Question

Show work and let me know if you have questions on the answer

Answer 1

Answer::

`y=2\cos\left((1)/(2)x\right)`

Explanation:

Given the general cosine function:

`\begin{gathered} y=a\cos(bx+c)+d \\ a,b,c\text{ and d are constants} \end{gathered}`
`\begin{gathered} \text{The amplitude}=|a| \\ \text{ The period, }T=(2\pi)/(|b|) \end{gathered}`

We want to determine the function that has the following properties:

• Amplitude = 2

,

• Period = 4π

Using the period formula given above:

`\begin{gathered} 4\pi=(2\pi)/(|b|) \\ |b|*4\pi=2\pi \\ \lvert b\rvert=(2\pi)/(4\pi) \\ b=(1)/(2) \end{gathered}`

From the given options, the function that satisfies the required property is:

`y=2\cos\left((1)/(2)x\right)`