《高分求数学题一定要正确》已知f(x)等于sin(x加四分之七派)加cos(x减四分之三派)x属于R
问题描述:
《高分求数学题一定要正确》已知f(x)等于sin(x加四分之七派)加cos(x减四分之三派)x属于R
(一)求f(x)的最小正周期和最小值,(二)已知cos(b减a)等于五分之四,cos(b加a)等于负五分之四,0
答
1
f(x)=sin(x+7π/4)+cos(x-3π/4) =cos(π/2-(x-π/4))+cos(x-3π/4)
=2cos(x-3π/4)T=2π x=-π/4 最小值f(-π/4)=-2
2
f(b)^2-2=4cos(b-3π/4)^2-2=2cos(2b-π/2)=2sin(2b)
sin2b=(3/5)*(4/5)-(4/5)(3/5)=0