三角函数周期 三角函数的周期怎么算比如：y=
\u6c42\u4e09\u89d2\u51fd\u6570\u5468\u671f\u65b9\u6cd5\u6839\u636e\u9898\u76ee\u7c7b\u578b\uff0c\u4e00\u822c\u53ef\u4ee5\u6709\u4e09\u79cd\u65b9\u6cd5\u6c42\u5468\u671f\uff1a
1\u3001\u5b9a\u4e49\u6cd5\uff1a\u9898\u76ee\u4e2d\u63d0\u5230f\uff08x\uff09=f\uff08x+C\uff09,\u5176\u4e2dC\u4e3a\u5df2\u77e5\u91cf\uff0c\u5219C\u4e3a\u8fd9\u4e2a\u51fd\u6570\u7684\u4e00\u4e2a\u6700\u5c0f\u5468\u671f\u3002
\u4f8b\u9898\uff1a
2\u3001\u516c\u5f0f\u6cd5\uff1a\u5c06\u4e09\u89d2\u51fd\u6570\u7684\u51fd\u6570\u5173\u7cfb\u5f0f\u5316\u4e3a\uff1ay=Asin(wx+B)+C\u6216y=Acos(wx+B)+C\uff0c \u5176\u4e2dA,w,B,C\u4e3a\u5e38\u6570\u3002\u5219\u5468\u671fT=2\u03c0/w\uff0c\u5176\u4e2dw\u4e3a\u89d2\u901f\u5ea6\uff0cB\u4e3a\u76f8\u89d2\uff0cA\u4e3a\u5e45\u503c\u3002\u82e5\u51fd\u6570\u5173\u7cfb\u5f0f\u5316\u4e3a\uff1aAcot(wx+B)+C\u6216\u8005tan(wx+B)+C\uff0c\u5219\u5468\u671f\u4e3aT=\u03c0/w\u3002
\u4f8b\u9898\uff1a
3\u3001\u5b9a\u7406\u6cd5\uff1a\u5982\u679cf(x)\u662f\u51e0\u4e2a\u5468\u671f\u51fd\u6570\u4ee3\u6570\u548c\u5f62\u5f0f\u7684\uff0c\u5373\u662f\uff1a\u51fd\u6570f(x)=f1(x)+f2(x)\uff0c\u800cf1(x)\u7684\u5468\u671f\u4e3aT1, f2(x)\u7684\u5468\u671f\u4e3aT2\uff0c\u5219f(x)\u7684\u5468\u671f\u4e3aT=P2T1=P1T2\uff0c\u5176\u4e2dP1\u3001P2N\uff0c\u4e14\uff08P1\u3001P2\uff09=1
\u2235f\uff08x+ P1T2\uff09=f1\uff08x+ P1T2\uff09+f2\uff08x+ P1T2\uff09
=f1\uff08x+ P2T1\uff09+ f2\uff08x+ P1T2\uff09
= f1\uff08x\uff09+ f2\uff08x\uff09
=f\uff08x\uff09
\u2234P1T2\u662ff\uff08x\uff09\u7684\u5468\u671f\uff0c\u540c\u7406P2T1\u4e5f\u662f\u51fd\u6570f\uff08x\uff09\u7684\u5468\u671f\u3002
ps\uff1a\u5f53T\u4e3a\u4e00\u4e2a\u4e09\u89d2\u51fd\u6570\u7684\u5468\u671f\u65f6\uff0cNT\u4e5f\u4e3a\u8fd9\u4e2a\u4e09\u89d2\u51fd\u6570\u7684\u5468\u671f\u3002\u5176\u4e2dN\u4e3a\u4e0d\u4e3a0\u7684\u6b63\u6574\u6570\u3002
\u4f8b\u9898\uff1a
\u4e09\u89d2\u51fd\u6570\u90fd\u6709\u5468\u671f,\u6bcf\u4e00\u79cd\u4e09\u89d2\u51fd\u6570\u7684\u6700\u5c0f\u6b63\u5468\u671f,\u5e76\u7528T\u8868\u793a, \u8981\u7262\u8bb0\uff1a
\u6b63\u5f26\u51fd\u6570sinx\u548c\u4f59\u5f26\u51fd\u6570cosx\u7684\u6700\u5c0f\u5468\u671f,T=2\u03c0,\u6b63\u5207\u51fd\u6570tanx\u548c\u4f59\u5207\u51fd\u6570cotx\u7684\u6700\u5c0f\u6b63\u5468\u671f T=\u03c0.
\u9047\u5230x\u524d\u7684\u7cfb\u6570\u4e0d\u662f\u201d1\u201c\u65f6,\u8981\u7528x\u524d\u7684\u7cfb\u6570\u53bb\u9664\u6700\u5c0f\u6b63\u5468\u671f.
\u4f8b\u5982,sin2x\u7684\u6700\u5c0f\u6b63\u5468\u671fT=2\u03c0/2=\u03c0;
sin(x/2)\u7684\u6700\u5c0f\u6b63\u5468\u671fT=2\u03c0/(1/2)=4\u03c0;
cos(4x), T=2\u03c0/4=\u03c0/2;
tan3x, T=\u03c0/3.
xotx/2, T==\u03c0/(1/2)=2\u03c0.
=asin^2(θ/3)(sinθ/3)
=a(1-cos2θ/3)/2(sinθ/3)
=a/2(1-cos2θ/3)(sinθ/3)
注意到cos2θ/3的周期为T=3π
而sinθ/3的周期为6π
故整个函数的周期为6π
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