sinx+2sin2x+3sin3x+4sin4x+.+nsinnx求和
[-(cos x,isinx)-(cos 2x,isin 2x)-...(cox nx,isin nx)]'=-[cos n(n+1)x/2,i sin n(n+1)x/2 ]'=(2n+1)/2 [sin n(n+1)x/2,i cos n(n+1)x/2]sinx+2sin2x+3sin3x+4sin4x+.+nsinnx=(2n+1)/2 sin n(n+1)x/2绛旓細sinx鍛ㄦ湡鏄2蟺 2sin2x鍛ㄦ湡鏄 3cos3x鍛ㄦ湡鏄2蟺/3 鎵浠ュ懆鏈熸槸杩欎笁涓殑鏈灏忓叕鍊嶆暟 2=6/3 1=3/3 2/3=2/3 6,3,2鐨勬渶灏忓叕鍊嶆暟鏄6 鎵浠2蟺锛屜锛2蟺/3鐨勬渶灏忓叕鍊嶆暟鏄6蟺/3 鍗2蟺
绛旓細宸﹁竟鏈澶1+2=3锛屽洜姝わ紝sin3x鈮0 鎶樺紑锛屾秷鍘籧osx,寰椾竴涓sinx鐨6娆℃柟绋嬨倀=sinx 16t^6-24t^3-12t^2+12t+9=0 f(t)=16t^6-24t^3-12t^2+12t+9,fmin=0.7496688887>0,鏃犺В銆
绛旓細sinXsin2X=sinX*2sinXcosX=2sin^2XcosX
绛旓細Sinx涓sin2x鍚屼竴鏁拌酱涓婂浘鍍 sinx鍑芥暟锛屽嵆姝ｅ鸡鍑芥暟锛屼笁瑙掑嚱鏁扮殑涓绉嶃傛寮﹀嚱鏁版槸涓夎鍑芥暟鐨勪竴绉嶃傚浜庝换鎰忎竴涓疄鏁皒閮藉搴旂潃鍞竴鐨勮锛堝姬搴﹀埗涓瓑浜庤繖涓疄鏁帮級锛岃岃繖涓鍙堝搴旂潃鍞竴纭畾鐨勬寮﹀約inx锛岃繖鏍凤紝瀵逛簬浠绘剰涓涓疄鏁皒閮芥湁鍞竴纭畾鐨勫約inx涓庡畠瀵瑰簲锛屾寜鐓ц繖涓搴旀硶鍒欐墍寤虹珛鐨勫嚱鏁帮紝琛ㄧず涓簓=sinx...
绛旓細鏈澶у间负3
绛旓細[-(cos x,isinx)-(cos 2x,isin 2x)-...(cox nx,isin nx)]'=-[cos n(n+1)x/2,i sin n(n+1)x/2 ]'=(2n+1)/2 [sin n(n+1)x/2,i cos n(n+1)x/2]sinx+2sin2x+3sin3x+4sin4x+...+nsinnx =(2n+1)/2 sin n(n+1)x/2 ...
绛旓細sin2x=2sinxcosx銆傚鏋淴鏄竴涓搴︾殑璇,閭ｄ箞瀹冪殑鍘熷叕寮忔槸锛歴in锛圶+Y锛=sinXcosY+cosXsinY銆傝繖鍏跺疄鏄敱涓よ鍜岀殑姝ｅ鸡鍏紡锛岀敱sin锛坸+y锛=sinxcosy+cosxsiny寰楀埌銆傛澶,杩樻湁鍑犱釜涓夎鎭掔瓑寮忥細cos锛坸-y锛=cosxcosy+sinxsiny sin锛坸-y锛=sinxcosy-cosxsiny 鎯虫帹瀵煎嚭鍚勭浜屽嶈鍏紡锛屽彧闇灏嗗拰瑙掑叕寮...
绛旓細sin2x=sinx*2sinxcosx=2sin_xcosx=2锛1-cos_x锛塩osx=2cosx-2cos_x銆俿in鎸囧湪鐩磋涓夎褰腑锛屾寮︽槸鍕句笌寮︾殑姣斾緥銆傚彜浠ｈ鐨勫嬀涓夎偂鍥涘鸡浜斾腑鐨勫鸡锛屽氨鏄洿瑙掍笁瑙掑舰涓殑鏂滆竟銆傝偂灏辨槸浜虹殑澶ц吙锛屽彜浜虹О鐩磋涓夎褰腑闀跨殑閭ｄ釜鐩磋杈逛负鑲°
绛旓細sinx+sin2x+sin3x+...+sin(nx)绛変簬1/2*(cot(x/2)-cot(x/2)*cos(nx)+sin(nx))銆傝В锛氬洜涓篶os(A-B)-cos(A+B)=2sinAsinB锛岄偅涔2sinx*sin(x/2)=cos(x-x/2)-cos(x+x/2)=cos(x/2)-cos(3x/2)2sin(2x)*sin(x/2)=cos(2x-x/2)-cos(2x+x/2)=cos(3x/2)-cos(5x...
绛旓細搴旇宸笉澶 鍕夊己鐪嬪惂
