高一数学必修直线的倾斜角与斜率用.ppt

高一新课标人教版 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 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 y x o Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 直线的倾斜角 x y o 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. p o y x y p o x p o y x p o y x 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： )180,0 oo a Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. x y o 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 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 日常生活中，还有没有表示倾斜程度的量？ 前进量 升 高 量 问题引入问题引入 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 定义：倾斜角不是90的直线，它的倾斜角的正切 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 小结 1、倾斜角的定义及其范围 2、斜率的定义及斜率与倾斜角的相互转化 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. p o y x y p o x p o y x p o y x 0 90= 90 90 180 = 0 k=0k 0k不存在k0 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 如图，当为钝角是， 钝角 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 3、直线的斜率公式： 综上所述，我们得到经过两点 的直线的斜率公式 ： Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 、如图，已知A(4,2)、B(-8,2)、C(0,-2)，求 直线AB、BC、CA的斜率，并判断这 些直线 的倾斜角是什么角？ y x o . . . . . . AB C 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 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.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 例2、已知三点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 N(-8,3) M(2,2 ) P Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 小 结： 一、求直线的倾斜角和斜率 二、利用斜率相同判定三点共线 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. N(-8,3) M(2,2 ) P 因为入射角等于反射角 )0 , 2( P - 反射点 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slid