人教A版高中數(shù)學(xué)必修4第一章 三角函數(shù)1.5 函數(shù)y=Asin(ωx+φ)的圖象習(xí)題(4).doc

人教版高中數(shù)學(xué)同步練習(xí)1.5函數(shù)yAsin(x)的圖象(一)課時(shí)目標(biāo)1.了解、A對(duì)函數(shù)f(x)Asin(x)的圖象的影響.2.掌握ysin x與f(x)Asin(x)圖象間的變換關(guān)系用“圖象變換法”作yAsin(x) (A0，0)的圖象1對(duì)ysin(x)，xR的圖象的影響ysin(x) (0)的圖象可以看作是把正弦曲線ysin x上所有的點(diǎn)_(當(dāng)0時(shí))或_(當(dāng)0)對(duì)ysin(x)的圖象的影響函數(shù)ysin(x)的圖象，可以看作是把ysin(x)的圖象上所有點(diǎn)的橫坐標(biāo)_(當(dāng)1時(shí))或_(當(dāng)00)對(duì)yAsin(x)的圖象的影響函數(shù)yAsin(x)的圖象，可以看作是把ysin(x)圖象上所有點(diǎn)的縱坐標(biāo)_(當(dāng)A1時(shí))或_(當(dāng)0A0，0)的圖象也可由ycos x的圖象變換得到1.5函數(shù)yAsin(x)的圖象(一)答案知識(shí)梳理1向左向右|2.縮短伸長(zhǎng)不變3伸長(zhǎng)縮短A倍A，AAA4ysin(x)ysin(x)yAsin(x)作業(yè)設(shè)計(jì)1B2.C3.D4B將函數(shù)ysin 2x的圖象向左平移個(gè)單位，得到函數(shù)ysin2(x)，即ysin(2x)cos 2x的圖象，再向上平移1個(gè)單位，所得圖象的函數(shù)解析式為y1cos 2x.5Bysin(2x)ysin2(x)sin(2x)6C把函數(shù)ysin x的圖象上所有的點(diǎn)向左平行移動(dòng)個(gè)單位長(zhǎng)度后得到函數(shù)ysin的圖象，再把所得圖象上所有的點(diǎn)的橫坐標(biāo)縮短到原來(lái)的倍，得到函數(shù)ysin的圖象7sin x8ycos 2x9.解析ysin xcoscos向右平移個(gè)單位后得ycos，2k，kZ，2k，kZ.的最小正值是.1011解由ysin x的圖象通過(guò)變換得到函數(shù)ysin的圖象有兩種變化途徑：ysin xysin ysinysin xysin 2x ysin.12解(1)由已知函數(shù)化為ysin.欲求函數(shù)的單調(diào)遞減區(qū)間，只需求ysin的單調(diào)遞增區(qū)間由2k2x2k (kZ)，解得kxk (kZ)，原函數(shù)的單調(diào)減區(qū)間為 (kZ)(2)f(x)sincoscoscos2.ycos 2x是偶函數(shù)，圖象關(guān)于y軸對(duì)稱，只需把yf(x)的圖象向右平移個(gè)單位即可13Aysin 2xcoscoscoscosycos2(x)cos(2x)14D方法一正向變換yf(x)yf(2x)yf，即yf，所以fsin 2x.令2xt，則2