Question

What is the period, the equation of the midline, and amplitude of the function y = -sin 3x?

Answer 1

`\text{period = }(2\pi)/(3),\text{ midline is y = 0, the amplitude = 1 (option B)}`Step-by-step explanation:
`\begin{gathered} \text{Given function:} \\ y\text{ = }-\sin \text{ 3x} \end{gathered}`

we apply the sine function formula:

`\begin{gathered} y\text{ = }a\sin (bx\text{ + c) + d} \\ \end{gathered}`
`\begin{gathered} \text{comparing both}\colon \\ \text{a = -1},\text{ b = }3,\text{ c = 0, d = 0} \end{gathered}`
`\begin{gathered} \text = \\ \text{Amplitude = 1} \\ \text{period = }(2\pi)/(b) \\ \text{period = }(2\pi)/(3) \end{gathered}`
`\begin{gathered} \text{midline = vertical shift = d} \\ \text{midline = d = 0} \end{gathered}`
`\text{period = }(2\pi)/(3),\text{ midline is y = 0, the amplitude = 1 (option B)}`