Question

已知π/6<a<π/2,且cos(a-π/6)=15/17,求cosa,sina的值

刚学 求讲的详细一点。。。

Answer 1

解：
∵π/6<a<π/2
∵0<a-π/6<π/3
∵cos(a-π/6)=15/17
∴sin(a-π/6)=8/17
cosa=cos[(a-π/6)+(π/6)]
=(√3/2)*cos(a-π/6)-(1/2)*sin(a-π/6)
=(√3/2)*(15/17)-(1/2)*(8/17)
=(15√3-8)/34
sina=sin[(a-π/6)+(π/6)]
=sin(a-π/6)cosπ/6+cos(a-π/6)sinπ/6
=(√3/2)*(8/17)+(1/2)*(15/17)
=8√3/34+15/34
=(8√3+15)/34