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

显示全部楼层 · 2011-6-29 20:31:12

千问 · 2011-6-29 20:31:12

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...

千问 · 2011-6-29 20:31:12

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)-co...