What is the period of y = sin(3x)?

sin 3 x = sin ( 3 x + 2 π ) = sin [ 3 ( x + 2 π/ 3 ) ] = sin 3 x

This means "after the arc rotating three time of ( x + ( 2  π /3 ) ) , sin 3x comes back to its initial value"

So, the period of sin 3x is 2 π /3 .