Answer: [tex]\bold{B)\quad y=4sin\bigg(\dfrac{3}{2}x+\dfrac{2\pi}{3}\bigg)}[/tex]
Step-by-step explanation:
A sin graph is a cosine graph shifted to the left [tex]\dfrac{\pi}{2}[/tex] units.
[tex]y=4cos\bigg(\dfrac{3}{2}x + \dfrac{\pi}{6}\bigg)\qquad \implies y=4sin\bigg(\dfrac{3}{2}x+\dfrac{\pi}{6}+\dfrac{\pi}{2}\bigg)\\\\\\.\qquad \qquad \qquad \qquad \qquad \implies y=4sin\bigg(\dfrac{3}{2}x+\dfrac{4\pi}{6}\bigg)\\\\\\.\qquad \qquad \qquad \qquad \quad \implies \large\boxed{y=4sin\bigg(\dfrac{3}{2}x+\dfrac{2\pi}{3}\bigg)}[/tex]
