函数y=sinx+(√3)cosx,x∈[0,π/2]的单调增区间是

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/19 16:57:14
函数y=sinx+(√3)cosx,x∈[0,π/2]的单调增区间是函数y=sinx+(√3)cosx,x∈[0,π/2]的单调增区间是函数y=sinx+(√3)cosx,x∈[0,π/2]的单调增区

函数y=sinx+(√3)cosx,x∈[0,π/2]的单调增区间是
函数y=sinx+(√3)cosx,x∈[0,π/2]的单调增区间是

函数y=sinx+(√3)cosx,x∈[0,π/2]的单调增区间是
y=sinx+√3cosx
=2*[sinx*(1/2)+cosx*(√3/2)]
=2*[sinx*cos(π/3)+cosx*sin(π/3)]
=2sin(x+π/3)
增区间是 2kπ-π/2≤x+π/3≤2kπ+π/2
∴ 2kπ-5π/6≤x≤2kπ+π/6
结合给出的x∈[0,π/2]
∴ 函数的增区间是[0,π/6]

y=sinx+(√3)cosx
=2(1/2sinx+√3/2cosx)
=2sin(x+π/3)
∵x∈[0,π/2]
∴π/3≤x+π/3≤5π/6
∵增区间
∴π/3≤x+π/3≤π/2
∴0≤x≤π/6
单调增区间是:[0,π/6]