Question

求助：高一数学题一道

已知cosθ=-3/5,θ∈(0,π),求sin(θ+π/4)的值

Answer 1

因为θ∈(0,π),所以sinθ>0
sinθ^2+cosθ^2=1，cosθ=-3/5,
所以sinθ=4/5
sin(θ+π/4)=sinθcosπ/4+cosθsinπ/4=4/5×根号2/2+（-3/5）×根号2/2=根号2/10

Answer 2

因为θ∈(0,π),所以sinθ＞0
sinθ=4/5
sin(θ+π/4)=sinπ/4cosθ+cosπ/4sinθ
=√2/2(cosθ+sinθ)
=√2/2×1/5
=√2/10

Answer 3

由cosθ=-3/5,θ∈(0,π)
θ∈(π/2,π)
sinθ=4/5
sin(θ+π/4)
=sinθ*cosπ/4+cosθsinπ/4

Answer 4

两角和公式. sin(a+b)=sinacosb+cosasinb
cos=-3/5（θ∈(0,π)），则sinθ=4/5；
sin（θ+π）=sinθcosπ/4+cosθsinπ/4
=√2/10

Answer 5

sin（x+pai/4)=sinxcospai/4+cosxshipai/4
cosx=-3/5,x>pai/2
sinx=4/5
代入得十分之根号2