正切函数的图像和性质【-】

1、正切函数的图像和性质高中数学 必修4 第一章 第三节扬中第二高级中学 包云 我们已经学习了正弦、余弦函数的图像 我们是怎么得到其的图像的呢？一、复习回顾思考 利用单位圆中的三角函数线作图 由一个周期到整个定义域二、探索新知通过回顾，对我们研究正切函数图像有什么启发吗？探究：问题 正切函数 是否为周期函数？ 是周期函数， 是它的一个周期先利用正切线作出一个周期内的图象f(x)利用正切线一个周期内的图像的图像渐近线xy0 xy0正切曲线正切函数的图像1.定义域：2.值域：R3.周期性： 4.奇偶性： 奇函数，图象关于原点对称：6.渐近线方程： 7.对称中心：Z k 增区间三、善于归纳 正切函数的性

2、质无对称轴例1求函数 的定义域那么函数 的定义域是：所以由可得：所以函数 的定义域是：四、灵活运用解：令求函数的定义域练一练换元例2 比较以下各组中两个正切函数值的大小与解：在 上是增函数又与且 是增函数解：又利用单调性PS:要把两个角放在同一个单调区间上 例3求以下函数的单调区间：换元思想这个题目应该注意什么例4xy0解：观察正切曲线，写出满足条件的 的取值范围 正切函数的图像和性质 定义域值域周期奇偶性 单调增区间对称中心渐近线方程奇函数小结Zk,k2xp+p自我小结谈谈本节课你的收获是什么？哪部分知识掌握的比较好？还有什么不清楚的细节吗？作业 1.课本 P34 一、二、三2.用列表的方式

3、归纳总结正弦、 余弦、正切函数的图像和性质谢谢！再见EEDDDDDDCCCyyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppooooonnnnnmmmmmlllllkkkkkjjjjjiiiiihhhhhgggggfffffeeeeedddddcccccbbbbbbaaaaa99999888887777766666555554444433333222221111100000+-)(*&%$!#ZZZZZYYYYYYXXXXXWWWWWVVVVVUUUUUTTTTTSSSSSRRRRRQQQQQPPPPPOOOOONNNNNMMMMMLLLLL

4、KKKKKJJJJJIIIIIHHHHHGGGGGFFFFFEEEEEDDDDDCCCCCBBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppooooonnnnnmmmmmlllllkkkkkjjjjjiiiiihhhhhgggggfffffeeeeeedddddcccccbbbbbaaaaa99999888887777766666555554444433333222221111100000+-)(*&%$!#ZZZZZYYYYYXXXXXWWWWWVVVVVUUUUUTTTTTSSSSSRRRRRQQQQQPPP

5、PPOOOOONNNNNMMMMMLLLLLKKKKKJJJJJIIIIIHHHHHGGGGGFFFFFEEEEEDDDDDDCCCCCBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppooooonnnnnmmmmmlllllkkkkkjjjjjiiiiihhhhhggggggfffffeeeeedddddcccccbbbbbaaaaa99999888887777766666555554444433333222221111100000+-)(*&%$!#ZZZZZYYYYYXXXXXWWWWWVVVVVUUUUUT

6、TTTTSSSSSRRRRRQQQQQPPPPPOOOOONNNNNMMMMMLLLLLKKKKKJJJJJIIIIIHHHHHGGGGGGFFFFFEEEEEDDDDDCCCCCBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppooooonnnnnmmmmmlllllkkkkkjjjjjjiiiiihhhhhgggggfffffeeeeedddddcccccbbbbbaaaaa99999888887777766666555554444433333222221111100000+-)(*&%$!#ZZZZZYYYY

7、YXXXXXWWWWWVVVVVUUUUUTTTTTSSSSSRRRRRQQQQQPPPPPOOOOONNNNNMMMMMLLLLLKKKKKJJJJJJIIIIIHHHHHGGGGGFFFFFEEEEEDDDDDCCCCCBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppooooonnnnnmmmmmllllllkkkkkjjjjjiiiiihhhhhgggggfffffeeeeedddddcccccbbbbbaaaaa99999888887777766666555554444433333222221-)(*&%

