[tex]\text{period = }\frac{2\pi}{3},\text{ midline is y = 0, the amplitude = 1 (option B)}[/tex]Explanation:[tex]\begin{gathered} \text{Given function:} \\ y\text{ = }-\sin \text{ 3x} \end{gathered}[/tex]
we apply the sine function formula:
[tex]\begin{gathered} y\text{ = }a\sin (bx\text{ + c) + d} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{comparing both}\colon \\ \text{a = -1},\text{ b = }3,\text{ c = 0, d = 0} \end{gathered}[/tex][tex]\begin{gathered} \text{Amplitude = |a| = |-1|} \\ \text{Amplitude = 1} \\ \text{period = }\frac{2\pi}{b} \\ \text{period = }\frac{2\pi}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{midline = vertical shift = d} \\ \text{midline = d = 0} \end{gathered}[/tex][tex]\text{period = }\frac{2\pi}{3},\text{ midline is y = 0, the amplitude = 1 (option B)}[/tex]
