举报
maomao675
(1)、|a|=√[(sinx)^2+(cosx)^2]=1,|c|=1, a•c=-sinx, 设向量a、c的夹角为α, cosα= a•c/(|a|*|c|)=-sinx/1, x=π/3,cosα=-sin(π/3)=-根号3/2, α=150°, (2),a•b=(sinx)^2+sinxcosx =(1-cos2x)/2+sin2x/2 =1/2(sin2x-cos2x)+1/2 =√2/2[(√2/2)sin(2x)-√2/2cos(2x)]+1/2 =√2/2sin(2x-π/4)+1/2, f(x)=√2/2sin(2x-π/4)+1/2, x属于[-3/8Pai,Pai/4],则有2x-Pai/4属于[-Pai,Pai/4] 故有-1<=sin(2x-Pai/4)<=根号2/2 故f(x)∈[-√2/2+1/2,1]。