Given the function $y=3\cdot \sin \left(2x\right)$, what are its amplitude and period?

• A. Amplitude: $3$, Period: $\frac{\pi }{1}$
• B. Amplitude: $3$, Period: $\frac{2}{\pi }$
• C. Amplitude: $3$, Period: $\frac{2}{\pi }$
• D. Amplitude: $3$, Period: $\frac{\pi }{2}$

Answer: (C)

Verified step by step guidance

1. Identify the general form of the sine function: \(y = A \cdot \sin(Bx)\), where \(A\) is the amplitude and \(B\) affects the period.
2. Recall that the amplitude of a sine function is the absolute value of the coefficient \(A\) in front of the sine, so amplitude \(= |3| = 3\).
3. Recall the formula for the period of a sine function: \(\text{Period} = \frac{2\pi}{B}\), where \(B\) is the coefficient of \(x\) inside the sine function.
4. In the given function \(y = 3 \cdot \sin(2x)\), identify \(B = 2\).
5. Calculate the period using the formula: \(\text{Period} = \frac{2\pi}{2} = \pi\).