11-12学年高中数学1.3.2.1余弦函数的图象与性质课件新人教B版必修4.ppt

余弦函数的图象与性质 Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. )2 sin( cosxx???利用五点描图法画出 y =sin x的图象, 图象向两边延伸,得 1. 余弦函数的图象把函数 y =sin x的图象,向左平移单位即得到 y =cos x的图象。 2 ? Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 余弦函数的图象叫做余弦曲线。通过观察图象,我们不难发现,起着关键作用的点是五个点: (0,1), ( ,0)、(π,- 1), ( ,0), (2π, 1). 2 ? 2 3? Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 2. 余弦函数的性质: (1) 定义域: y =cos x的定义域为 R (2) 值域: ①由单位圆中的三角函数线,得结论: |cos x|≤1 (有界性) 再看正弦函数线(图象)验证上述结论: 所以 y =cos x的值域为[-1,1]; Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. ②对于 y =cos x当且仅当 x =2 k?k?Z时y ma x =1 , 当且仅当 x =2 k?+?k?Z时y min =-1, ③观察 R上的 y =cos x的图象可知当2k?- < x <2 k?+ ( k? Z)时, y =cos x >0 当2k?+ < x <2 k?+ ( k? Z)时, y =cos x <0 2 ?2 ?2 ?2 3? Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. (3). 周期性:(观察图象) ①余弦函数的图象是有规律不断重复出现的; ②规律是:每隔 2?重复出现一次(或者说每隔 2k?,k?Z重复出现) ③这个规律由诱导公式 cos(2 k?+x )=cos x也可以说明余弦函数的最小正周期是 T =2 π. Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile