f(x)=sin(x-π/4)+3cos(x+π/4)的单调递增区间

f(x)=sin(x-π/4)+3cos(x+π/4)的单调递增区间
f(x)=sin(x-π/4)+3cos(x+π/4)的单调递增区间

f(x)=sin(x-π/4)+3cos(x+π/4)的单调递增区间
f(x)=sin(x-π/4)+3cos(x+π/4)
=-cos（π/2+x-π/4)+3cos(x+π/4)
=-cos(x+π/4)+3cos(x+π/4)
=2cos(x+π/4)
π+2kπ≤x+π/4≤2π+2kπ
3π/4+2kπ≤x≤7π/4+2kπ

f(x)=sin(x-π/4)+3cos(x+π/4)
=sin(x-π/4)+3sin(π/2-x-π/4)
=sin(x-π/4)+3sin(π/4-x)
=sin(x-π/4)-3sin(x-π/4)
=-2sin(x-π/4)
所以单增区间为x-π/4∈[2kπ-π/2, 2kπ+π/2]
x∈[kπ-π/8, kπ+3π/8] k∈Z-...

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f(x)=sin(x-π/4)+3cos(x+π/4)
=sin(x-π/4)+3sin(π/2-x-π/4)
=sin(x-π/4)+3sin(π/4-x)
=sin(x-π/4)-3sin(x-π/4)
=-2sin(x-π/4)
所以单增区间为x-π/4∈[2kπ-π/2, 2kπ+π/2]
x∈[kπ-π/8, kπ+3π/8] k∈Z

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