（福建專）高考數(shù)學(xué)一輪復(fù)習(xí) 4.4 函數(shù)y=Asin(ωx+φ)的圖象及應(yīng)用課件 文

4.4函數(shù)y=Asin(x+)的圖象 及應(yīng)用知識梳理考點(diǎn)自測1.y=Asin(x+)的有關(guān)概念 2.用五點(diǎn)法畫y=Asin(x+)在一個周期內(nèi)的簡圖時,要找出的五個特征點(diǎn)如下表所示x+0 2 知識梳理考點(diǎn)自測3.由y=sin x的圖象得y=Asin(x+)(A0,0)的圖象的兩種方法|知識梳理考點(diǎn)自測y=Asin(x+)(A0,0)的圖象的作法:(1)五點(diǎn)法:用“五點(diǎn)法”作y=Asin(x+)的簡圖,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”(即“先后”)與“先伸縮后平移”(即“先后”).知識梳理考點(diǎn)自測 知識梳理考點(diǎn)自測D知識梳理考點(diǎn)自測D知識梳理考點(diǎn)自測6考點(diǎn)一考點(diǎn)二考點(diǎn)三函數(shù)函數(shù)y=Asin(x+)的圖象及變換的圖象及變換 考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三思考作函數(shù)y=Asin(x+)(A0,0)的圖象有哪些方法?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,對于后者可利用 來確定平移單位.考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三求函數(shù)求函數(shù)y=Asin(x+)的解析式的解析式(多考向多考向)考向1由函數(shù)的圖象求函數(shù)y=Asin(x+)的解析式例2函數(shù)y=Asin(x+)的部分圖象如圖所示,則()A考點(diǎn)一考點(diǎn)二考點(diǎn)三思考由y=Asin(x+)+b(A0,0)的圖象求其解析式的方法和步驟是怎樣的?考點(diǎn)一考點(diǎn)二考點(diǎn)三考向2由函數(shù)y=Asin(x+)的性質(zhì)求解析式考點(diǎn)一考點(diǎn)二考點(diǎn)三思考如何由函數(shù)y=Asin(x+)的性質(zhì)確定A,?考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三函數(shù)函數(shù)y=Asin(x+)性質(zhì)的應(yīng)用性質(zhì)的應(yīng)用 考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三思考如何求解三角函數(shù)圖象與性質(zhì)的綜合問題?解題心得解決三角函數(shù)圖象與性質(zhì)綜合問題的方法:先將y=f(x)化為y=asin x+bcos x的形式,再用輔助角公式化為y=Asin(x+)的形式,最后借助y=Asin(x+)的性質(zhì)(如周期性、對稱性、單調(diào)性等)解決相關(guān)問題.考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三考點(diǎn)一考點(diǎn)二考點(diǎn)三1.由函數(shù)y=Asin(x+)的圖象確定A,的題型,常常以“五點(diǎn)法”中的五個點(diǎn)作為突破口,要從圖象的升降情況找準(zhǔn)第一個“零點(diǎn)”和第二個“零點(diǎn)”的位置.要善于抓住特殊量和特殊點(diǎn).2.函數(shù)y=Asin(x+)的圖象與x軸的每一個交點(diǎn)均為其對稱中心,若函數(shù)f(x)=Asin(x+)的圖象關(guān)于點(diǎn)(x0,0)成中心對稱,則x0+=k(kZ);經(jīng)過函數(shù)y=Asin(x+)圖象的最高點(diǎn)或最低點(diǎn),且與x軸垂直的直線都為其對稱軸,兩個相鄰對稱軸的距離是半個周期.若函數(shù)f(x)=Asin(x+)的圖象關(guān)于直線x=x0對稱,則x0+=k+(kZ).考點(diǎn)一考點(diǎn)二考點(diǎn)三1.在三角函數(shù)的平移變換中,無論是先平移再伸縮,還是先伸縮再平移,只要平移|個單位,都是相應(yīng)的解析式中的x變?yōu)閤|.2.函數(shù)y=Asin(x+)(A0,0)的單調(diào)區(qū)間的確定,基本思想是把(x+)看作一個整體,若0.