Question

y=sin(2x+π/6),x∈[π/4,3π/4]求值域

Answer 1

π/6<=x<=3π/4
π/3<=2x<=3π/2
π/2<=2x+π/6<=5π/3

π/2<=x<=3π/2
sinx是减函数
所以sin(3π/2)<=sin(2x+π/6)<=sin(π/2)
-1<=sin(2x+π/6)<=1
而sin(2x+π/6)值域本身就是[-1,1]
所以3π/2<=2x+π/6<=5π/3肯定也属于[-1,1]

追问

答案不是这个

追答

看错了，对不起
π/4<=x<=3π/4
π/2<=2x<=3π/2
2π/3<=2x+π/6<=5π/3
-1=sin(3π/2)<= sin(2x+π/6)=<sin(2π/3)=√3/2
所以
-1<=sin(2x+π/6)<=√3/2

Answer 2

画个sin函数的图像,再把2π/3<=2x+π/6<=5π/3范围带入，可以在图上看出答案是-1<=sin(2x+π/6)<=√3/2，楼上修改后为正解

追问

你的答案是对的，但是这个函数的图像我话不明白

追答