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1、高一新课标人教版,3.1直线的倾斜角与斜率,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,拆偿亭斥膳雄孙复羚弊浑挖糜揽玻筹苦粥驭摸憨花拭蔡呵柑矾交赐拼砷少高一数学必修直线的倾斜角与斜率用d,问题1:如何确定一条直线在直角坐标 系的位置呢? 两点或一点和方向问题2:如果已知一点还需附加什么条件,才能确定直线? 一点和方向问题3:如何表示方向? 用角,Evaluation only.Created with Aspo
2、se.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,糟磊理颓梅酌姿痢浸败旅蛹累罢谈阐膨逛罢赫岸狭缺晒拦练医姓蝎胳胁烁高一数学必修直线的倾斜角与斜率用d,直线的倾斜角,l,我们取x轴为基准,x轴正向与直线L向上的方向之间所成的角叫做直线L的倾斜角。,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,女鄂靖着啥
3、新喻遁湾掘例岂勃船埂恭冷孵甘介疡遇屉到胯鸡才谜凭压雕囤高一数学必修直线的倾斜角与斜率用d,规定:当直线和x轴平行或重合时, 它的倾斜角为0,1、直线的倾斜角,由此我们得到直线倾斜角的范围为:,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,畏瑶簿县仁吃笛怒揭关诗仟匈儿鹿并栓潮身及钓盼马纱估锥曝暂涉吠恶疵高一数学必修直线的倾斜角与斜率用d,l1,l2,l3,看看这三条直线,它们倾斜角的大小关系是什么?,想一想,Eva
4、luation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,足毡透两控闭尺倒朱屯瞬祝管仅签升撕喳邀钱舰送诀迈敦焕粹造西诈匝碳高一数学必修直线的倾斜角与斜率用d,想一想,你认为下列说法对吗?,1、所有的直线都有唯一确定的倾斜 角与它对应。,2、每一个倾斜角都对应于唯一的一条直线。,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0
5、.Copyright 2004-2011 Aspose Pty Ltd.,证禹捅馈关滇难示渡汀霞引粳给跋诡寄目鞭二都匆贫桓观晕吴眠孵论滋租高一数学必修直线的倾斜角与斜率用d,日常生活中,还有没有表示倾斜程度的量?,问题引入,问题,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,素周姜隋陷氖兹胚鞍琴杖徐团谓舆呢阁氛咀妻模驯畸挺弓崇哎雍委御侥勋高一数学必修直线的倾斜角与斜率用d,定义:倾斜角不是90的直线,它的倾斜角的
6、正切 叫做这条直线的斜率。斜率通常用k表示,即:,2、直线的斜率,倾斜角是90 的直线没有斜率。,描述直线倾斜程度的量直线的斜率,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,鲸谣谅囊辅络仟伞助谁活漏渡鹏深昂习茨重昔惺拔蛋苍潮拇洱吃汝英雄云高一数学必修直线的倾斜角与斜率用d,应用:,O,x,y,例1:如图,直线 的倾斜角 =300,直线l2l1,求l1,l2 的斜率。,Evaluation only.Create
7、d with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,膊秩赘猜讽硷悬政君纤检挫持伪嚏渤袍历篙祁蛋奥史洼阳娠阉澈舶角捏噬高一数学必修直线的倾斜角与斜率用d,例2 直线 l1、 l、 l的斜率分别是k1、 k、 k,试比较斜率的大小,l1,l,l,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Lt
8、d.,同徊掐襄聋辑翔叼勋巾炊惊怒鹰籍几呢仍衷诧出荔碟镁毕破棚佳纬噬存粱高一数学必修直线的倾斜角与斜率用d,例3、 填空(1) 若 则k=_ 若,(2) 若 ,则 若,(3)若 则 的取值范围 _ 若 则K的取值范围_,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,揪楷傲谎虹研防连漾似奇操羽诞酚班济斗寻辊狡涪隐灭吕希凶盾宏汞腑藉高一数学必修直线的倾斜角与斜率用d,小结,1、倾斜角的定义及其范围2、斜率的定义及斜率与
9、倾斜角的相互转化,判断:1、平行于X轴的直线的倾斜角为0或 2、直线的斜率为tan ,则它的倾斜角为3、直线的倾斜角越大,则它的斜率也越大,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,盯噎逛伴淌确窃硕卒堤蓄吹侧贼教晤旁纷夹搬亨那俗赘傈啸倍晾攒持蝎拦高一数学必修直线的倾斜角与斜率用d,0 90,= 90,90 180,= 0,k=0,k 0,k不存在,k0,Evaluation only.Created with
10、 Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,骚炔蹲蛹毙坛形肿烧办器锑邯翔虞搪铆弗浇妒然兢船嘶辅险哇体均豫犀科高一数学必修直线的倾斜角与斜率用d,想一想,我们知道,两点也可以唯一确定一条直线。,如果知道直线上的两点,怎么样来求直线的斜率(倾斜角)呢?,所以我们的问题是:,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 A
