(完整版)高中數(shù)學(xué)必修4第一章第三章知識(shí)點(diǎn)經(jīng)典題型,推薦文檔

1、第三章三角恒等變換1、角三角函數(shù)的基本關(guān)系： (1)sin2a+ cos2a= 1 (sin2a= 1- cos2a,cos2a= 1- sin2a)；(2)sina = tanasina= tanacosa, cosa= sina cosatana2、函數(shù)的誘導(dǎo)公式：(1)sin (2ka+a)= sina， cos(2ka+a)= cosa， tan (2ka+a)= tana(k z)(2)sin (a+a)= -sina， cos(a+a)= -cosa， tan (a+a)= tana(3)sin (-a)= -sina， cos(-a)= cosa， tan (-a)= - tan

2、a(4)sin (a-a)= sina， cos(a-a)= -cosa， tan (a-a)= - tana 口訣：函數(shù)名稱不變，符號(hào)看象限5 sin aaaa( ) 2 -a = cosa，cos 2 -a = sina(6)sin 2 +a = cosa，cos 2 +a= -sina口訣：正弦與余弦互換，符號(hào)看象限3、兩角和與差的正弦、余弦和正切公式： cos(a-a)= cosacosa+ sinasinacos (a+a)= cosacosa-sinasina；sin (a-a)= sinacosa- cosasinasin (a+a)= sinacosa+ cosasina；ta

3、n(a-a)=tan(a+a)=tana- tan a 1+ tanatan atana+ tan a 1- tanatan a4、二倍角的正弦、余弦和正切公式： sin 2a= 2 sinacosa 1 sin 2a= sin 2 a+ cos2 a 2 sinacosa= (sina cosa)2 cos 2a= cos2a- sin2a= 2 cos2a-1 = 1- 2 sin2a 升冪公式1+ cosa= 2cos2 a2cos2 a= cos2a+1,1- cosa= 2 sin 2 a2sin2 a= 1- cos 2a 降冪公式2，2tan 2a= 2 tana1- tan2a

4、5.把兩個(gè)三角函數(shù)的和或差化為“一個(gè)三角函數(shù)”ba 2 + b 2acosa bsina=sin(aa)，tana=.a例題：1sin105cos105的值為()1a.41b433c. 41d 42. 若 sin24，490，則 tanatanb 與 1 的大小關(guān)系為() atanatanb1b. tanatanb1ctanatanb1d不能確定9. 函數(shù) f(x)sin2x-cos2x 的最小正周期是()a. a2b. c. 2d .41111. 解析 原式2sin2102sin304.答 案 b132. 解 析 (cossin)21sin2144.又42，cos90，a，b 分別都為銳角

5、則有 tana0，tanb0，tanc0.又c(ab)，tanatanbtanctan(ab)1tanatanb0， 即 tanatanb1.答 案 b2)9. 解析 f(x)sin2x-cos2x=sin(2x- a4答 案 b“”“”at the end, xiao bian gives you a passage. minand once said, people who learn to learn are very happy people. in every wonderful life, learning is an eternal theme. as a professiona

6、l clerical and teaching position, i understand the importance of continuous learning, life is diligent, nothing can be gained, only continuous learning can achieve better self. only by constantly learning and mastering the latest relevant knowledge, can employees from all walks of life keep up with the pace of enterprise development and innovate to meet the needs of the market. this document is also edited by my studi