求函数y=cos+(√3)sinx,x∈[π/6,2π/3]的值域

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/27 02:13:49
求函数y=cos+(√3)sinx,x∈[π/6,2π/3]的值域
x){igS7T&kkiÞ$铥OΆ|+m4@ʴ@􍴁+ 4PI $b\ m <;ltg+ d6 {:VuHz`A}똂 q$ I3t c!"z

求函数y=cos+(√3)sinx,x∈[π/6,2π/3]的值域
求函数y=cos+(√3)sinx,x∈[π/6,2π/3]的值域

求函数y=cos+(√3)sinx,x∈[π/6,2π/3]的值域
y=2(sinx*√3/2+cosx*1/2)
=2(sinxcosπ/6+cosxsinπ/6)
=2sin(x+π/6)
π/3

y=cos+(√3)sinx
=2(1/2cosx+√3/2sinx)
=2(sinπ/6cosx+cosπ/6sinx)
=2 sin(π/6+x)
x∈[π/6,2π/3] π/6+x∈[π/3,5π/6] sin(π/6+x)∈[1/2,1]
y∈[1,2]