f=sinx-cosx的最大值 怎么算？具体怎么转换 函数f(x)=sinx-cosx的最大值是多少？怎么算啊？我...
f\uff08x\uff09=sinx-cosx\u7684\u6700\u5927\u503c\u89e3\uff1a(\u53cb\u60c5\u63d0\u793a\uff1a\u8f85\u52a9\u89d2\u516c\u5f0f\uff1aasinx+bcosx=(\u221a(a^2+b^2))sin(x+\u03b1)\uff0c\u5176\u4e2dtan\u03b1=b/a)
f(x)=(\u221a2)sin(x-\u03c0/4)
\u6545\u5f53x-\u03c0/4=\u03c0/2+2k\u03c0\uff0c\u5373x=3\u03c0/4+2k\u03c0\u65f6\uff0c\u51fd\u6570f(x)\u6709\u6700\u5927\u503c\u221a2.
f(x)=sinx-cosx=\u221a2sin(x-\u03c0/4)
\u6240\u4ee5f(x)\u7684\u6700\u5927\u503c\u4e3a\u221a2
f=sinx-cosx=cos(π/2-x)-cosx=-2sin(π/4)sin(π/4-x)=-√2sin(π/4-x)
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绛旓細sin²x+cos²x-2sinxcosx=(sinx-cosx)²鈮0 鎵浠 sin²x+cos²x鈮2sinxcosx 鎵浠 y²=(sinx+cosx)²=sin²x+cos²x+2sinxcosx鈮in²x+cos²x+sin²x+cos²x=2 鎵浠 y鐨勬渶澶у涓衡垰2 ...
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绛旓細f(x)= ( sinx - cosx) |cosx| = ( sinx - cosx)cosx = sinx.cosx - (cosx)^2 = (1/2)sin2x - (1/2)(1+ cos2x)=(鈭2/2)sin(2x-蟺/4) - 1/2 max f(x) = f(11蟺/8) = 鈭2/2 - 1/2 ie 鏈澶у f锛坸锛=锛sinx-cosx锛夛綔cosx锝=鈭2/2+ 1/2 ...
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绛旓細=鈭2sin(x+蟺/4)鈭碝鐨勫煎煙涓篬-鈭2锛屸垰2]鍙堚埖M²=(sinx+cosx)²=sin²x+cos²x+2sinxcosx=1+2sinxcosx 鈭磗inxcosx=(M²-1)/2 鈭磞=(M²-1)/2+M=(1/2)(M-1)²-1 鈭礛鐨勫煎煙鏄痆-鈭2锛屸垰2]鈭鏈澶у鏄綋M=-鈭2鏃讹紝y=鈭2+1/2 ...
