To determine the period of the function [tex]\( y = \sin(3x) \)[/tex], we first need to understand the general form of a sine function. 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 sine wave.
The period of the sine function [tex]\( y = \sin(bx) \)[/tex] is given by:
[tex]\[
\text{Period} = \frac{2\pi}{b}
\][/tex]
In this specific problem, the sine function is [tex]\( y = \sin(3x) \)[/tex]. By comparing this to the general form [tex]\( y = \sin(bx) \)[/tex], we can see that [tex]\( b = 3 \)[/tex].
Now, we substitute [tex]\( b \)[/tex] with 3 into the formula for the period of the sine function:
[tex]\[
\text{Period} = \frac{2\pi}{3}
\][/tex]
Hence, the period of the function [tex]\( y = \sin(3x) \)[/tex] is:
[tex]\[
\text{Period} = \frac{2\pi}{3}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{2\pi}{3}}
\][/tex]
