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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)定義域關于原點對稱
2、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?正弦函數(shù)余弦函數(shù)定義
3、域RR值域[-1,1]當x=2kπ+π/2時ymax=1當x=2kπ+3π/2時ymin=-1[-1,1]當x=2kπ時,ymax=1當x=2kπ+π時,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對稱性對稱軸x=π/2+kπ對稱中心(kπ,0)對稱軸x=kπ對稱中心(π/2+kπ,0)正弦、余弦函數(shù)的奇偶性、單調(diào)性例1不通過求值,指出下列各式大于0還是小于0:(1)sin()–sin()(2)cos()-cos()解:
4、?又y=sinx在上是增函數(shù)?sin()0cos()=cos=coscos()=cos=cos解:??cos5、x解:?單調(diào)增區(qū)間為單調(diào)減區(qū)間為?解:定義域為減區(qū)間當即當即為增區(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)圖象關于原點對稱