f(x)=sinx+sin(x+π/2)x∈R,求f(x)的最小正周期,最大值,最小值

題目：

f(x)=sinx+sin(x+π/2)x∈R,求f(x)的最小正周期,最大值,最小值

解答：

∵f(x)=sinx+sin(x+π/2)
=sinx+cosx
=√2sin(x+π/4)
∴f(x)的最小正周期T=2π
∵x∈R,當sin(x+π/4)=－1時
f(x)min=－√2