Given: A cosine function with amplitude: 6, period: 2 pie, vertical shift: 0, and horizontal shift-
[tex]\frac{2\pi}{3}[/tex]
Required: To determine the function.
Explanation: The cosine function is defined as-
[tex]y=Acos(Bx-C)+D[/tex]
where
[tex]\begin{gathered} A=Amplitude \\ \frac{2\pi}{B}=Period \\ \frac{C}{B}=Phase\text{ shift} \\ D=Verical\text{ shift} \end{gathered}[/tex]
Hence, the required function is-
[tex]y=6cos(x-\frac{2\pi}{3})+0[/tex]
Final Answer: The function is-
[tex]y=6cos(x-\frac{2\pi}{3})[/tex]
Hence, Option D is correct.
