解
∵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
解
∵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