sinα=-8/17,α∈(3π/2,2π),求sin(π/6+α)

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sinα=-8/17,α∈(3π/2,2π),求sin(π/6+α)

sinα=-8/17,α∈(3π/2,2π),求sin(π/6+α)
sinα=-8/17,α∈(3π/2,2π),求sin(π/6+α)

sinα=-8/17,α∈(3π/2,2π),求sin(π/6+α)

∵a∈(3π/2,2π)
∴cosa>0
∵sina=-8/17
∴cosa=√1-sin²a=15/17
∴sin(π/6+a)
=sinπ/6cosa+cosπ/6sina
=1/2×(15/17)+(√3/2)×(-8/17)
=(15-8√3)/34