Question

find the amplitude of the sinusoidal function.
simplify any fractions.
amplitude =

Explanation:

Step1: Recall Amplitude Definition

Amplitude of a sinusoidal function is the maximum distance from the midline (or equilibrium position) to the peak (or trough) of the wave. It can be calculated as half the distance between the maximum and minimum values of the function.

Step2: Identify Max and Min Values

From the graph, the maximum value (peak) of the function is \( 3 \) and the minimum value (trough) is \( -3 \).

Step3: Calculate Amplitude

Using the formula for amplitude: \( \text{Amplitude} = \frac{\text{Max Value} - \text{Min Value}}{2} \). Substituting the values, we get \( \frac{3 - (-3)}{2} = \frac{6}{2} = 3 \).

Answer:

\( 3 \)