Since for x = 0 the equation is different from 0, we can conclude that the equation has the form of:
[tex]y=a\cos (bx)[/tex]
Where:
a = Amplitude
b = Angular frequency
The angular frequency is:
[tex]b=\frac{2\pi}{T}[/tex]
Where:
T = Period
From the graph the period is:
[tex]\begin{gathered} T=4\pi \\ so\colon \\ b=\frac{2\pi}{4\pi} \\ b=\frac{1}{2} \end{gathered}[/tex]
Since the minimum value of the function is -4 we can conclude that the amplitude is 4, but the function is negative since it is reflected across the x-axis, therefore, the equation of the function is:
[tex]y=-4\cos (\frac{1}{2}x)[/tex]