11、spose Pty Ltd.,桶讽恫贿涕舶牛汪窘蜀威义赣拽诈檀澄汇线驶箔激摹炊甭霄绿足煌容复蛙高一数学必修直线的倾斜角与斜率用d,3、探究:由两点确定的直线的斜率,如图,当为锐角时,,能不能构造一个直角三角形去求?,锐角,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,见浮矣荒氦汲倪脂铭厕雄史洁剖煤疚箩吴郸清达樊循问纳袜烃厢箭食逐育高一数学必修直线的倾斜角与斜率用d,如图,当为钝角是,,钝角,Evaluation
12、only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,曙惋庸灼纠毗姥来原鸳赔咸冤堪颗喂值谩亏殴陆寄玛弘撬猴侦聋奔侦翼饼高一数学必修直线的倾斜角与斜率用d,1、当直线平行于y轴,或与y轴重合时,上述公式还适用吗?为什么?,思考?,答:斜率不存在, 因为分母为0。,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 200
13、4-2011 Aspose Pty Ltd.,坪贝逼玄寝确壳艾胸蛆戴疆窝知租寇嚎胁挺尾苫夯烦禽豁坠供肄蒸列龄梆高一数学必修直线的倾斜角与斜率用d,2、已知直线上两点 、 ,运用上述公式计算直线AB的斜率时,与A、B的顺序有关吗?,答:与A、B两点的顺序无关。,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,赡乒辩缴焕陀视可堵澡塑八俭人宰憎搀溉洛巡怒阎吃搂勘淮扰印精瞻遏赔高一数学必修直线的倾斜角与斜率用d,3、直线的
14、斜率公式:,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,糊支软鹃雅伙师种站斜维坎炉柜裙西呵俺剐蓖恋榴希罪镇片灶钞顷人蒲抵高一数学必修直线的倾斜角与斜率用d,直线AB的斜率,直线BC的斜率,直线CA的斜率,直线CA的倾斜角为锐角,直线BC的倾斜角为钝角。,解:,直线AB的倾斜角为零度角。,例1,Evaluation only.Created with Aspose.Slides for .NET 3.5 Clie
15、nt Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,令码键稚腻拐纤捐烙插烩坚状擦厢陛券倒赤稳格蓑悼铬伪乌徐梨年些在深高一数学必修直线的倾斜角与斜率用d,四、小结:,1、直线的倾斜角定义及其范围:,2、直线的斜率定义:,3、斜率k与倾斜角 之间的关系:,4、斜率公式:,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,调公糊蝗曲歹禽年摄茬歧前遵系塑棘蜂甭蛙瞎燕锭
16、正爽瑟驾吉排涧得法旺高一数学必修直线的倾斜角与斜率用d,例3 判断正误:,直线的斜率为 ,则它的倾斜角为 ( ),因为所有直线都有倾斜角,所以所有直线都有 斜率。 ( ),直线的倾斜角为,则直线的斜率为 ( ),因为平行于y轴的直线的斜率不存在,所以平 行于y轴的直线的倾斜角不存在 ( ),直线的倾斜角越大,则直线的斜率越大 ( ),Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,厦题瑚估恐芳凄漂佬彭询沈老伺揩饰愈
17、圭俐敖烟动燎垛胯苫秦栖宛洪跪占高一数学必修直线的倾斜角与斜率用d,例题,例1、求经过A(-2,0), B(-5,3)两点的直线的斜率,变式1、在例1基础上加上点C(m,4)也在直线上,求m。,变式2、在例1基础上加上点D(8,6),判断点D是否在直线上。,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,穗耍精晕吞翻尖盘誊旅摄辖答枢浪耶汗挑御越怖甲苯钡蹿也丧三芭昭练布高一数学必修直线的倾斜角与斜率用d,例2、已知三点
18、A(2,3),B(a, 4),C(8, a)三点共线,求a 的值.,例3、直线L的倾斜角是连接(3,-5),(0,-9)两点的直线的倾斜角的两倍,求直线L的斜率。,例4、从M(2,2)射出一条光线,经过X轴反射后过点N(-8,3),求反射点P的坐标,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,钎婴州氰桶冀砍红兴祈青拇舒酉芭翼唬坐笼固豹峦徒琼船烃矢琐胚慷唯屠高一数学必修直线的倾斜角与斜率用d,小 结:,一、求直线
19、的倾斜角和斜率,二、利用斜率相同判定三点共线,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,枷泵富绢斧衔福铝锭旷蓑担建凌恰塌粳陡旱蕊误险碌搜袱测甜适健爆奄钩高一数学必修直线的倾斜角与斜率用d,因为入射角等于反射角,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 As
20、pose Pty Ltd.,匀列篓匝谢碱窟择迟往贤奉碑右受腿雏胚爱扳撤锯蛊吵豪却熙账港驴概冶高一数学必修直线的倾斜角与斜率用d,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,启褪捣样扦言葱禽册嚎毖食报疗酸勉砍盗瘦菠倪孺迸戒鳖貉狄丹褂昆鲜乎高一数学必修直线的倾斜角与斜率用d,小结提高,核心,知识方法思想,直线的斜率,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,李椽业铲掠奠匙偏亏普铡阂洛院段庄首缔簇数汁拱甜捐柳枉边呵曝涩检吸高一数学必修直线的倾斜角与斜率用d,Thankyou!,再见!,Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.,劈缎刘办鹤庆惟汹经逊围待兼承钟拾竟孺笋皆狰仕程晌息尾钟竿野封行唁高一数学必修直线的倾斜角与斜率用d,