若函数f(x)=sin(wx+阿发)+cos(wx+阿发)(w>0,绝对值阿发

来源：学生作业帮助网编辑：作业帮时间：2024/05/04 14:19:15

若函数f(x)=sin(wx+阿发)+cos(wx+阿发)(w>0,绝对值阿发
若函数f(x)=sin(wx+阿发)+cos(wx+阿发)(w>0,绝对值阿发

若函数f(x)=sin(wx+阿发)+cos(wx+阿发)(w>0,绝对值阿发
f(x)=sin(wx+阿发)+cos(wx+阿发)
=√2 [√2∕2 sin(wx+阿发) + √2∕2 cos(wx+阿发) ] （提取√2,根号2）
=√2 [cos45°sin(wx+阿发) + sin45° cos(wx+阿发) ]
=√2 sin(wx+阿发+45°)
=√2 cos(wx+阿发- 45°) （因为和偶函数有关,化为余弦比较好）
∵最小正周期为π,所以w=2,
又因为f(x)为偶函数,coswx本身是偶函数,所以,
(阿发- 45°)=2kπ,k为整数,最简形式为当k=0时,此时f(x)=√2cos2x

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