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把一块含45°的直角三角板ODE放在如图所示的直角坐标系中,已知动点P在斜边OD上运动,点A的坐标为(0,2),当线段AP最短时,则点P的坐标为()A.(0,0)B.(22,22)C.(12,12)D.(1-数学

[db:作者]  2020-01-06 00:00:00  零零社区

题文

把一块含45°的直角三角板ODE放在如图所示的直角坐标系中,已知动点P在斜边OD上运动,点A的坐标为(0,),当线段AP最短时,则点P的坐标为(  )
A.(0,0) B.( C.() D.()

题型:单选题  难度:偏易

答案

B

据专家权威分析,试题“把一块含45°的直角三角板ODE放在如图所示的直角坐标系中,已知动..”主要考查你对  垂直的判定与性质,解直角三角形,用坐标表示位置  等考点的理解。关于这些考点的“档案”如下:

垂直的判定与性质解直角三角形用坐标表示位置

考点名称:垂直的判定与性质

  • 垂线的定义:
    两条直线相交所成的四个角中,有一个角是直角时,就说这两条直线互相垂直。其中一条直线叫做另一条直线的垂线,它们的交点叫做垂足。
    直线AB,CD互相垂直,记作“AB⊥CD”(或“CD⊥AB”),读作“AB垂直于CD”(或“CD垂直于AB”)。
    垂线的性质:
    性质1:过一点有且只有一条直线与已知直线垂直。
    性质2:连结直线外一点与直线上各点的所有线段中,垂线段最短。简称:垂线段最短。
    垂直的判定:垂线的定义。

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
    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
    tan70=2.7474774194546216 tan71=2.904210877675822 tan72=3.0776835371752526
    tan73=3.2708526184841404 tan74=3.4874144438409087 tan75=3.7320508075688776
    tan76=4.0107809335358455 tan77=4.331475874284153 tan78=4.704630109478456
    tan79=5.144554015970307 tan80=5.671281819617707 tan81=6.313751514675041
    tan82=7.115369722384207 tan83=8.144346427974593 tan84=9.514364454222587
    tan85=11.43005230276132 tan86=14.300666256711942 tan87=19.08113668772816
    tan88=28.636253282915515 tan89=57.289961630759144
    tan90=(无限)

考点名称:用坐标表示位置

  • 点的坐标的概念:
    点的坐标用(a,b)表示,其顺序是横坐标在前,纵坐标在后,中间有“,”分开,横、纵坐标的位置不能颠倒。
    平面内点的坐标是有序实数对,当a≠b时,(a,b)和(b,a)是两个不同点的坐标。

  • 各象限内点的坐标的特征 :
    点P(x,y)在第一象限;点P(x,y)在第二象限
    点P(x,y)在第三象限;点P(x,y)在第四象限

    坐标轴上的点的特征:
    点P(x,y)在x轴上y=0,x为任意实数
    点P(x,y)在y轴上x=0,y为任意实数
    点P(x,y)既在x轴上,又在y轴上x,y同时为零,即点P坐标为(0,0)。

    点P(x,y)到坐标轴及原点的距离:
    (1)点P(x,y)到x轴的距离等于|y|;
    (2)点P(x,y)到y轴的距离等于|x|;
    (3)点P(x,y)到原点的距离等于

  • 坐标表示位置步骤:
    利用平面直角坐标系绘制区域内一些地点分布情况的平面图的过程如下:
    (1)建立坐标系,选择一个适当的参照点为原点,确定X轴、y轴的正方向;
    (2)根据具体问题确定适当的比例尺,在坐标轴上标出单位长度;
    (3)在坐标平面内画出这些点,写出各点的坐标和各个地点的名称。



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