正切函數(shù)的性質(zhì)與圖象課件

人教A版高中數(shù)學(xué)必修4人教A版高中數(shù)學(xué)必修41正切函數(shù)的性質(zhì)與圖象正切函數(shù)的性質(zhì)與圖象2復(fù)習(xí)正余弦函數(shù)的性質(zhì)正弦函數(shù)余弦函數(shù)定義域值域單調(diào)性奇偶性最小正周期RR[-1,1][-1,1]奇函數(shù)偶函數(shù)2π2π復(fù)習(xí)正余弦函數(shù)的性質(zhì)正弦函數(shù)余弦函數(shù)定義域值域單調(diào)性奇偶3(1)周期性由誘導(dǎo)公式正切函數(shù)是周期函數(shù),周期是π正切函數(shù)的性質(zhì)(1)周期性由誘導(dǎo)公式正切函數(shù)是周期函數(shù),正切函數(shù)的性質(zhì)4(2)奇偶性由誘導(dǎo)公式正切函數(shù)是奇函數(shù).(2)奇偶性由誘導(dǎo)公式正切函數(shù)是奇函數(shù).5(3)單調(diào)性yxTOA(1,0)yxTOA(1,0)xyTOA(1,0)yxTOA(1,0)(Ⅳ)(Ⅰ)(Ⅱ)(Ⅲ)xxxx正切函數(shù)在內(nèi)是增函數(shù).正切函數(shù)在開(kāi)區(qū)間內(nèi)都是增函數(shù)(3)單調(diào)性yxTOA(1,0)yxTOA(1,0)xyTO6(4)值域yxOA(1,0)(Ⅰ)TxxyOA(1,0)(Ⅱ)Tx正切函數(shù)的值域是實(shí)數(shù)RxTxTxTxT(4)值域yxOA(1,0)(Ⅰ)TxxyOA(1,0)(Ⅱ7正切函數(shù)的圖象課件演示y=tanxxy-11O正切函數(shù)的圖象課件演示y=tanxxy-11O8例6求函數(shù)的定義域、周期和單調(diào)區(qū)間.解:函數(shù)的自變量x應(yīng)滿(mǎn)足所以函數(shù)的定義域是例6求函數(shù)的定義域、周期和單調(diào)區(qū)間.9因此函數(shù)的周期為2例6求函數(shù)的定義域、周期和單調(diào)區(qū)間.因此函數(shù)的周期為2例6求函數(shù)的定義域10因此函數(shù)的單調(diào)遞增區(qū)間是例6求函數(shù)的定義域、周期和單調(diào)區(qū)間.因此函數(shù)的單調(diào)遞增區(qū)間是例6求函數(shù)的11求函數(shù)y=tan3x的定義域解函數(shù)y=tan3x的定義域?yàn)榫毩?xí)求函數(shù)y=tan3x的定義域解函數(shù)y=tan3x的定義域?yàn)?2求下列函數(shù)的周期:求下列函數(shù)的周期:13小結(jié)正切函數(shù)的性質(zhì)定義域值域奇偶性周期性單調(diào)性以π為周期的周期函數(shù)奇函數(shù)在開(kāi)區(qū)間內(nèi)都是增函數(shù)R小結(jié)正切函數(shù)的性質(zhì)定義域值域奇偶性周期性單調(diào)性以