Question

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

Explanation:

Step1: Recall Amplitude Formula

The amplitude of a sinusoidal function is half the distance between the maximum and minimum values. The formula is \( \text{Amplitude} = \frac{\text{Max} - \text{Min}}{2} \).

Step2: Identify Max and Min Values

From the graph, the maximum value (peak) of the function is \( -1 \) and the minimum value (trough) is \( -3 \). Wait, no—wait, looking at the y - axis, the peaks seem to be at \( y=-1 \) and troughs at \( y = - 3 \)? Wait, no, maybe I misread. Wait, the graph: let's check the y - coordinates. Wait, the grid: the vertical axis (y - axis) has marks. Let's see, the peak is at \( y=-1 \) and the trough is at \( y=-3 \)? Wait, no, maybe the maximum is \( -1 \) and minimum is \( -3 \). Then the distance between max and min is \( (-1)-(-3)=2 \). Then amplitude is \( \frac{2}{2}=1 \)? Wait, no, maybe I got the max and min wrong. Wait, another way: amplitude is the distance from the midline to a peak (or trough). Let's find the midline. The midline is the average of max and min. If max is \( -1 \) and min is \( -3 \), midline is \( \frac{-1 + (-3)}{2}=\frac{-4}{2}=-2 \). Then the distance from midline (\( -2 \)) to peak (\( -1 \)) is \( |-1-(-2)| = 1 \). So amplitude is 1.

Answer:

1