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

Explanation:

Step1: Substitute x - value into function

For (x =-\frac{\pi}{2}), (y = 3\sin(-\frac{\pi}{2}+\frac{\pi}{2})=3\sin(0) = 0).

Step2: Repeat for other x - values

For (x =-\frac{\pi}{4}), (y = 3\sin(-\frac{\pi}{4}+\frac{\pi}{2})=3\sin(\frac{\pi}{4})=\frac{3\sqrt{2}}{2}). ...

Answer:

When (x =-\frac{\pi}{2},y = 0); (x=-\frac{\pi}{4},y=\frac{3\sqrt{2}}{2}); (x = 0,y = 3); (x=\frac{\pi}{4},y=\frac{3\sqrt{2}}{2}); (x=\frac{\pi}{2},y = 0); (x=\frac{3\pi}{4},y=-\frac{3\sqrt{2}}{2}); (x=\pi,y=- 3); (x=\frac{5\pi}{4},y=-\frac{3\sqrt{2}}{2}); (x=\frac{3\pi}{2},y = 0)