Question

Plz help me with this

Answer 1

Answer:  $\bold{B)\quad y=4sin\bigg(\dfrac{3}{2}x+\dfrac{2\pi}{3}\bigg)}$

Step-by-step explanation:

A sin graph is a cosine graph shifted to the left $\dfrac{\pi}{2}$ units.

$y=4cos\bigg(\dfrac{3}{2}x + \dfrac{\pi}{6}\bigg)\qquad \implies y=4sin\bigg(\dfrac{3}{2}x+\dfrac{\pi}{6}+\dfrac{\pi}{2}\bigg)\\\\\\.\qquad \qquad \qquad \qquad \qquad \implies y=4sin\bigg(\dfrac{3}{2}x+\dfrac{4\pi}{6}\bigg)\\\\\\.\qquad \qquad \qquad \qquad \quad \implies \large\boxed{y=4sin\bigg(\dfrac{3}{2}x+\dfrac{2\pi}{3}\bigg)}$