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1、4 4.4 4函數(shù)函數(shù)y=Ay=Asin(sin(x+x+)的的 圖象及應(yīng)用圖象及應(yīng)用第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)知識(shí)梳理-2-知識(shí)梳理雙基自測(cè)2311.y=Asin(x+)的有關(guān)概念 x+第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)知識(shí)梳理-3-知識(shí)梳理雙基自測(cè)2312.用五點(diǎn)法畫y=Asin(x+)在一個(gè)周期內(nèi)的簡(jiǎn)圖時(shí),要找出的五個(gè)特征點(diǎn)如下表所示0 2 第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)知識(shí)梳理-4-知識(shí)梳理雙基自測(cè)2313.由y=sin

2、 x的圖象得y=Asin(x+)(A0,0)的圖象的兩種方法第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)知識(shí)梳理2-5-知識(shí)梳理雙基自測(cè)3415 第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)知識(shí)梳理-6-知識(shí)梳理雙基自測(cè)23415 答案解析解析關(guān)閉 答案解析關(guān)閉第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)知識(shí)梳理-7-知識(shí)梳理雙基自測(cè)23415 答案解析解析關(guān)閉 答案解析關(guān)閉第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)知識(shí)梳理-

3、8-知識(shí)梳理雙基自測(cè)234154.將函數(shù)f(x)=sin x-cos x的圖象向左平移m(m0)個(gè)單位長(zhǎng)度,若所得圖象對(duì)應(yīng)的函數(shù)為偶函數(shù),則m的最小值為()答案解析解析關(guān)閉 答案解析關(guān)閉第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)知識(shí)梳理-9-知識(shí)梳理雙基自測(cè)23415 答案解析解析關(guān)閉 答案解析關(guān)閉第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)知識(shí)梳理-10-知識(shí)梳理雙基自測(cè)23415自測(cè)點(diǎn)評(píng)1.利用圖象變換由y=sin x的圖象得到y(tǒng)=Asin(x+)(A0,0)(xR)的圖象,若先平移后伸縮,則平移的量是|

4、個(gè)單位;若先伸縮再平移,則平移的量是 個(gè)單位.2.三角函數(shù)圖象的對(duì)稱中心就是圖象與x軸的交點(diǎn),若函數(shù)f(x)=Asin(x+)圖象的對(duì)稱中心為(x0,0),則f(x0)=0.3.有關(guān)三角函數(shù)性質(zhì)的題目,要將三角函數(shù)化為y=Asin(x+)的形式,最大值、最小值與A的符號(hào)有關(guān).y=Asin(x+)的圖象的兩個(gè)相鄰對(duì)稱軸之間的距離是半個(gè)周期.4.函數(shù)y=Asin(x+)(0)的圖象橫向伸長(zhǎng),周期變大,x的系數(shù)變小;橫向縮短,周期變小,x的系數(shù)變大.第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-11-考點(diǎn)1考點(diǎn)2考點(diǎn)3第四章第四章4.4函數(shù)函數(shù)y=A

5、sin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-12-考點(diǎn)1考點(diǎn)2考點(diǎn)3(1)請(qǐng)將上表數(shù)據(jù)補(bǔ)充完整,并直接寫出函數(shù)f(x)的解析式;(2)將y=f(x)圖象上所有點(diǎn)向左平移(0)個(gè)單位長(zhǎng)度,得到y(tǒng)=g(x)的圖象,若y=g(x)圖象的一個(gè)對(duì)稱中心為 ,求的最小值.思考作函數(shù)y=Asin(x+)(A0,0)的圖象有哪些方法?第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-13-考點(diǎn)1考點(diǎn)2考點(diǎn)3第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-14-考點(diǎn)1考點(diǎn)2考點(diǎn)3第四章第四章4.4函

6、數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-15-考點(diǎn)1考點(diǎn)2考點(diǎn)3解題心得1.函數(shù)y=Asin(x+)(A0,0)的圖象的兩種作法:(1)五點(diǎn)法:用“五點(diǎn)法”作y=Asin(x+)的簡(jiǎn)圖,主要是通過變量代換,設(shè)z=x+,由z取 來求出相應(yīng)的x,通過列表,計(jì)算得出五點(diǎn)坐標(biāo),描點(diǎn)后得出圖象.(2)圖象變換法:由函數(shù)y=sin x的圖象通過變換得到y(tǒng)=Asin(x+)的圖象,有兩種主要途徑“先平移后伸縮”與“先伸縮后平移”.2.變換法作圖象的關(guān)鍵是看x軸上是先平移后伸縮還是先伸縮后平移,對(duì)于后者可利用 來確定平移單位.第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的

7、圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-16-考點(diǎn)1考點(diǎn)2考點(diǎn)3(1)求這個(gè)簡(jiǎn)諧運(yùn)動(dòng)的振幅、周期、初相;(2)用“五點(diǎn)法”作出它在一個(gè)周期內(nèi)的圖象;第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-17-考點(diǎn)1考點(diǎn)2考點(diǎn)3第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-18-考點(diǎn)1考點(diǎn)2考點(diǎn)3描點(diǎn)連線得函數(shù)圖象,如圖所示.第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-19-考點(diǎn)1考點(diǎn)2考點(diǎn)3考向一由函數(shù)的圖象求函數(shù)y=Asin(x+)的解析式例

8、2函數(shù)y=Asin(x+)的部分圖象如圖所示,則()思考由y=Asin(x+)+b(A0,0)的圖象求其解析式的方法和步驟是怎樣的?A 第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-20-考點(diǎn)1考點(diǎn)2考點(diǎn)3第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-21-考點(diǎn)1考點(diǎn)2考點(diǎn)3第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-22-考點(diǎn)1考點(diǎn)2考點(diǎn)3考向二由函數(shù)y=Asin(x+)的性質(zhì)求解析式(1)求和的值;思考如何由函數(shù)y=Asin(x+)的性質(zhì)確

9、定A,?第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-23-考點(diǎn)1考點(diǎn)2考點(diǎn)3第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-24-考點(diǎn)1考點(diǎn)2考點(diǎn)3解題心得1.由圖象確定y=Asin(x+)+b(A0,0)的解析式的步驟和方法:第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-25-考點(diǎn)1考點(diǎn)2考點(diǎn)3(3)求:代入法:把圖象上的一個(gè)已知點(diǎn)代入來求.第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-26-考點(diǎn)1考點(diǎn)2考點(diǎn)32.由函數(shù)y=Asin(x+)的性質(zhì)確定其解析式的方法:由函數(shù)的最值確定A,由函數(shù)的周期性確定,由函數(shù)的奇偶性或?qū)ΨQ性確定.要注意的取值范圍.第四章第四章4.4函數(shù)函數(shù)y=Asin(x+)的圖象及應(yīng)用的圖象及應(yīng)用知識(shí)梳理核心考點(diǎn)核心考點(diǎn)-27-考點(diǎn)1考點(diǎn)2考點(diǎn)3對(duì)點(diǎn)訓(xùn)練對(duì)點(diǎn)訓(xùn)練2(1)函數(shù)f(x)=cos(x+)的部分圖象如圖所示,則f(x)的單調(diào)遞減區(qū)間為()D(2)已知函數(shù)y=Asin(x+)(A0,0,00,0)的單調(diào)區(qū)間的確定,基本思想是把x+看作一個(gè)整體,若0.