如图这道题是如何把cos变sin的 特别是后面为什么要加兀/2?

sin\u56fe\u50cf\u548ccos\u56fe\u50cf

\u628a\u6a2a\u5750\u6807\u6269\u5927\u4e3a2\u500d\uff0c\u5219x\u7684\u7cfb\u6570\u4e581/2
sin(x/2+\u03c0/4)
\u5047\u8bbe\u662f\u5411\u5de6\u79fb\u03c0/3
\u5219x\u6362\u6210x+\u03c0/3
sin[(x+\u03c0/3)/2+\u03c0/4]=sin(x/2+5\u03c0/12)
\u5982\u679c\u662f\u5411\u53f3\u79fb\u5219x\u6362\u6210x-\u03c0/3


\u5148\u5de6\u79fb\u03c0/3
\u5219x\u6362\u6210x+\u03c0/3
=sin[(x+\u03c0/3)+\u03c0/4]=sin(x+7\u03c0/12)
\u5728\u6a2a\u5750\u6807\u6269\u5927\u4e3a2\u500d\uff0c\u5219x\u7684\u7cfb\u6570\u4e581/2
\u662fsin(x/2+7\u03c0/12)


\u89e3\uff1asin2x\u7684\u56fe\u50cf\u53d8\u6210sinx\u7684\u56fe\u50cf
sin2x\u7684\u5468\u671f\u4e3a2\u03c0/2=\u03c0
sinx\u7684\u5468\u671f\u4e3a2\u03c0
\u9664\u4e86\u5468\u671f\u53d8\u4e3a\u4e00\u534a\uff0c\u5176\u4ed6\u7684\u4e0d\u53d8

sin2x\u7684\u4e00\u4e2a\u5b8c\u6574\u7684\u5468\u671f\uff1a[0,\u03c0]
sinx\u7684\u4e00\u4e2a\u5b8c\u6574\u7684\u5468\u671f\uff1a[0,2\u03c0]

根据诱导公式

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