函数f(x)=sin(x+π/6)在下列区间内递减的是[-π/2,π/2],[-π,0],[-2π/3,2π/3],[π/2,2π/3]请告诉我答案及解题过程!谢谢!我打错了,sin前有个3

Question

函数f(x)=sin(x+π/6)在下列区间内递减的是
[-π/2,π/2],[-π,0],[-2π/3,2π/3],[π/2,2π/3]
请告诉我答案及解题过程
!谢谢!
我打错了,sin前有个3

Answer 1

∵递减
∴令π/2+2kπ≤x+π/6≤3π/2+2kπ
解得π/3+2kπ≤x≤4π/3+2kπ
∴在[π/2,2π/3]范围内是递减的
没有影响,因为sin前×3说明原函数的值域扩大为[-3,3]了,与增减区间没关系.