人教A版高中數(shù)學(xué)（必修第一冊）同步講義 5.3誘導(dǎo)公式（原卷版）

第第頁第04講5.3誘導(dǎo)公式課程標(biāo)準學(xué)習(xí)目標(biāo)①掌握誘導(dǎo)公式的內(nèi)容、規(guī)律適用范圍。②了解誘導(dǎo)公式的作用。③會用誘導(dǎo)公式進行化簡、求值、證明恒等式理解與掌握誘導(dǎo)公式的內(nèi)容，會用誘導(dǎo)公式進行相關(guān)的運算知識點一：公式二SKIPIF1<0SKIPIF1<0SKIPIF1<0知識點二：公式三SKIPIF1<0SKIPIF1<0SKIPIF1<0知識點三：公式四SKIPIF1<0SKIPIF1<0SKIPIF1<0知識點四：公式五SKIPIF1<0SKIPIF1<0知識點五：公式六SKIPIF1<0SKIPIF1<0知識點六：公式七SKIPIF1<0SKIPIF1<0知識點七：SKIPIF1<0SKIPIF1<0題型01給角求值問題【典例1】已知SKIPIF1<0的終邊上有一點SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例2】求值：(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0；(4)SKIPIF1<0.【典例3】利用公式求下列三角函數(shù)值：(1)SKIPIF1<0：(2)SKIPIF1<0；(3)SKIPIF1<0；(4)SKIPIF1<0.【變式1】SKIPIF1<0．【變式2】求下列各三角函數(shù)值：(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0；(4)SKIPIF1<0．【變式3】求值：(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0.題型02給值(式)求值問題【典例1】已知SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例2】已知SKIPIF1<0，則SKIPIF1<0.【典例3】已知角SKIPIF1<0的頂點在坐標(biāo)原點，始邊與SKIPIF1<0軸非負半軸重合，終邊與射線SKIPIF1<0（SKIPIF1<0）重合，則SKIPIF1<0.【變式1】若SKIPIF1<0，則SKIPIF1<0.【變式2】已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0.【變式3】已知SKIPIF1<0，則SKIPIF1<0．題型03三角函數(shù)的化簡求值問題【典例1】已知在平面直角坐標(biāo)系中，點SKIPIF1<0在角SKIPIF1<0終邊上，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例2】已知SKIPIF1<0.(1)化簡SKIPIF1<0；(2)若SKIPIF1<0是第三象限角，且SKIPIF1<0，求SKIPIF1<0的值.【典例3】如圖，在平面直角坐標(biāo)系SKIPIF1<0中，鈍角SKIPIF1<0的始邊與SKIPIF1<0軸的非負半軸重合，終邊與半徑為SKIPIF1<0的圓相交于點SKIPIF1<0，過點SKIPIF1<0作SKIPIF1<0軸的垂線，垂足為點SKIPIF1<0，SKIPIF1<0．

