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