函数f(x)= ∣sinπx/2∣+∣cosπx/2∣的最小正周期是__1_____
f(x)=∣sinπx/2∣+∣cosπx/2∣
=√[∣sinπx/2∣+∣cosπx/2∣]²
=√[1+2|sin(πx/2)*cos(πx/2)|]
=√[1+|sin(πx)|]
∵ y=sinπx的周期是2π/π=2
∴ y=sinπx的周期是1
∴ f(x)的周期T=1
函数f(x)= ∣sinπx/2∣+∣cosπx/2∣的最小正周期是__1_____
f(x)=∣sinπx/2∣+∣cosπx/2∣
=√[∣sinπx/2∣+∣cosπx/2∣]²
=√[1+2|sin(πx/2)*cos(πx/2)|]
=√[1+|sin(πx)|]
∵ y=sinπx的周期是2π/π=2
∴ y=sinπx的周期是1
∴ f(x)的周期T=1