(1)求SKIPIF1<0的值；(2)求SKIPIF1<0的值．【典例4】已知SKIPIF1<0.(1)若SKIPIF1<0，求SKIPIF1<0的值；(2)若SKIPIF1<0，求SKIPIF1<0的值.【變式1】已知SKIPIF1<0是第三象限角，且SKIPIF1<0，則SKIPIF1<0．【變式2】化簡：SKIPIF1<0．【變式3】已知SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的值.【變式4】（1）已知方程SKIPIF1<0，求SKIPIF1<0的值．（2）已知SKIPIF1<0，求SKIPIF1<0的值；題型04利用誘導(dǎo)公式證明三角恒等式【典例1】求證：SKIPIF1<0＝SKIPIF1<0．【典例2】設(shè)SKIPIF1<0.求證：SKIPIF1<0.【變式1】求證：SKIPIF1<0．【變式2】若SKIPIF1<0，求證：SKIPIF1<0.題型05誘導(dǎo)公式在三角形中的應(yīng)用【典例1】SKIPIF1<0中，若SKIPIF1<0，則SKIPIF1<0形狀為．【典例2】已知角A為銳角，SKIPIF1<0，(1)求角A的大?。?2)求SKIPIF1<0的值．【變式1】若SKIPIF1<0的內(nèi)角A，B，C滿足SKIPIF1<0，則A與B的關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【變式2】（多選）已知銳角三角形SKIPIF1<0中，設(shè)SKIPIF1<0，SKIPIF1<0則下列判斷正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0題型06誘導(dǎo)公式與同角函數(shù)基本關(guān)系的應(yīng)用【典例1】已知SKIPIF1<0，則SKIPIF1<0．【典例2】已知角SKIPIF1<0的頂點在坐標(biāo)原點，始邊與x軸非負半軸重合，終邊經(jīng)過函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）的定點M.(1)求SKIPIF1<0的值；(2)求SKIPIF1<0的值.【典例3】給出下列三個條件：①角SKIPIF1<0的終邊經(jīng)過點SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0．請從這三個條件中任選一個，解答下列問題：(1)若SKIPIF1<0為第四象限角，求SKIPIF1<0的值；(2)求SKIPIF1<0的值．【變式1】（1）求SKIPIF1<0的值.（2）求證：SKIPIF1<0.【變式2】已知函數(shù)SKIPIF1<0.(1)化簡SKIPIF1<0(2)若SKIPIF1<0，且SKIPIF1<0，求SKIPIF1<0的值.【變式3】已知SKIPIF1<0.(1)化簡SKIPIF1<0；(2)若SKIPIF1<0，且SKIPIF1<0為第四象限角，求SKIPIF1<0的值.A夯實基礎(chǔ)一、單選題1．SKIPIF1<0等于（

）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．已知SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．在平面直角坐標(biāo)系xOy中，角SKIPIF1<0和角SKIPIF1<0的頂點均與原點O重合，始邊均與x軸的非負半軸重合，它們的終邊關(guān)于直線SKIPIF1<0對稱，若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．已知函數(shù)SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的值為（

）A．3 B．4 C．5 D．67．已知函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）的圖像過定點SKIPIF1<0，且角SKIPIF1<0的始邊與SKIPIF1<0軸的正半軸重合，終邊過點SKIPIF1<0，則SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知SKIPIF1<0是第四象限角，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．以下各式化簡結(jié)果正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<010．已知角SKIPIF1<0的頂點與原點O重合，始邊與x軸非負半軸重合，它的終邊過點SKIPIF1<0，角SKIPIF1<0的終邊與角SKIPIF1<0的終邊關(guān)于y軸對稱，將OP繞原點逆時針旋轉(zhuǎn)SKIPIF1<0后與角SKIPIF1<0的終邊重合，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、填空題11．若SKIPIF1<0，則SKIPIF1<0．12．如圖，A，B是單位圓O上的點，且B在第二象限，C是圓O與x軸的正半軸的交點，A點的坐標(biāo)為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0.

四、解答題13．已知SKIPIF1<0.(1)化簡SKIPIF1<0；(2)若SKIPIF1<0是第三象限角，且SKIPIF1<0，求SKIPIF1<0的值.14．在平面直角坐標(biāo)系SKIPIF1<0中，角SKIPIF1<0以O(shè)x為始邊，它的終邊與單位圓交于第二象限內(nèi)的點SKIPIF1<0.(1)若SKIPIF1<0，求SKIPIF1<0及SKIPIF1<0的值；(2)若SKIPIF1<0，求點SKIPIF1<0的坐標(biāo).15．如圖，在平面直角坐標(biāo)系SKIPIF1<0中，鈍角SKIPIF1<0的始邊與SKIPIF1<0軸的非負半軸重合，終邊與半徑為SKIPIF1<0的圓相交于點SKIPIF1<0，過點SKIPIF1<0作SKIPIF1<0軸的垂線，垂足為點SKIPIF1<0，SKIPIF1<0．

(1)求SKIPIF1<0的值；(2)求SKIPIF1<0的值．16．已知SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的值.B能力提升1．已知函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）的圖像過定點SKIPIF1<0，且角SKIPIF1<0的始邊與SKIPIF1<0軸的正半軸重合，終邊過點SKIPIF1<0，則SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．若SKIPIF1<0的內(nèi)角A，B，C滿足SKIPIF1<0，則A與B的關(guān)系為（

）A．SKIPIF