1、5.4簡(jiǎn)單的三角恒等變換,第五章 三角函數(shù)、解三角形,NEIRONGSUOYIN,內(nèi)容索引,基礎(chǔ)知識(shí) 自主學(xué)習(xí),題型分類(lèi) 深度剖析,課時(shí)作業(yè),1,基礎(chǔ)知識(shí) 自主學(xué)習(xí),PART ONE,知識(shí)梳理,1.兩角和與差的余弦、正弦、正切公式,ZHISHISHULI,cos cos sin sin ,sin cos cos sin ,sin cos cos sin ,cos()cos cos sin sin (C() cos() (C() sin() (S() sin() (S(),2.二倍角公式,sin 2 ； cos 2 ； tan 2 .,2sin cos ,12sin2,cos2sin2,2cos

2、21,1.誘導(dǎo)公式與兩角和差的三角函數(shù)公式有何關(guān)系？,【概念方法微思考】,提示誘導(dǎo)公式可以看成和差公式中k (kZ)時(shí)的特殊情形.,2.怎樣研究形如f(x)asin xbcos x函數(shù)的性質(zhì)？,提示先根據(jù)輔助角公式asin xbcos x sin(x)，將f(x)化成f(x)Asin(x)k的形式，再結(jié)合圖象研究函數(shù)的性質(zhì).,基礎(chǔ)自測(cè),JICHUZICE,題組一思考辨析 1.判斷下列結(jié)論是否正確(請(qǐng)?jiān)诶ㄌ?hào)中打“”或“”) (1)存在實(shí)數(shù)，使等式sin()sin sin 成立.(),1,2,3,4,5,6,7,8,題組二教材改編,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,3.P

3、131T5sin 347cos 148sin 77cos 58 .,解析sin 347cos 148sin 77cos 58 sin(27077)cos(9058)sin 77cos 58 (cos 77)(sin 58)sin 77cos 58 sin 58cos 77cos 58sin 77,8,4.P146A組T4(2)tan 10tan 50 tan 10tan 50 .,1,2,3,4,5,6,7,8,題組三易錯(cuò)自糾,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,

4、3,4,5,6,7,4sin ,8,2,題型分類(lèi)深度剖析,PART TWO,第1課時(shí)兩角和與差的正弦、余弦和正切公式,題型一和差公式的直接應(yīng)用,自主演練,解析sin215cos215(cos215sin215),(1)使用兩角和與差的三角函數(shù)公式，首先要記住公式的結(jié)構(gòu)特征. (2)使用公式求值，應(yīng)先求出相關(guān)角的函數(shù)值，再代入公式求值.,題型二和差公式的靈活應(yīng)用,多維探究,命題點(diǎn)1角的變換,于是cos cos() cos()cos sin()sin ,命題點(diǎn)2三角函數(shù)式的變換,命題點(diǎn)3公式的逆用與變形,得sin22sin cos cos2sin22sin cos cos2 (sin2cos2)(

5、cos2sin2)2(sin cos sin cos )112sin(),(1)解決三角函數(shù)的求值問(wèn)題的關(guān)鍵是把“所求角”用“已知角”表示.當(dāng)“已知角”有兩個(gè)時(shí)，“所求角”一般表示為兩個(gè)“已知角”的和或差的形式；當(dāng)“已知角”有一個(gè)時(shí)，此時(shí)應(yīng)著眼于“所求角”與“已知角”的和或差的關(guān)系.,sin sin()sin()cos cos()sin ,思想方法,SIXIANGFANGFA,用聯(lián)系的觀點(diǎn)進(jìn)行三角變換,三角變換的關(guān)鍵是找到條件和結(jié)論中的角和式子結(jié)構(gòu)之間的聯(lián)系.變換中可以通過(guò)適當(dāng)?shù)夭鸾?、湊角或?qū)κ阶诱w變形達(dá)到目的.,例 (1)(2018紹興一中期中)(1tan 21)(1tan 20)(1ta

6、n 25)(1tan 24)的值為 A.2 B.4 C.8 D.16,解析(1tan 21)(1tan 20)(1tan 25)(1tan 24) 1tan(4524)(1tan 24)1tan(4525)(1tan 25),cos sin ，,3,課時(shí)作業(yè),PART THREE,基礎(chǔ)保分練,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,A.abc B.bac C.cab D.acb,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,

7、7,8,9,10,11,12,13,14,15,16,解析asin 40cos 127cos 40sin 127 sin(40127)sin 167sin 13，,sin(5645)sin 11，,sin 13sin 12sin 11，acb.,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,

8、11,12,13,14,15,16,所以cos()cos2() cos 2cos()sin 2sin(),1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,技能提升練,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,拓展沖刺練,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16