已知函数f(x)=2sin(x+π÷6),x属于【π÷2,π】,若sinx=4÷5,求函数f(x)的值.
问题描述:
已知函数f(x)=2sin(x+π÷6),x属于【π÷2,π】,若sinx=4÷5,求函数f(x)的值.
答
f(x)=2sin(x+30) =2(sinxcos30+cosxsin30) =2(sinx√3/2+cosx1/2) =√3sinx+cosx =√3*4/5-√(1-(sinx)^2) =4√3/5-√(1-16/25) =4√3/5-3/5 =(4√3-3)/5