Given the function $y=3\cdot \sin \left(x\right)$, what is the amplitude of the sinusoidal function?

• A. $2$
• B. $1$
• C. $0$
• D. $3$

Answer: (D)

Verified step by step guidance

1. Identify the general form of a sinusoidal function, which is given by \(y = A \cdot \sin(x)\) or \(y = A \cdot \cos(x)\), where \(A\) represents the amplitude.
2. Recall that the amplitude of a sinusoidal function is the absolute value of the coefficient multiplying the sine or cosine function.
3. Look at the given function \(y = 3 \cdot \sin(x)\) and identify the coefficient in front of \(\sin(x)\), which is 3.
4. Understand that the amplitude is the distance from the midline (usually the x-axis) to the peak of the wave, so it is always a positive value.
5. Conclude that the amplitude of the function \(y = 3 \cdot \sin(x)\) is \(|3| = 3\).