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

Explanation:

Step1: Recall amplitude formula

Amplitude $A=\frac{\text{max}-\text{min}}{2}$. From the graph, $\text{max} = 3$ and $\text{min}=-3$. So $A=\frac{3 - (-3)}{2}$.

Step2: Calculate amplitude

$A=\frac{3+3}{2}=\frac{6}{2}=3$.

Step3: Recall period concept

The period is the horizontal distance between two consecutive identical - shaped parts of the wave. From the graph, the wave repeats itself every $\frac{\pi}{2}-(-\frac{\pi}{2})$.

Step4: Calculate period

The period $T=\frac{\pi}{2}-(-\frac{\pi}{2})=\pi$.

Answer:

amplitude = 3 period = $\pi$