函数sin的平方πx的最小正周期/??
\u5df2\u77e5\u51fd\u6570f(x)=sin\u5e73\u65b9(x+\u03c0/4)- sin\u5e73\u65b9(x-\u03c0/4)\u7684\u6700\u5c0f\u6b63\u5468\u671f\u56e0\u4e3a(x+\u03c0/4)-(x-\u03c0/4)=\u03c0/2,\u6240\u4ee5x+\u03c0/4=\u03c0/2+(x-\u03c0/4),
\u6240\u4ee5sin(x+\u03c0/4)=sin[\u03c0/2-(x-\u03c0/4)]=cos(x-\u03c0/4)
\u6240\u4ee5sin\u5e73\u65b9(x+\u03c0/4)- sin\u5e73\u65b9(x-\u03c0/4)=cos^2(x-\u03c0/4)-sin^2(x-\u03c0/4)=cos2[(x-\u03c0/4)]=cos(2x-\u03c0/2)=sin2x
\u6240\u4ee5\u6700\u5c0f\u6b63\u5468\u671f2\u03c0/2=\u03c0
\u6709\u534a\u89d2\u516c\u5f0fsin²X=(1-cos2X)/2
y=sin²x+cos2x
=(1-cos2X)/2+cos2x
=1/2+cos2X/2
\u5468\u671f\u53ea\u53d6\u51b3\u4e8ecos2X
cos2X\u5468\u671f\u662f\u03c0
\u90a3\u4e48y=sin²x+cos2x\u7684\u5468\u671f\u4e5f\u662f\u03c0
所以最小正周期T=2π/2π=1
2
绛旓細鎵浠ュ彲寰楁渶灏忔鍛ㄦ湡涓猴細T=2蟺/2蟺=1
绛旓細鍙互鐢ㄩ檷骞傚叕寮忚В
绛旓細鍛ㄦ湡T=锛2蟺/蟺锛/2=1 鍥犱负-1锛渟in胃锛1 鎵浠sin蟺x^2鏈澶т负1 鎵浠in蟺x^2鏈灏鏄0
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