已知函数f(x)=sin(x+7π/4)+cos(x-3π/4),x∈R (1)求f(x)的最小正周期和最小值

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已知函数f(x)=sin(x+7π/4)+cos(x-3π/4),x∈R (1)求f(x)的最小正周期和最小值

已知函数f(x)=sin(x+7π/4)+cos(x-3π/4),x∈R (1)求f(x)的最小正周期和最小值
已知函数f(x)=sin(x+7π/4)+cos(x-3π/4),x∈R (1)求f(x)的最小正周期和最小值

已知函数f(x)=sin(x+7π/4)+cos(x-3π/4),x∈R (1)求f(x)的最小正周期和最小值
f(x)=sin(x+7π/4)+cos(x-3π/4)
=sin(x+2π-π/4)+cos(x-π+π/4)
=sin(x-π/4)+cos[-(π-x-π/4)]
=sin(x-π/4)+cos(π-x-π/4)
=sin(x-π/4)-cos(x+π/4)
=sin(x-π/4)-cos(x+π/2-π/4)
=sin(x-π/4)-cos(π/2+x-π/4)
=sin(x-π/4)+sin(x-π/4)
=2sin(x-π/4)
T=2π/1=2π
-2

f(x)=sin(x+7π/4)+cos(x-3π/4
=-sin(x+π/4)-cos(x-π/4)
=-(sinxcosπ/4+cosxsinπ/4)-(cosxcosπ/4+sinxsinπ/4)
=根号2(cosx+sinx)
=2sin(x+π/4)
所以最小正周期2π,最小值-2