8、$!#ZZZZZYYYYYXXXXXWWWWWVVVVVUUUUUTTTTTSSSSSRRRRRQQQQQPPPPPOOOOONNNNNMMMMMLLLLLKKKKKJJJJJIIIIIHHHHHGGGGGGFFFFFEEEEEDDDDDCCCCCBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppooooonnnnnmmmmmlllllkkkkkjjjjjjiiiiihhhhhgggggfffffeeeeedddddcccccbbbbbaaaaa99999888887777766666555554444433333

9、222221111100000+-)(*&%$!#ZZZZZYYYYYXXXXXWWWWWVVVVVUUUUUTTTTTSSSSSRRRRRQQQQQPPPPPOOOOONNNNNMMMMMLLLLLKKKKKJJJJJJIIIIIHHHHHGGGGGFFFFFEEEEEDDDDDCCCCCBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppooooonnnnnmmmmmllllllkkkkkjjjjjiiiiihhhhhgggggfffffeeeeedddddcccccbbbbbaaaaa9999988888777

10、7766666555554444433333222221111100000+-)(*&%$!#ZZZZZYYYYYXXXXXWWWWWVVVVVUUUUUTTTTTSSSSSRRRRRQQQQQPPPPPOOOOONNNNNMMMMMLLLLLLKKKKKJJJJJIIIIIHHHHHGGGGGFFFFFEEEEEDDDDDCCCCCBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppoooooonnnnnmmmmmlllihhhhhgggggfffffeeeeedddddcccccbbbbbaaaaa9999988

11、8887777766666555554444433333222221111100000+-)(*&%$!#ZZZZZYYYYYXXXXXWWWWWVVVVVUUUUUTTTTTSSSSSRRRRRQQQQQPPPPPOOOOONNNNNMMMMMLLLLLKKKKKJJJJJJIIIIIHHHHHGGGGGFFFFFEEEEEDDDDDCCCCCBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppooooonnnnnmmmmmmlllllkkkkkjjjjjiiiiihhhhhgggggfffffeeeeeddddd

12、cccccbbbbbaaaaa99999888887777766666555554444433333222221111100000+-)(*&%$!#ZZZZZYYYYYXXXXXWWWWWVVVVVUUUUUTTTTTSSSSSRRRRRQQQQQPPPPPOOOOONNNNNMMMMMLLLLLLKKKKKJJJJJIIIIIHHHHHGGGGGFFFFFEEEEEDDDDDCCCCCBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppoooooonnnnnmmmmmlllllkkkkkjjjjjiiiiihhh

13、hhgggggfffffeeeeedddddcccccbbbbbaaaaa999998888877777666665555544444333332222211111100000+-)(*&%$!#ZZZZZYYYYYXXXXXWWWWWVVVVVUUUUUTTTTTSSPPOOOOONNNNNMMMMMLLLLLKKKKKJJJJJJIIIIIHHHHHGGGGGFFFFFEEEEEDDDDDCCCCCBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppooooonnnnnmmmmmmlllllkkkkkjjjjji

14、iiiihhhhhgggggfffffeeeeedddddcccccbbbbbaaaaa99999888887777766666555554444433333222221111100000+-)(*&%$!#ZZZZZYYYYYXXXXXWWWWWVVVVVUUUUUTTTTTSSSSSRRRRRQQQQQPPPPPOOOOONNNNNMMMMMLLLLLLKKKKKJJJJJIIIIIHHHHHGGGGGFFFFFEEEEEDDDDDCCCCCBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppoooooonnnn

15、nmmmmmlllllkkkkkjjjjjiiiiihhhhhgggggfffffeeeeedddddcccccbbbbbaaaaa999998888877777666665555544444333332222211111100000+-)(*&%$!#ZZZZZYYYYYXXXXXWWWWWVVVVVUUUUUTTTTTSSSSSRRRRNNNNNMMMMMLLLLLKKKKKJJJJJJIIIIIHHHHHGGGGGFFFFFEEEEEDDDDDCCCCCBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppooo

16、oonnnnnmmmmmmlllllkkkkkjjjjjiiiiihhhhhgggggfffffeeeeedddddcccccbbbbbaaaaa99999888887777766666555554444433333222221111100000+-)(*&%$!#ZZZZZYYYYYXXXXXWWWWWVVVVVUUUUUTTTTTSSSSSRRRRRQQQQQPPPPPOOOOONNNNNMMMMMLLLLLLKKKKKJJJJJIIIIIHHHHHGGGGGFFFFFEEEEEDDDDDCCCCCBBBBBAAAAAzzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrr