f(x)=2sin(2x+π/6) x属于[π/12,π/2] 求值域

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 17:25:22
f(x)=2sin(2x+π/6)x属于[π/12,π/2]求值域f(x)=2sin(2x+π/6)x属于[π/12,π/2]求值域f(x)=2sin(2x+π/6)x属于[π/12,π/2]求值域π

f(x)=2sin(2x+π/6) x属于[π/12,π/2] 求值域
f(x)=2sin(2x+π/6) x属于[π/12,π/2] 求值域

f(x)=2sin(2x+π/6) x属于[π/12,π/2] 求值域
π/12<=x<=π/2
π/6<=2x<=π
π/3<=2x+π/6<=7π/6
sinx在[π/3,π/2]是增函数,[π/2,7π/6]是减函数
所以2x+π/6=π/2时最大=sinπ/2=1
2x+π/6=7π/6时最小=sin7π/6=-1/2
所以-1<=2sin(2x+π/6) <=2
值域[-1,2]

2x+pi/6 在区间pi/3 7pi/6
由sin图像可知值域在[-1 2]

[-1,2]
X=π/2时达到最小值,X=π/6时达到最大值