函数y=sin2xcos2x怎么化成1/2 sin4x,求过程
根据2倍角公式:sin(2x)=2sinxcosxy=sin2xcos2x=1/2(2sin2xcos2x)=1/2sin4x
sin4x=sin(2x+2x)=sin2xcos2x+sin2xcos2x 即倍角公式
sin2xcos2x=1/2sin4x
绛旓細y=f(x)=sin2xcos2x 鈭礷(-x)=sin(-2x)cos(-2x)=-sin2xcos2x=-f(x)鈭磃(x)涓哄鍑芥暟
绛旓細y=sin2xcos2x=1/2sin4x 鏈灏忔鍛ㄦ湡=2蟺/4 =蟺/2
绛旓細Y=sin2xcos2x=1/2*2sin2xcos2x=1/2sin4x 鎵浠ュ懆鏈烼=(2蟺卤2k蟺)/4=蟺/2卤k蟺/2锛宬涓烘暣鏁 浠=f(x)锛屽垯f(-x)=1/2sin(-4x)=-1/2sin4x=-f(x)鎵浠ユ槸濂鍑芥暟
绛旓細y=sin2xcos2x=(1/2)sin4x 鎵浠ワ細鏈灏忓懆鏈熶负蟺/2 鍗曡皟澧炲尯闂翠负[(k蟺)/2-蟺/8锛(k蟺/2)+蟺/8] 鍗曡皟鍑忓尯闂翠负[(k蟺)/2+蟺/8锛(k蟺/2)+3蟺/8]锛涙渶澶у间负1/2
绛旓細y=sin2xcos2x=1/2sin4x sinx鏄鍑芥暟锛屾墍浠in4x涔熸槸濂囧嚱鏁帮紝涓斿懆鏈熶负 2蟺/4 鍗 蟺/2
绛旓細f(x)=sinxcos2x f(-x)=sin(-x)cos(-2x)=-sinxcos2x =-f(x)鎵浠ユ槸濂鍑芥暟 鍏充簬鍛ㄦ湡瑙佷笅鍥
绛旓細y锛漵in2xcos2x =1/2sin4x T=2蟺/4=蟺/2
绛旓細y=sin2xcos2x=1/2脳锛2sin2xcos2x)=1/2脳sin4x 鏈澶у间负1/2 鏈灏忓间负-1/2
绛旓細y锛漵in2xcos2x =1/2sin4x T=2蟺/4=蟺/2
绛旓細鎶y=sin2x,鐨勫浘鍍忔部鐫妯酱寰宸﹀钩绉伙紙蟺/4锛変釜鍗曚綅銆傚氨浼氬緱鍒 y=cos2x,鈥斺旇繖鏄敱浜 y=sin2锛坸-蟺/4锛夛紳sin锛2x-蟺/2锛夛紳cos2x,