Question

函数f(x)=cos(3x+φ)是奇函数,则φ的值为

Answer 1

cos(x)是偶函数，周期为2π。所以，cos(3x)也是偶函数，周期是2π/3. cos(3x+φ)=cos{3（x+φ/3)}要变为奇函数，只需要向左或向右平移1/4个周期，所以，φ的值为3x(π/6+2Kπ/3)=π/2+2kπ,k∈z.

Answer 2

π/2+2kπ
奇函数 f(-x)=-f(x)
cos(-3+φ)=-cos(3x+φ)
令x=0
cos(φ)=-cos(φ)
0=-0
φ=π/2+2kπ