正余弦函數(shù)的單調(diào)性、奇偶性.ppt

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1、正弦、余弦函數(shù)的性質(zhì)X（奇偶性、單調(diào)性）四師一中任萬(wàn)里正弦、余弦函數(shù)的圖象和性質(zhì)y=sinx(x?R)x6?yo-?-12?3?4?5?-2?-3?-4?1?x6?o-?-12?3?4?5?-2?-3?-4?1?yy=cosx(x?R)定義域值域周期性x?Ry?[-1,1]T=2?正弦、余弦函數(shù)的奇偶性、單調(diào)性sin(-x)=-sinx(x?R)y=sinx(x?R)x6?yo-?-12?3?4?5?-2?-3?-4?1?是奇函數(shù)x6?o-?-12?3?4?5?-2?-3?-4?1?ycos(-x)=cosx(x?R)y=cosx(x?R)是偶函數(shù)定義域關(guān)于

2、原點(diǎn)對(duì)稱正弦、余弦函數(shù)的奇偶性正弦、余弦函數(shù)的奇偶性、單調(diào)性正弦函數(shù)的單調(diào)性y=sinx(x?R)增區(qū)間為[，]其值從-1增至1xyo-?-12?3?4?-2?-3?1?xsinx…0……?…-1010-1減區(qū)間為[，]其值從1減至-1？？？[+2k?,+2k?],k?Z[+2k?,+2k?],k?Z正弦、余弦函數(shù)的奇偶性、單調(diào)性余弦函數(shù)的單調(diào)性y=cosx(x?R)xcosx-?……0……?-1010-1增區(qū)間為其值從-1增至1[+2k?,2k?],k?Z減區(qū)間為，其值從1減至-1[2k?,2k?+?],k?Zyxo-?-12?3?4?-2?-3?1?正弦

3、函數(shù)余弦函數(shù)定義域RR值域[-1，1]當(dāng)x=2kπ+π/2時(shí)ymax=1當(dāng)x=2kπ+3π/2時(shí)ymin=-1[-1，1]當(dāng)x=2kπ時(shí)，ymax=1當(dāng)x=2kπ+π時(shí)，ymin=-1單調(diào)性[-π/2+2k?,π/2+2k?],增[π/2+2k?,3π/2+2k?],減[2k?-?,2k?],增[2k?,π+2k?],減奇偶性奇函數(shù)偶函數(shù)周期性T=2πT=2π對(duì)稱性對(duì)稱軸x=π/2+kπ對(duì)稱中心(kπ,0)對(duì)稱軸x=kπ對(duì)稱中心(π/2+kπ,0)正弦、余弦函數(shù)的奇偶性、單調(diào)性例1不通過(guò)求值，指出下列各式大于0還是小于0：(1)sin()–sin()(2)c

4、os()-cos()解：?又y=sinx在上是增函數(shù)?sin()0cos()=cos=coscos()=cos=cos解：??cos

5、(4)(3)y=(tan)sinx解：?單調(diào)增區(qū)間為單調(diào)減區(qū)間為?解：定義域?yàn)闇p區(qū)間當(dāng)即當(dāng)即為增區(qū)間。作業(yè)：課本：P464、5、6正弦、余弦函數(shù)的奇偶性、單調(diào)性y=sinxyxo-?-12?3?4?-2?-3?1?y=sinx(x?R)圖象關(guān)于原點(diǎn)對(duì)稱