cos(x+四分之派)=4/5,x∈(-∏/4,0)则sin(x) =

题目

cos(x+四分之派)=4/5,x∈(-∏/4,0)则sin(x) =

答案

∵x∈(-π/4,0)
∴x+π/4∈(0,π/4)
∵cos(x+π/4)=4/5
∴sin(x+π/4)=3/5
sinx=sin(x+π/4-π/4)
=sin(x+π/4)cosπ/4-cos(x+π/4)sinπ/4
=(3/5)*(√2/2)-(4/5)*(√2/2)
=-√2/10