已知两个向量a=(cosx,sinx),b=(2根号2+sinx,2根号2-cosx),f(x)=ab,x属于【0,π】
问题描述:
已知两个向量a=(cosx,sinx),b=(2根号2+sinx,2根号2-cosx),f(x)=ab,x属于【0,π】
(1)求f(x)的值域
(2)若ab=1,求cos(x+7π/12)
答
(1) f(x)=ab=2√2cosx+sinxcosx+2√2sinx-sinxcosx=2√2(sinx+cosx) = 2√2 × √2/2sin(x+π/4) = 2sin(x+π/4)x属于【0,π】,(x+π/4)属于【π/4,5π/4】,sin(x+π/4)属于【-√2/2,1】.所以 f(x)的值域为【...