cos3x值域及其周期
\u51fd\u6570y=5sin3x 12'cos3x\u7684\u503c\u57df\u548c\u5468\u671f\u5206\u522b\u4e3a\u591a\u5c11\u51fd\u6570\u5e94\u8be5\u662fy=5sin3x +12'cos3x\u5427
\u82e5\u662f
\u89e3y=5sin3x +12'cos3x
=13(5/13sin3x+12/13cos3x)
=13sin(3x+\u03b8)
\u6545\u51fd\u6570\u7684\u5468\u671fT=2\u03c0/3
\u51fd\u6570\u7684\u503c\u57df\u4e3a[-13,13]
-1<=cos3x<=1
-1<=-cos3x<=1
\u6240\u4ee5\u503c\u57df[-1,1]
值域-1到1闭区间，周期2π/3
值域 【1，-1】 周期2п/3
【-1,1】周期为2丌/3
绛旓細鍊煎煙鏄:-3鍒3, 鍛ㄦ湡鏄:-蟺/2+2k蟺鍒3蟺/2+2k蟺
绛旓細鍑芥暟搴旇鏄痽=5sin3x +12'cos3x鍚 鑻ユ槸 瑙=5sin3x +12'cos3x =13(5/13sin3x+12/13cos3x)=13sin(3x+胃)鏁呭嚱鏁扮殑鍛ㄦ湡T=2蟺/3 鍑芥暟鐨鍊煎煙涓篬-13,13]
绛旓細cos3x=cos(蟺/2-x)===> 3x=2k蟺+(蟺/2-x)鎴 3x=2k蟺-(蟺/2-x)===> x=(4k+1)蟺/8 鎴 x=(4k-1)蟺/4銆傚洜涓篺(x)=sin3x+3cosx鐨鍛ㄦ湡涓2蟺锛屾墍浠ュ叾鏈澶у煎拰鏈灏忓煎彲浠ュ湪涓涓懆鏈焄0,2蟺]鍐呯爺绌躲傚湪涓涓懆鏈焄0,2蟺]鍐咃紝鍑芥暟椹荤偣鏈夊叚涓細X1=蟺/8锛孹2=5蟺/8锛孹3=3...
绛旓細y=cos3x鏄湁鐣屽嚱鏁拌繕鏄棤鐣屽嚱鏁帮紵浣欏鸡鍑芥暟鐨勫畾涔夊煙涓猴紙-鈭烇紝鈭烇級锛鍊煎煙鏄蓟-1锛1锛姐傛墍浠ユ槸鏈夌晫鍑芥暟銆
绛旓細銆愬垎鏋愩戝埄鐢ㄤ笁瑙掑嚱鏁扮殑鎭掔瓑鍙樻崲鍖栫畝鍑芥暟鐨勮В鏋愬紡锛屽啀鍒╃敤姝ｅ鸡鍑芥暟鐨勬湁鐣屾ф眰寰楀嚱鏁鍊煎煙锛庛愯В绛斻cos3xsin2x=3cos2x−sin2x2sinxcosx=3−tan2x2tanx锛屼护t=tanx锛屽垯t=0锛屼笖3−tan2x2tanx=3−t22t=−2 t2−3t锛屽綋t>0鏃讹紝t2−3t>0锛屽彲寰...
绛旓細1-cosxcos2xcos3x =1-(1/2)*(cos3x+cosx)cos3x =1-(1/2)*(cos3x)^2-(1/2)*cosxcos3x =1-(1/4)*(1+cos6x)-(1/4)*(cos4x+cos2x)=3/4-(1/4)*cos6x-(1/4)*cos4x-(1/4)*cos2x =(1/4)*[(1-cos6x)+(1-cos4x)+(1-cos2x)]~(1/4)*[(1/2)*36x^2+(1...
绛旓細sin2x娌℃湁姣2蟺鏇村皬鐨勬鍛ㄦ湡 浜庢槸 鍑芥暟f(x)=cos3x sin2x鏈灏忔鍛ㄦ湡涓2蟺 鍥犱负杩欑鍑芥暟鐨勫懆鏈熷叾瀹炴槸2n蟺鏈夋棤鏁颁釜锛屼竴鑸敤鏈灏忓叕鍊嶆暟 鍑芥暟鐨勬ц川鍢 1銆佸畾涔夊煙锛3^(2x-1)-1/9>=0 3^(2x-1)>=1/9=3^(-2)2x-1>=-2 x>=-1/2 鍊煎煙锛歽>=02銆亂=(1/2)^(x^2-6x 17)=(1/...
绛旓細cos3x=cos(2x+x)=cos2xcosx-sin2xsinx=2cosx³-cosx-2sinx²cosx=2cosx³-cosx-2(1-cosx²)cosx=4cosx³-3cosx y=(cos3x-cosx)/cosx=4(cosx²-1)=-4sinx²鍙坈osx涓嶄负0锛宻inx²=1-cosx²涓嶄负1 鎵浠鍊煎煙鏄紙-4锛0]浠ヤ笂cosx²,...
绛旓細鍜屼竴鑸殑涓夎鍑芥暟涓鏍凤紝鍊煎煙鏄細锛-1锛1锛
绛旓細y=sin^2 (3x)=(1-cos6x)/2 鏈灏忔鍛ㄦ湡T=蟺/3 鍊煎煙[0,1]
