find the amplitude and period of the sinusoidal function. simplify any fractions.

Explanation:

Step1: Determine the amplitude

The amplitude $A$ of a sinusoidal function is half the vertical distance between the maximum and minimum values. The maximum value of the function from the graph is $y = 4$ and the minimum value is $y=-4$. So, $A=\frac{4 - (- 4)}{2}$. $A=\frac{4 + 4}{2}=\frac{8}{2}=4$.

Step2: Determine the period

The period $T$ of a sinusoidal function is the horizontal distance between two consecutive peaks (or troughs or any two - corresponding points). From the graph, we can see that the distance between two consecutive peaks is $\frac{\pi}{2}$.

Answer:

Amplitude: $4$, Period: $\frac{\pi}{2}$