Question

1. what is the amplitude of the function \\(y = 3 \sin x\\)?

f. \\(\frac{1}{3}\\)
g. 1
h. 3
j. 6

Explanation:

Identify the standard form of a trigonometric function

The given function is \(y = 3 \sin x\). The standard form of a sine function is:

$$y = A \sin(Bx - C) + D$$

Determine the amplitude from the coefficient

The amplitude of the function \(y = A \sin(Bx - C) + D\) is given by the absolute value of the coefficient \(A\):

$$\text{Amplitude} = |A|$$

For the function \(y = 3 \sin x\), we have \(A = 3\).

Calculate the final amplitude value

Evaluating the absolute value:

$$\text{Amplitude} = |3| = 3$$

This matches option H.

Answer:

• F. \(\frac{1}{3}\)
• G. 1
• H. 3 (Correct answer)
• J. 6