Answer: [tex]\bold{A)\quad y=3\ cos\bigg(x-\dfrac{\pi}{2}\bigg)+3}[/tex]
Step-by-step explanation:
[tex]\text{The standard form of a cosine equation is: y=A cos(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]
In the graph,
- A (amplitude) = 3
- D (vertical shift) = +3
- P (period) = [tex]\dfrac{\pi}{2}[/tex] to the right
[tex]\implies \large\boxed{y=3\ cos\bigg(x-\dfrac{\pi}{2}\bigg)+3}[/tex]
see graph below as verification
