如图,四边形ABCD为矩形,AB=4,AD=3,动点M、N分别从D、B同时出发,以1个单位/秒的速度运动,点M沿DA向终点A运动,点N沿BC向终点C运动,过点N作NP⊥BC,交AC于点P,连接MP,-九年级数学

  • 等腰三角形的判定:
    1.定义法:在同一三角形中,有两条边相等的三角形是等腰三角形。
    2.判定定理:在同一三角形中,有两个角相等的三角形是等腰三角形(简称:等角对等边)。
    3.顶角的平分线,底边上的中分线,底边上的高的重合的三角形是等腰三角形。

  • 考点名称:解直角三角形

    • 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=0.01745240643728351 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

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