题目

已知cosQ=3/5,Q∈(0,π/2) （1）求sin(Q+π/4) （2）求sin(2Q+π/2)

提问时间：2021-01-21

答案

(1)
∵Q∈(0,π/2)
∴sinQ>0
∵cosQ=3/5
∴sinQ=4/5
∴sin(Q+π/4)
=sinQcos(π/4)+cosQsin(π/4)
=(4/5)(√2)/2+(3/5)(√2)/2
=(7/5)(√2)/2
(2)sin(2Q+π/2)
=cos(2Q)
=2(cosQ)^2-1
=2(3/5)^2-1
=-7/25.