y=sinx+cosx可化成
sinx+cosx==\u221a2sin(x+\u03c0/4) ,\u50cf\u8fd9\u79cd\u9898\u76ee\u53ef\u4ee5\u5316\u6210y= Asin(wx+b)\uff0c\u91cc\u9762\u7684A\uff0cw,b\u662f\u600e\u4e48\u6c42\u51fa\u6765\u7684\uff1fA=\u221a(1²+1²)=\u221a2(\u770b\u4e24\u4e2a\u524d\u9762\u7684\u7cfb\u6570)
w=1(\u770bx\u524d\u9762\u7684\u7cfb\u6570)
tanb=1/1=1
\u6240\u4ee5b=\u03c0/4(\u8fd9\u91ccb\u4e5f\u662f\u770bsinx\u4e0ecosx\u524d\u9762\u7684\u7cfb\u6570\u7684\u6bd4\u503c)
(1)\u03b1 =45\u00b0 f(x)=2sin(x+\u03c0/4)+sin2x
\u56e0\u4e3a0<x<\u03c0 \u6240\u4ee5\u5f53x=3\u03c0/4\u65f6 fIx)\u53d6\u6700\u5c0f\u503c\u4e3a-1
(2) a.c=0\u5f97sinxcos\u03b1+2sin\u03b1cos\u03b1+sin\u03b1cosx+2sin\u03b1cos\u03b1=0
\u5373sin(x+\u03b1)+4sin\u03b1cos\u03b1=0
\u53c8cos60\u00b0=a.b/|a||b|=cos(x-\u03b1)
\u6240\u4ee5x=\u03b1-60\u00b0\u6216\u03b1+60\u00b0
\u82e5x=\u03b1-60\u00b0 \u5219\u67090\uff1dsin(x+\u03b1)+4sin\u03b1cos\u03b1=sin(2\u03b1-60\u00b0)+2sin2\u03b1 \u6574\u7406\u5f97tan2\u03b1=\u221a3/5
\u82e5x=\u03b1+60\u00b0 \u5219\u67090=sin(x+\u03b1)+4sin\u03b1cos\u03b1=sin(2\u03b1+60\u00b0)+2sin2\u03b1 \u6574\u7406\u5f97tan2\u03b1=-\u221a3/5
=√2*[sinx*(√2/2) +cosx*(√2/2)]
=√2*[sinx*cos(π/4) +cosx*sin(π/4)]
=√2*sin(x +π/4)
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