Answer::
[tex]y=2\cos\left(\frac{1}{2}x\right)[/tex]
Explanation:
Given the general cosine function:
[tex]\begin{gathered} y=a\cos(bx+c)+d \\ a,b,c\text{ and d are constants} \end{gathered}[/tex][tex]\begin{gathered} \text{The amplitude}=|a| \\ \text{ The period, }T=\frac{2\pi}{|b|} \end{gathered}[/tex]
We want to determine the function that has the following properties:
• Amplitude = 2
,
• Period = 4π
Using the period formula given above:
[tex]\begin{gathered} 4\pi=\frac{2\pi}{|b|} \\ |b|\times4\pi=2\pi \\ \lvert b\rvert=\frac{2\pi}{4\pi} \\ b=\frac{1}{2} \end{gathered}[/tex]
From the given options, the function that satisfies the required property is:
[tex]y=2\cos\left(\frac{1}{2}x\right)[/tex]
