Question

find the amplitude of the sine curve shown below.

x
8
4
2

Explanation:

Step1: Recall the definition of amplitude

The amplitude of a sine curve \(y = a\sin(bx)\) is \(|a|\), which is the maximum distance from the mid - line to the peak (or trough) of the curve.

Step2: Identify the maximum value from the graph

Looking at the graph, the maximum \(y\) - value of the sine curve is \(4\). The mid - line of a standard sine curve (which oscillates between positive and negative values) is \(y = 0\). The distance from \(y = 0\) to \(y=4\) (or \(y = 0\) to \(y=-4\)) is calculated as \(|4 - 0|=4\) (or \(|- 4-0| = 4\)).

Answer:

4