
cos34=0.8290375725550417cos35=0.8191520442889918cos36=0.8090169943749474
cos37=0.7986355100472928cos38=0.7880107536067219cos39=0.7771459614569709
cos40=0.766044443118978cos41=0.754709580222772cos42=0.7431448254773942
cos43=0.7313537016191705cos44=0.7193398003386512cos45=0.7071067811865476
cos46=0.6946583704589974cos47=0.6819983600624985cos48=0.6691306063588582
cos49=0.6560590289905074cos50=0.6427876096865394cos51=0.6293203910498375
cos52=0.6156614753256583cos53=0.6018150231520484cos54=0.5877852522924731
cos55=0.5735764363510462cos56=0.5591929034707468cos57=0.5446390350150272
cos58=0.5299192642332049cos59=0.5150380749100544cos60=0.5000000000000001
cos61=0.4848096202463371cos62=0.46947156278589086cos63=0.4539904997395468
cos64=0.43837114678907746cos65=0.42261826174069944cos66=0.4067366430758004
cos67=0.3907311284892737cos68=0.3746065934159122cos69=0.35836794954530015
cos70=0.3420201433256688cos71=0.32556815445715675cos72=0.30901699437494745
cos73=0.29237170472273677cos74=0.27563735581699916cos75=0.25881904510252074
cos76=0.24192189559966767cos77=0.22495105434386514cos78=0.20791169081775923
cos79=0.19080899537654491cos80=0.173********693041cos81=0.156********023092
cos82=0.139********006546cos83=0.12186934340514749cos84=0.10452846326765346
.0871********
cos88=0.03489949670250108cos89=0.0174524064372836
cos90=0
tan1=0.017455064928217585tan2=0.03492076949174773tan3=0.052407779283041196
tan4=0.06992681194351041tan5=0.08748866352592401tan6=0.10510423526567646
tan7=0.122784*********6tan8=0.14054083470239145tan9=0.158********453627
tan10=0.176********846497tan11=0.19438030913771848tan12=0.2125565616700221
tan13=0.230868*********1tan14=0.24932800284318068tan15=0.2679491924311227
tan16=0.2867453857588079tan17=0.30573068145866033tan18=0.3249196962329063
tan19=0.34432761328966527tan20=0.36397023426620234tan21=0.3838640350354158
tan22=0.4040262258351568tan23=0.4244748162096047tan24=0.4452286853085361
tan25=0.4663076581549986tan26=0.4877325885658614tan27=0.5095254494944288
tan28=0.5317094316614788tan29=0.554309051452769tan30=0.5773502691896257
tan31=0.6008606190275604tan32=0.6248693519093275tan33=0.6494075931975104
tan34=0.6745085168424265tan35=0.7002075382097097tan36=0.7265425280053609
tan37=0.7535540501027942tan38=0.7812856265067174tan39=0.8097840331950072
tan40=0.8390996311772799tan41=0.8692867378162267tan42=0.9004040442978399
tan43=0.9325150861376618tan44=0.9656887748070739tan45=0.9999999999999999
.0355********
tan49=1.150********10092tan50=1.19175359259421tan51=1.234897156535051
tan52=1.2799416321930785tan53=1.3270448216204098tan54=1.3763819204711733
tan55=1.4281480067421144tan56=1.4825609685127403tan57=1.5398649638145827
tan58=1.6003345290410506tan59=1.6642794823505173tan60=1.7320508075688767
tan61=1.8040477552714235tan62=1.8807264653463318tan63=1.9626105055051503
tan64=2.050303841579296tan65=2.144506*********6tan66=2.246036773904215
tan67=2.355852365823753tan68=2.4750868534162946tan69=2.6050890646938023
tan70=2.7474774194546216tan71=2.904210877675822tan72=3.0776835371752526
tan73=3.2708526184841404tan74=3.4874144438409087tan75=3.7320508075688776
.010*********
tan79=5.144554015970307tan80=5.671281819617707tan81=6.313751514675041
tan82=7.115369722384207tan83=8.144346427974593tan84=9.514364454222587
tan85=11.43005230276132tan86=14.300666256711942tan87=19.08113668772816
tan88=28.636253282915515tan89=57.289961630759144
tan90=(无限)
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- 直角三角形 函数 列举