题目

答出再给分已知向量a=(1,sin2x)b=(cos2x,1)x属于R f(x)=ab若f(a/2)=3√2/5且a属于(π/2,π)试求sina

提问时间：2021-01-04

答案

f(x)
=a.b
=(1,sin2x).(cos2x,1)
=cos2x+sin2x
f(a/2) = cosa + sina = 3√2/5
=> (cosa)^2 = (3√2/5 - sina)^2
2(sina)^2 - (6√2/5) sina -7/25 =0
50(sina)^2 - 30√2sina -7 =0
sina = (30√2 + 40√2)/100
= 7√2/10