Question

f(x)=sin(2x+α)(-π＜α＜0),图像关于x=π/8对称,求y=f(x)在[-π/4,π/2]上的值域

Answer 1

x=π/8,sin【2（π/8）+α]=1或-1,此时α=π/4(舍去）或α=-3π/4

所以f(x)=sin(2x-3π/4）

因为x的范围是[-π/4,π/2]

所以2x-3π/4的范围是[-5π/4,π/4]

y=f(x)在[-π/4,π/2]上的值域为【-1,√2/2】