函数f(x)=sin2x-cos2x是
\u51fd\u6570f\uff08x\uff09=sin2x\u00b7cos2x\u662ffx=\uff08sin4x\uff09/2
sin\uff084x+2\u03c0\uff09=sin\uff084\uff08x+\u03c0/2\uff09\uff09=sin4x\u6240\u4ee5\u5468\u671f\u662f\u03c0/4
sin4x=-sin-4x \u6240\u4ee5\u662f\u5947\u51fd\u6570
\u6240\u4ee5\u662fD
\u4e09\u89d2\u51fd\u6570\uff01\u7528\u516c\u5f0f\u89e3\uff01\u4e8c\u500d\u89d2\u516c\u5f0f\uff01\u624b\u673a\u4e0a\u9762\u4e0d\u597d\u89e3\uff01
f(x)=sin²x-cos²x = -cos(2x)是偶函数，最小正周期是π
D正确
用辅助角公式 根号2sin(2x 3派/4） 选D
C f(x)= 根号2正弦（2x-四分之 ）
绛旓細锛1锛 f(x)=sin2x- 3 cos2x=2sin(2x- 蟺 3 ) 锛涒︼紙4鍒嗭級鍥 x鈭圼 蟺 4 锛 蟺 2 ] 锛屾墍浠 蟺 6 鈮2x- 蟺 3 鈮 2蟺 3 锛涘綋 x= 蟺 4 鏃讹紝 f(x ) min =f( 蟺 4 )=1 鈥︼紙6鍒...
绛旓細瑙ｏ細鍥犱负f(x)=a*sin 2x-(cos x)^2+sin x^2杩囩偣锛埾/6锛1锛夋墍浠(x)=a*(鈭3/2)-(鈭3/2)^2+1/4 =a*(鈭3/2)-3/4+1/4=1 鍙互寰楀埌a*(鈭3/2)=3/2 a=鈭3 鍋氭绫婚鐩殑鏂规硶锛氬皢棰樹腑鎵杩扮殑瀹氱偣甯﹀叆鏈煡鍑芥暟灏辫兘姹傚嚭鏈煡鍑芥暟鎴栬呰姹傜殑鏈煡鏁癮銆
绛旓細sin²a=16/25 绗洓璞￠檺 cosa=3/5,sina=-4/5 f(a)=[1-鈭2sin(2a-45)]/cosa =[1-鈭2(sin2acos45-cos2asin45)]/cosa =[1-鈭2(sin2a*鈭2/2-cos2a*鈭2/2)]/cosa =(1-sin2a+cos2a)/cosa =(1-2sinacosa+2cos²a-1)/cosa =-2sina+2cosa =14/5 ...
绛旓細锛1锛 f(x)= 1 2 sin2x- 3 cos2x+1 2 + 1 2 3 = ( 1 2 sin2x- 3 2 cos2x) = sin(2x- 蟺 3 ) T=蟺锛涳紙2锛夌敱 - 蟺 2 +2k蟺鈮2x- 蟺 3 鈮 蟺 2 +2k蟺(k鈭坺) 锛屽彲寰楀崟...
绛旓細瑙ｏ細(1)f(x)锛漵in(2x锛嬒/6)锛媠in(2x锛嵪/6)锛2cos²x 锛漵in2xcos蟺/6锛媍os2xsin蟺/6锛媠in2xcos蟺/6锛峜os2xsin蟺/6锛2cos²x 锛2sin2xcos蟺/6锛2cos²x 锛濃垰3sin2x锛媍os2x锛1 锛2sin(2x锛嬒/6)锛1 鈭碉紞1鈮in(2x锛嬒/6)鈮1 鈭磃(x)max锛1脳2...
绛旓細锛1锛夆埖f锛坸锛=cos2x+sin2x= 2 锛 2 2 cos2x+ 2 2 sin2x锛= 2 sin锛2x+ 蟺 4 锛夛紝鈭-1鈮in锛2x+ 蟺 4 锛夆墹1锛屸埓f锛坸锛夌殑鏈澶у间负 2 锛屸埖蠅=2锛屸埓鍛ㄦ湡T= 2蟺 2 =蟺锛涳紙2锛夆埖f锛 伪 2 + ...
绛旓細瑙ｄ箣寰 - 蟺 3 +k蟺鈮鈮 蟺 6 +k蟺 锛坘鈭圸锛夛紝鈭鍑芥暟f锛坸锛鐨勯掑鍖洪棿鏄 [- 蟺 3 +k蟺锛 蟺 6 +k蟺] 锛宬鈭圸锛庯紙鈪★級鐢眆锛坸锛夆墺2锛屽緱 2sin(2x+ 蟺 6 )+1鈮2 锛坘鈭圸锛夛紝鍗 sin(2x+ 蟺 6 )鈮 1 2 ...
绛旓細2 2 锛涘綋x= 3蟺 8 鏃讹紝sin锛2x- 蟺 4 锛夊彇寰楁渶澶у1鐢辨鍙緱锛f锛坸锛鍦ㄥ尯闂 [0锛 蟺 2 ] 涓婄殑鏈澶у间负f锛 3蟺 8 锛=2 2 锛涙渶灏忓间负f锛0锛=-2锛
绛旓細2sinx(cosx-sinx) cosx-sinx =sin2x 锛屸埓f锛坸锛夌殑鏈灏忔鍛ㄦ湡涓合锛7鍒嗭級锛堚叀锛夆埖 cos( 蟺 4 +x)= 3 5 鈭 f(x)=sin2x=-cos(2x+ 蟺 2 )=-2co s 2 (x+ 蟺 4 )+1 = -2脳 9 25 +1= 7 25 锛
绛旓細锛堚厾锛 f(x)= 3 2 sin2x- 1 2 cos2x- 1 2 = sin(2x- 蟺 6 )- 1 2 锛 T= 2蟺 2 =蟺 锛屾晠f锛坸锛夌殑鏈灏忔鍛ㄦ湡涓合锛庯紙鈪★級鍥犱负0鈮鈮 蟺 2 锛屾墍浠 - 蟺 6 鈮2x- 蟺 6 鈮 5蟺 ...
