如图所示,已知:点A(0,0),B(3,0),C(0,1)在△ABC内依次作等边三角形,使一边在x轴上,另一个顶点在BC边上,作出的等边三角形分别是第1个△AA1B1,第2个△B1A2B2,第3个△B2A-数学

首页 > 考试 > 数学 > 初中数学 > 等边三角形/2020-05-20 / 加入收藏 / 阅读 [打印]

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=0.01745240643728351 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

    • 最新内容
    • 相关内容
    • 网友推荐
    • 图文推荐