Question

what is the period of $y = \sin(3x)$?
$\bigcirc\\ \frac{\pi}{3}$
$\bigcirc\\ \frac{2\pi}{3}$
$\bigcirc\\ 3\pi$
$\bigcirc\\ 6\pi$

Explanation:

Step1: Recall the period formula for sine function

The general form of a sine function is \( y = \sin(Bx) \), and its period \( T \) is given by the formula \( T=\frac{2\pi}{|B|} \).

Step2: Identify the value of \( B \) in the given function

In the function \( y = \sin(3x) \), we can see that \( B = 3 \).

Step3: Calculate the period using the formula

Substitute \( B = 3 \) into the period formula \( T=\frac{2\pi}{|B|} \). Since \( |3| = 3 \), we have \( T=\frac{2\pi}{3} \).

Answer:

\(\frac{2\pi}{3}\) (corresponding to the option \(\boldsymbol{\frac{2\pi}{3}}\))