函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)

函數(shù)y＝Asin(ωx＋φ)的圖像及性質(zhì)函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)復(fù)習(xí)目標(biāo)

1.了解函數(shù)y＝Asin(ωx＋φ)的物理意義，能畫(huà)出函數(shù)的圖象，了解參數(shù)A、ω、φ對(duì)函數(shù)圖象變化的影響．2.了解三角函數(shù)是描述周期變化現(xiàn)象的重要函數(shù)模型，會(huì)用三角函數(shù)解決一些簡(jiǎn)單的實(shí)際問(wèn)題.考題規(guī)律

1.“五點(diǎn)法”作圖及圖象的變換是考查的重點(diǎn)．2.結(jié)合三角恒等變換考查y＝Asin(ωx＋φ)的性質(zhì)及簡(jiǎn)單應(yīng)用是考查的熱點(diǎn)．函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)

2．若函數(shù)f(x)＝sin(ωx＋φ)的部分圖像如圖，則ω和φ的取值是()C函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)B函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)5．關(guān)于函數(shù)y＝－2sin(2x＋)的圖象有以下四個(gè)結(jié)論：①振幅是－2；②最小正周期是π；③直線x＝是它的一條對(duì)稱軸；④圖象關(guān)于點(diǎn)(，0)對(duì)稱．其中正確命題的序號(hào)是

.(注：將你認(rèn)為正確的命題的序號(hào)都填上)②③④函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)1.y＝Asin(ωx＋φ)的有關(guān)概念y＝Asin(ωx＋φ)(A>0，ω>0)，x∈[0，＋∞)表示一個(gè)振動(dòng)量時(shí)振幅周期頻率相位初相T＝f＝＝

知識(shí)梳理函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)2.函數(shù)y＝sinx的圖象變換得到y(tǒng)＝Asin(ωx＋φ)的圖象的步驟法一法二函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)3．用五點(diǎn)法畫(huà)y＝Asin(ωx＋φ)的圖像用五點(diǎn)法畫(huà)y＝Asin(ωx＋φ)在一個(gè)周期內(nèi)的簡(jiǎn)圖時(shí)，要找五個(gè)特征點(diǎn)．如下表所示：02π函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)考點(diǎn)一y＝Asin(ωx＋φ)的圖像

鞏固性題組函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)【變式遷移】（?。┮阎瘮?shù)f(x)＝sin.在坐標(biāo)系內(nèi)，用五點(diǎn)法畫(huà)出函數(shù)y＝f(x)在一個(gè)周期內(nèi)的圖象.函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)考點(diǎn)二求函數(shù)解析式及圖象變換7.

設(shè)f(x)＝Asin(ωx＋φ)(A＞0，ω＞0，|φ|≤)，最高點(diǎn)M(2，)，由最高點(diǎn)運(yùn)動(dòng)到相鄰的最低點(diǎn)N時(shí)，曲線與x軸交于點(diǎn)(6,0)．(1)求f(x)的表達(dá)式；(2)說(shuō)明y＝f(x)的圖象可由y＝sinx的圖象經(jīng)過(guò)怎樣的變換得到．函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)圖像變換包括平移變換、伸縮變換，應(yīng)分清變換順序．(1)平移變換①沿x軸平移，按“左加右減”法則；②沿y軸平移，按“上加下減”法則．函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)【變式遷移】（ⅱ）下圖是函數(shù)y＝Asin(ωx＋φ)(x∈R)在區(qū)間的圖象，為了得到這個(gè)函數(shù)的圖象，只要將y＝sinx(x∈R)的圖象上所有的點(diǎn)()得到.函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)A．向左平移個(gè)單位長(zhǎng)度，再把所得各點(diǎn)的橫坐標(biāo)縮短到原來(lái)的倍，縱坐標(biāo)不變B．向左平移個(gè)單位長(zhǎng)度，再把所得各點(diǎn)的橫坐標(biāo)伸長(zhǎng)到原來(lái)的2倍，縱坐標(biāo)不變C．向左平移個(gè)單位長(zhǎng)度，再把所得各點(diǎn)的橫坐標(biāo)縮短到原來(lái)的倍，縱坐標(biāo)不變D．向左平移個(gè)單位長(zhǎng)度，再把所得各點(diǎn)的橫坐標(biāo)伸長(zhǎng)到原來(lái)的2倍，縱坐標(biāo)不變A函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)考點(diǎn)三圖像與性質(zhì)的綜合問(wèn)題提高性題組

函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)

(ⅲ)已知函數(shù)f(x)＝sin(ωx＋)，其中ω>0.若函數(shù)f(x)的圖象的相鄰兩條對(duì)稱軸之間的距離等于.(1)求函數(shù)f(x)的解析式；(2)求最小正實(shí)數(shù)m，使得函數(shù)f(x)的圖象向左平移m個(gè)單位后所對(duì)應(yīng)的函數(shù)是偶函數(shù)．【變式遷移】函數(shù)y=Asin(ωx+φ)的圖像及性質(zhì)(2)

解

：函數(shù)f(x)的圖象向左平移m個(gè)單位后所對(duì)應(yīng)的函數(shù)為g(x)＝sin[3(x＋m)＋]．g(x)是偶函數(shù)當(dāng)且僅當(dāng)3m＋＝kπ＋(k∈Z)，即m＝(k∈Z)．從而，最小正實(shí)數(shù)m

＝.解：(1)因?yàn)閒(x)＝sin(ωx＋)．依題意，.又T＝，故ω