find the period and amplitude of the function.\n\n$y = - 2\\sin(\\frac{2}{3}x)$\n\ngive the exact values…

Explanation:

Step1: Recall period formula

For $y = A\sin(Bx)$, the period $T=\frac{2\pi}{|B|}$. Here $B = \frac{2}{3}$. $T=\frac{2\pi}{\left|\frac{2}{3}\right|}$

Step2: Calculate the period

$T=\frac{2\pi}{\frac{2}{3}}=2\pi\times\frac{3}{2}=3\pi$

Step3: Recall amplitude formula

For $y = A\sin(Bx)$, the amplitude is $|A|$. Here $A=-2$. Amplitude $=| - 2| = 2$

Answer:

Period: $3\pi$ Amplitude: $2$