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

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

f(x)=sinx+sin(x+π/2)x∈R,求f(x)的最小正周期,最大值,最小值
∵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,当sin(x+π/4)=-1时
f(x)min=-√2