若函数f(x)=sin(x+φ)/3,φ∈0,2Π是偶函数,则φ=A=Π/2B=2Π/3C=3Π/2D=5Π/3

Question

若函数f(x)=sin(x+φ)/3,φ∈【0,2Π】是偶函数,则φ=
A=Π/2
B=2Π/3
C=3Π/2
D=5Π/3

Answer 1

f(x)=sin(x+φ/3)为偶函数,
x=0时,f(x)取得最大值或最小值
∴ φ/3=kπ+π/2,
∴ φ=3kπ+3π/2,
∵ φ∈[0,2π]
∴ φ=3π/2
所以选择C