Question

已知sin（a+六分之派）=-4/5,a属于（-二分之派到二分之π），求sina的值

Answer 1

解：∵a∈(-π/2,π/2)
∴a+π/6∈(-π/3,2π/3)
∵sin(a+π/6)=-4/5<0
∴a+π/6∈(-π/3,0)，即a+π/6在第四象限
∴cos(a+π/6)>0
∴cos(a+π/6)=√[1-(sin(a+π/6))^2]=3/5
故sina=sin[(a+π/6)-π/6]
=cos(π/6)sin(a+π/6)+sin(π/6)cos(a+π/6)
=(√3/2)(-4/5)+(1/2)(3/5)
=(3-4√3)/10。