PLEASE last one to graduate!!
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Answer:
[tex]y=4\sin(\frac{3}{2}x+\frac{2\pi}{3})[/tex]
Step-by-step explanation:
The graph of the cosine function can be obtained by shifting the sine function to the left by [tex]\frac{\pi}{2}[/tex] units.
The given cosine function is:
[tex]y=4\cos(\frac{3}{2}x+\frac{\pi}{6})[/tex]
When we shift this function to the left by [tex]\frac{\pi}{2}[/tex] units, we obtain a sine function
[tex]y=4\sin(\frac{3}{2}x+\frac{\pi}{6}+\frac{\pi}{2})[/tex]
[tex]y=4\sin(\frac{3}{2}x+\frac{2\pi}{3})[/tex]
These two functions have the same graph
The second option is correct.