Answer:
[tex]y = 4 \cos( \frac{8}{3}x ) - 3[/tex]
Step-by-step explanation:
Based on the description, the Cosine function is of the form;
[tex]y = a \cos \: bx + c[/tex]
Where |a| is the amplitude. We have that the amplitude is 4 so a=4.
The period is given as
[tex] \frac{3\pi}{4} [/tex]
This can help us find the b-value.
[tex] \frac{2\pi}{b} = \frac{3\pi}{4} \\ \implies \: b = \frac{8}{3} [/tex]
The vertical translation is 3 units down so c=-3.
Hence the equation is
[tex]y = 4 \cos( \frac{8}{3}x ) - 3[/tex]
