Question

which of the following is the period of $\sin(\frac{x}{3})$?
a. $6\pi$
b. $\frac{2\pi}{3}$
c. $2\pi$

Explanation:

Step1: Recall the period formula

For \(y = A\sin(Bx + C)+D\), the period \(T=\frac{2\pi}{|B|}\).

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

In \(y = \sin(\frac{x}{3})\), \(B=\frac{1}{3}\).

Step3: Calculate the period

Substitute \(B = \frac{1}{3}\) into \(T=\frac{2\pi}{|B|}\), we get \(T=\frac{2\pi}{\frac{1}{3}}=6\pi\).

Answer:

A. \(6\pi\)