化難為易化繁為簡(jiǎn)2019年4月版——選擇、填空篇——f(x)(3sinxcos)(3cosxsin)22【秒解】根據(jù)口訣：和差不變,積商減半,易知均為,則2f(x)(3sinxcosx)(3cosxsinx)B四大特色助快速解題◎100個(gè)秒解技巧◎80個(gè)精妙二級(jí)結(jié)論◎10年高考真題為例◎700個(gè)例題深入剖析12f速解“奇函數(shù)＋Cf1aS與nnn210059、三角函數(shù)巧用特值法、估算法解三角函數(shù)圖像問題sin(2x)◆例1y）2xxxx2484xy1當(dāng)x選,,22f(x)cos(x)◆例則）f(x)y1xO154414341434(k),kZ(2k),kZ,k,2k1313(2k(k,k),kZ,2k),kZ444451130f(x)x在f(x)T2()2,44,又,)(4413∴f(x)(2k.),kZ,2k44y1xO14541434,◆例fxsinxcosx0,xR,fxfxx.則xx2x)f(x),430f(x)在xf(x)xfx,)1∴sin(2x∴.與,42y1xy則的◆例f()xx）8484bbxabx),)ax22a③f(x)2x2x2sin(2x)4①f1②f(x);0f(x)2x在x)f(x)=OAf(x)4TTyOA42OA選42yy21AOOxBπ◆例文11)f(x)2xx)）2π2x6sinx,f(x)2xx)2與ycos2xy6sinx,2在選f(x)xy6ycos2x1xO4x2(2sin(x)(|)◆例6y)6610111011,,66y2x21124取2當(dāng)函數(shù)的周期T比比,121161x,y選y2sin(2x)當(dāng)632y2T44x11xR()y=1的()y=fx◆例文fx=3sinwx+coswx(w>0),112則()2）fx323baasinxbcosxabsin(x),(tan22bf(x)31f(x)y軸sinxbcosxabsin(x),(tan)22a()fx2y=1TAB比比選33y2y1xxBA35f(x)08f(x)sin(2x)若且f(x)則|xx|）xx031212213())(()()3363x0當(dāng)x,f(x)sin(2xf(x)sin(2x)在)f(0)32333f(x)f(x)f(x)與y和))232|xx|xx0x0f(0)f()01332112x|近則|x.3213A◆例9:yP(x,cosx)x,y,BC22x00O1||（,O)）Bsin(2x||0623121222yBA(P)x21當(dāng)x,|OA|,P2|OB|012sin(2x)=60與0y2sinxy2cosx23則=.sinx與yy2sinxy2cosx與,ycosxy6yxDCxBycosx22CD=TB222yAOxBCy2xB22又2322而CB=T,2∴T22fxx◆例7)yy2（）yf(x)yf(x)yf(x)xyf(x)(22ysin圖像y②ysinxx2xyO22y選DxO2(x)x◆例fxx,,,0xxx且xm1212m|f(x)f(x)||f(x)f(x)||f(x)f(x)|12231m(mmN)則.mm)【