The period of the cosine function is 2π radians. That is, the value of cos(Θ) repeats every 2π radians. Therefore whatever value of the variable in the function argument causes the argument to change by an amount equal to 2π is the period of the function.
The argument of cos(x/3) is x/3. What value of x makes x/3 = 2π
x/3 = 2π
x = 6π
Therefore the period of y =cos(x/3) is 6π
