For the function $y=\sin \left(3x\right)$, what is the period?

• A. $\frac{\pi }{3}$
• B. $6\pi$
• C. $\frac{2\pi }{3}$
• D. $2\pi$

Answer: (C)

Verified step by step guidance

1. Recall that the general form of a sine function is \(y = \sin(bx)\), where \(b\) affects the period of the function.
2. The period \(T\) of the sine function is given by the formula \(T = \frac{2\pi}{b}\).
3. Identify the value of \(b\) in the given function \(y = \sin(3x)\), which is \(b = 3\).
4. Substitute \(b = 3\) into the period formula to get \(T = \frac{2\pi}{3}\).
5. Thus, the period of the function \(y = \sin(3x)\) is \(\frac{2\pi}{3}\).