已知函数f(x)=cos(四分之派)求fx的最小正周期及最值
\u5df2\u77e5\u51fd\u6570fx=2cos\u62ec\u53f7x\u52a0\u56db\u5206\u4e4b\u6d3e\u00d7cos\u62ec\u53f7x\u51cf\u56db\u5206\u4e4b\u6d3e \u3001\u518d\u52a0\u4e0a\u6839\u53f73sin2x \u6c42\u00b7\u51fd\u6570\u503c\u57df\u548c\u6700\u5c0f\u6b63\u5468\u671f\u8fd9\u4e2a\u662f\u6211\u505a\u7684\u6b65\u9aa4~
f(x)=(\u221a3/2)sin2wx\uff0d(1/2)cos2wx\uff0d(1/2)=sin(2wx\uff0d\u03c0/6)\uff0d(1/2)\u3002\u5468\u671fT=2\u03c0/|w|=\u03c0\uff0c\u5219w=1\uff1b\u6b64\u65f6f(x)=sin(2x\uff0d\u03c0/6)\uff0d(1/2)\u589e\u533a\u95f4\u662f2k\u03c0\uff0d\u03c0/2\u22642x\uff0d\u03c0/6\u22642k\u03c0\uff0b\u03c0/2\uff0c\u5f97\uff1ak\u03c0\uff0d\u03c0/6\u2264x\u2264k\u03c0\uff0b\u03c0/3
f(x)=cos(四分之派)=√2/2, 这是一条平行于x轴的直线，不是周期函数，所以不存在最小的正周期若f(x)=cos(π/4)x的话，最小的正周期T=8,最大值y=1,最小值y=-1
绛旓細f(x)=cos(鍥涘垎涔嬫淳)=鈭2/2, 杩欐槸涓鏉″钩琛屼簬x杞寸殑鐩寸嚎锛屼笉鏄懆鏈熷嚱鏁帮紝鎵浠ヤ笉瀛樺湪鏈灏忕殑姝ｅ懆鏈 鑻(x)=cos(蟺/4)x鐨勮瘽锛屾渶灏忕殑姝ｅ懆鏈烼=8,鏈澶у紋=1,鏈灏忓紋=-1
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绛旓細姹備笉瀹氱Н鍒嗭細鈭玞os⁶x dx 瑙ｏ細閫掓帹鍏紡锛氣埆cosⁿxdx=(1/n)(cosⁿ⁻¹xsinx)+[(n-1)/n]鈭玞osⁿ⁻²xdx 鍘熷紡=(1/6)(cos⁵xsinx)+(5/6)鈭玞os⁴xdx=(1/6)(cos⁵xsinx)+(5/6)[(1/4)(cos³xsinx)...
绛旓細璁鍑芥暟f(X)=sin(鍥涘垎涔嬫淳x-鍏垎涔嬫淳)-cos鍥涘垎涔嬫淳x銆(1)姹俧x鐨勫崟璋冨鍖洪棿(2)鑻灞炰簬(0,4)姹倅=f(x)鐨勫煎煙... 璁惧嚱鏁癴(X)=sin(鍥涘垎涔嬫淳x-鍏垎涔嬫淳)-cos鍥涘垎涔嬫淳x銆(1)姹俧x鐨勫崟璋冨鍖洪棿(2)鑻灞炰簬(0,4)姹倅=f(x)鐨勫煎煙 灞曞紑 ...
绛旓細f(x)=cos 鍥涙鏂 x-2sinxcos x-sin鍥涙鏂箈 锛(cos²x+sin²x)(cos²x-sin²x)-sin2x =cos2x-sin2x =鈭2*cos(2x+蟺/4)(1).鐢变笂鍙煡鍑芥暟f(x)鐨勬渶灏忔鍛ㄦ湡T=2蟺/2=蟺 (2).鍥犱负x鈭圼0,蟺/2]鍗2x鈭圼0,蟺]鍒2x+蟺/4鈭圼蟺/4,5蟺/4]鎵浠ュ綋2x+蟺...
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绛旓細-蟺+2k蟺鈮はx+蟺/4鈮2k蟺 瑙ｅ緱2k蟺-5蟺/4鈮は墄鈮2k蟺-蟺/4 浠=1锛3蟺/4鈮は墄鈮7蟺/4 鍙埾/2鈮鈮は锛屾墍浠ハ壪/2鈮は墄鈮は壪 鎵浠ハ壪/2鈮3蟺/4涓斚壪鈮7蟺/4 瑙ｅ緱3/2鈮は夆墹7/4
绛旓細f(x)=2鈭3脳sin(x+蟺/4)路cos(x+蟺/4)-sin(2x+3蟺)=鈭3sin(2x+蟺/2)+sin2x =鈭3cos2x+sin2x =2(cos蟺/6路cos2x+sin蟺/6路sin2x)=2cos(2x-蟺/6)鈭碩=2蟺/2=蟺
