Y=2sin(2X+π/6)的值域X∈[π/12,π/2]求值域

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Y=2sin(2X+π/6)的值域X∈[π/12,π/2]求值域

Y=2sin(2X+π/6)的值域X∈[π/12,π/2]求值域
Y=2sin(2X+π/6)的值域
X∈[π/12,π/2]
求值域

Y=2sin(2X+π/6)的值域X∈[π/12,π/2]求值域
π/12<=x<=π/2
π/6<=2x<=π
π/3<=2x+π/6<=7π/6
所以2x+π/6=π/2,y最大=2
2x+π/6=7π/6,y最小=-1

cos2x=1-2sin^2x
所以y=(1-cos2x)/2-(sin2x)/2 +1/2
=-(sin2x+cos2x)/2+1
=-√2sin(2x+π/4)/2+1

所以值域[-√2/2+1,√2/2+1]