求函数的值域:(1)y=|sinx|-2sinx (2)y=sin|x|+|sinx|

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求函数的值域:(1)y=|sinx|-2sinx (2)y=sin|x|+|sinx|

求函数的值域:(1)y=|sinx|-2sinx (2)y=sin|x|+|sinx|
求函数的值域:(1)y=|sinx|-2sinx (2)y=sin|x|+|sinx|

求函数的值域:(1)y=|sinx|-2sinx (2)y=sin|x|+|sinx|
1、sinx≥0
y=-sinx
∴y∈[-1,0]
sinx<0
y=-3sinx
∴y∈(0,3]
2、x≥0 ①x∈[2kπ,2kπ+π] k=0,1,2. y=2sinx ∴y∈[0,2]
②x∈[2kπ+π,2kπ+2π] k=0,1,2. y=0
x<0 ①x∈[2kπ,2kπ+π] k=0,-1,-2. y=0
②x∈[2kπ+π,2kπ+2π] k=0,-1,-2. y=-2sinx y∈[-2,0]
∴y∈[-2,2]

(1) sinx>0 => y=-sinx => -1<=y<0
sinx<=0 => y=-3sinx => 0<=y<=3
=> -1<=y<=3
(2)
sinx>0且x>0 =>y=2sinx => 0sinx<0且x<0 => y=sinx-sinx =0
=>0<=y<=2