Question

PLEASE last one to graduate!!

Answer 1

Answer:

$y=4\sin(\frac{3}{2}x+\frac{2\pi}{3})$

Step-by-step explanation:

The graph of the cosine function can be obtained by shifting the sine function to the left by $\frac{\pi}{2}$ units.

The given cosine function is:

$y=4\cos(\frac{3}{2}x+\frac{\pi}{6})$

When we shift this function to the left by $\frac{\pi}{2}$ units, we obtain a sine function

$y=4\sin(\frac{3}{2}x+\frac{\pi}{6}+\frac{\pi}{2})$

$y=4\sin(\frac{3}{2}x+\frac{2\pi}{3})$

These two functions have the same graph

The second option is correct.