1、正切函數(shù)的圖像和性質(zhì)高中數(shù)學 必修4 第一章 第三節(jié)揚中第二高級中學 包云 我們已經(jīng)學習了正弦、余弦函數(shù)的圖像 我們是怎么得到其的圖像的呢？一、復習回顧思考 利用單位圓中的三角函數(shù)線作圖 由一個周期到整個定義域二、探索新知通過回顧，對我們研究正切函數(shù)圖像有什么啟發(fā)嗎？探究：問題 正切函數(shù) 是否為周期函數(shù)？ 是周期函數(shù)， 是它的一個周期先利用正切線作出一個周期內(nèi)的圖象f(x)利用正切線一個周期內(nèi)的圖像的圖像漸近線xy0 xy0正切曲線正切函數(shù)的圖像1.定義域：2.值域：R3.周期性： 4.奇偶性： 奇函數(shù)，圖象關于原點對稱：6.漸近線方程： 7.對稱中心：Z k 增區(qū)間三、善于歸納 正切函數(shù)的性

2、質(zhì)無對稱軸例1求函數(shù) 的定義域那么函數(shù) 的定義域是：所以由可得：所以函數(shù) 的定義域是：四、靈活運用解：令求函數(shù)的定義域練一練換元例2 比較以下各組中兩個正切函數(shù)值的大小與解：在 上是增函數(shù)又與且 是增函數(shù)解：又利用單調(diào)性PS:要把兩個角放在同一個單調(diào)區(qū)間上 例3求以下函數(shù)的單調(diào)區(qū)間：換元思想這個題目應該注意什么例4xy0解：觀察正切曲線，寫出滿足條件的 的取值范圍 正切函數(shù)的圖像和性質(zhì) 定義域值域周期奇偶性 單調(diào)增區(qū)間對稱中心漸近線方程奇函數(shù)小結(jié)Zk,k2xp+p自我小結(jié)談談本節(jié)課你的收獲是什么？哪部分知識掌握的比較好？還有什么不清楚的細節(jié)嗎？作業(yè) 1.課本 P34 一、二、三2.用列表的方式

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