determine the amplitude and period of the function. graph the function. y = - 3 cos 2/3x the amplitude is 3…

Explanation:

Step1: Recall period - formula for cosine function

The general form of a cosine function is $y = A\cos(Bx - C)+D$, and its period $T$ is given by $T=\frac{2\pi}{|B|}$.

Step2: Identify the value of B

For the function $y=-3\cos(\frac{2}{3}x)$, we have $B = \frac{2}{3}$.

Step3: Calculate the period

Substitute $B=\frac{2}{3}$ into the period - formula $T=\frac{2\pi}{|B|}$. Since $|B|=\left|\frac{2}{3}\right|=\frac{2}{3}$, then $T=\frac{2\pi}{\frac{2}{3}}$. Using the rule of dividing by a fraction ($a\div\frac{b}{c}=a\times\frac{c}{b}$), we get $T = 2\pi\times\frac{3}{2}=3\pi$.

Answer:

$3\pi$