To determine the period of the function [tex]\( y = \sin(3x) \)[/tex], we need to use the property related to the period of sinusoidal functions.
The general form of a sine function is [tex]\( y = \sin(bx) \)[/tex], where [tex]\( b \)[/tex] is a constant that affects the period of the function. The period [tex]\( T \)[/tex] of a sine function [tex]\( y = \sin(bx) \)[/tex] is given by the formula:
[tex]\[ T = \frac{2\pi}{b} \][/tex]
In the given function [tex]\( y = \sin(3x) \)[/tex], the constant [tex]\( b \)[/tex] is 3. Applying the formula to find the period:
[tex]\[ T = \frac{2\pi}{3} \][/tex]
Therefore, the period of the function [tex]\( y = \sin(3x) \)[/tex] is [tex]\( \frac{2\pi}{3} \)[/tex].
So the correct answer is:
[tex]\[ \frac{2\pi}{3} \][/tex]
