新高考數(shù)學(xué)一輪復(fù)習(xí)講義 第19講 三角恒等變換（原卷版）

第19講三角恒等變換（精講）題型目錄一覽①公式的直接應(yīng)用②輔助角公式的應(yīng)用③三角函數(shù)式的化簡(jiǎn)④給值求值問(wèn)題⑤給值求角問(wèn)題一、知識(shí)點(diǎn)梳理一、知識(shí)點(diǎn)梳理一、兩角和與差的正余弦與正切①SKIPIF1<0； ②SKIPIF1<0；③SKIPIF1<0； 二、二倍角公式①SKIPIF1<0；②SKIPIF1<0； ③SKIPIF1<0；三、降冪公式SKIPIF1<0四、輔助角公式SKIPIF1<0（其中SKIPIF1<0）．【常用結(jié)論】拆分角的變形：①SKIPIF1<0；SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0；④SKIPIF1<0；⑤SKIPIF1<0．二、題型分類精講二、題型分類精講題型一公式的直接應(yīng)用策略方法應(yīng)用公式化簡(jiǎn)求值的策略(1)首先要記住公式的結(jié)構(gòu)特征和符號(hào)變化規(guī)律．例如兩角差的余弦公式可簡(jiǎn)化為“同名相乘，符號(hào)相反”．(2)注意與同角三角函數(shù)基本關(guān)系、誘導(dǎo)公式的綜合應(yīng)用．(3)注意配方法、因式分解和整體代換思想的應(yīng)用．【典例1】SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例2】下列各式中，值為SKIPIF1<0的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【題型訓(xùn)練】一、單選題1．SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．設(shè)SKIPIF1<0，則SKIPIF1<0等于（

）A．-2 B．2 C．-4 D．44．已知角SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．若SKIPIF1<0為銳角，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．SKIPIF1<06．已知SKIPIF1<0，則SKIPIF1<0的值是（

）A．SKIPIF1<0 B．2 C．SKIPIF1<0 D．SKIPIF1<0二、填空題7．計(jì)算：SKIPIF1<0______.8．若cosα＝－SKIPIF1<0，α是第三象限的角，則sinSKIPIF1<0＝____________.9．SKIPIF1<0____________．10．已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0__________．題型二輔助角公式的應(yīng)用【典例1】求函數(shù)SKIPIF1<0的最大值（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【題型訓(xùn)練】一、單選題1．該函數(shù)SKIPIF1<0的最大值是（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．函數(shù)SKIPIF1<0的最小正周期和最大值分別是（

）A．SKIPIF1<0和SKIPIF1<0 B．SKIPIF1<0和2 C．SKIPIF1<0和SKIPIF1<0 D．SKIPIF1<0和23．）已知SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．SKIPIF1<0的值所在的范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空題5．已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最大值為________6．若SKIPIF1<0，則SKIPIF1<0__________．7．函數(shù)SKIPIF1<0的最大值為______．題型三三角函數(shù)式的化簡(jiǎn)策略方法1．三角函數(shù)式的化簡(jiǎn)要遵循“三看”原則2．三角函數(shù)式化簡(jiǎn)的方法(1)弦切互化，異名化同名，異角化同角，降冪或升冪．(2)在三角函數(shù)式的化簡(jiǎn)中“次降角升”和“次升角降”是基本的規(guī)律，根號(hào)中含有三角函數(shù)式時(shí)，一般需要升次．【典例1】已知SKIPIF1<0，則SKIPIF1<0的值是（

）A．SKIPIF1<0 B．不存在 C．SKIPIF1<0或不存在 D．SKIPIF1<0【典例2】已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【題型訓(xùn)練】一、單選題1．已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知SKIPIF1<0，則SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知銳角SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的值為（

）A．1 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空題8．函數(shù)SKIPIF1<0的最小正周期為__________．9．已知SKIPIF1<0為鈍角，SKIPIF1<0，則SKIPIF1<0的值為______.10．已知SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的值是______.題型四給值求值問(wèn)題策略方法給值求值：一般是給出某些角的三角函數(shù)值，求另外一些角的三角函數(shù)值，解題的關(guān)鍵在于“變角”，使相關(guān)角相同或具有某種關(guān)系．【典例1】已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【題型訓(xùn)練】一、單選題1．已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．SKIPIF1<04．已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知SKIPIF1<0，SKIPIF1<0為銳角，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．已知SKIPIF1<0，且SKIPIF1<0，則cosβ=（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．0二、填空題10．已知SKIPIF1<0，則SKIPIF1<0__________.11．已知SKIPIF1<0，則SKIPIF1<0________.12．已知SKIPIF1<0，則SKIPIF1<0__________．13．已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0________．題型五給值求角問(wèn)題策略方法給值求角：實(shí)質(zhì)上可轉(zhuǎn)化為“給值求值”，即通過(guò)求角的某一個(gè)三角函數(shù)值來(lái)求角．在選取函數(shù)時(shí)，遵循以下原則：①已知正切函數(shù)值，選正切函數(shù)．②已知正、余弦函數(shù)值，若角的范圍是0，π2，選正、余弦函數(shù)皆可，若角的范圍是(0，π)，選余弦函數(shù)，若角的范圍是【典例1】已知SKIPIF1<0，則SKIPIF1<0的值可能為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【題型訓(xùn)練】一、單選題1．設(shè)SKIPIF1<0，SKIPIF1<0是方程SKIPIF1<0的兩根，且SKIPIF1<0，則SKIPIF1<0（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<02．已知SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0=（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<03．已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的值是（

）A．